Improve Fast In Go Milton N. Bradley 2008, 2010
Table Of Contents
Introduction Chapter 1 - The Role Of Fighting In Go Chapter 2 - Important Stones Chapter 3 - Strong/Weak Stones Chapter 4 - Peeps And Cuts Chapter 5 - Sector Lines, Enclosure & Connectivity Chapter 6 - S.W.O.T. Analysis Chapter 7 - A Sampling Of Major Fighting Scenarios Epilogue Glossary Of Japanese Go Terms
Introduction About This Book�s On-Line Publication
The on line publication of this book provides two quite extraordinary assets: - It�s FREE. - It�s perfectable!
A printed book is fixed in form and content, and remains essentially immutable from the moment of its publication. So except for the inclusion of a separate list of errata or the subsequent issue of a second edition, any errors of omission or commission it contains remain unchanged forever. In sharp contrast, whatever flaws this on line publication possesses can be readily corrected, if only you, the reader, are kind enough to communicate your perceptions to me. If anything substantive has been omitted, it can be added. If anything is unworthy of inclusion, it can be excised. If I got anything wrong, including typos and diagrammatic and/or commentary errors, it can be corrected. If more or better examples are needed, they can be provided. And if anything is insufficiently clear, it can be clarified. All that�s necessary to achieve a �perfect� presentation is for the reader to provide me with the appropriate positive feedback. Just click the link below or at the end of any chapter, and send me an email detailing the problems you perceive, and - this is most important - specifics of exactly what you suggest as their correction. This is not quite like Wikipedia, where the reader can directly modify the presentation, but it�s close. In order for this process to be successful, when you provide your feedback it�s essential that you include your rating (AGA or other), so that I can properly evaluate the perspective from which your caveat has originated. Obviously, if a high Dan tells me that I�ve got something wrong it will carry more weight than if a double digit Kyu player makes the same claim, but all positive comments will be treated with the respect they deserve. Finally, if you like the book, and especially if you�re in its target audience and agree that it has significantly improved your understanding (and rating!), I�d much appreciate your communicating that to me. It�s really the only thing that will make the vast amount of time and effort that went into its creation worthwhile. Introduction This book is not a Go primer nor even a second book, so it presumes that the reader intending to profit from it already has a firm grasp (if perhaps not yet complete mastery) of the basic rules of Go, as well as the fundamentals of life and death, Joseki, and Fuseki. When deciding whether or not it will be worth the time and effort necessary to profit from a Go tutorial such as this, the most relevant criterion employed will almost necessarily be the amount and rapidity of improvement in your rating that you can expect in return. Although it�s manifestly impossible to correctly assess this without an in-depth appraisal of your individual intellect and countless other factors, some highly relevant insight into this matter can nevertheless be gained from considering the author�s own experience. As originally conceived, this book�s objective was to provide players from double digit to perhaps 5 Kyu with crucial insights into the key issues of deciding what, where, and why to play next. But as a result of my own experience, I�ve just come to realize that the range of players who can find in it the insights that can and will lead to significant improvement in their Go skill (and rating) extends at least to 1D AGA! How and why I�ve come to that startling conclusion is related next. With the possible rare exception of a few geniuses at the very top of the Go professional ratings, every Go player throughout its extensive history has eventually reached a skill and rating plateau which they never thereafter exceed. For many players, intermediate plateaus also often hold sway for a number of months or even years, but ultimately a final, highest level is reached and then continues until age induced decline takes over, if the player is fortunate enough to live that long. As I�ve observed during the 60 years of my own Go playing experience, depending on the player these final plateaus range all the way from high double digit Kyu for the least apt (most of whom drop out in frustration), to high ranked 9P. But the one seemingly invariant
factor characterizing them all is that once a certain amount of time has elapsed (typically 10 years or more), or age has been reached (typically 60-65), the player�s then operative plateau is final, and is never thereafter transcended! But what has just happened in my own Go playing life violates both of those seemingly impenetrable time barriers! I�m now 83, suffering from the incurable, invariably fatal Acute Amyloid Leukemia, and have been at a 1D AGA plateau for over 20 years. But despite that, my latest results definitively demonstrate that I�m now no weaker than 3D AGA, and most probably 4D, and, perhaps most startling of all, am unquestionably still improving! When I watch games on IGS between players rated 4D* (= 7D AGA) and above, I now quickly and easily find their exact moves a vast majority of the time! The key that the reader should be aware of is that this ability didn�t develop immediately after I had organized the key ideas and translated that into this book, but only reached its current state of fruition after another couple of years of integration of those ideas into my thinking. But as noted, I�m quite old by any standard and consequently undoubtedly more fixed in my thinking than the average player who will read this book, so I have every confidence that those of you who put forth the requisite effort can, as I�ve done, reap rewards of Go rating beyond your fondest expectations! Now about the book itself. At its most fundamental level, playing Go is heavily dependent upon pattern recognition. As a result, an essential factor in progressing from beginner to intermediate and beyond is perfecting knowledge of the key recurrent local patterns, especially as embodied in Tesuji and Joseki. This knowledge constitutes the tactical bedrock upon which Go skill is built, but even its mastery is insufficient to make one a strong player! What�s missing is the ability to visualize and then act appropriately on those patterns in actual global board contexts, and that latter capability can only be realized in the service of key strategic ideas like those developed in this book. Preeminent among these key ideas is that fighting is the heart and soul of Go, to the degree that the final outcome of a high proportion of well played games is decided directly or indirectly by big battles. For that reason, mastering the art of fighting is one of the most productive of the essential steps in becoming a strong player. There are two quite different but equally essential aspects of fighting: 1. Deciding where, when and why it�s appropriate to fight. 2. Knowing how to fight. This book focuses on the former. Its basic premise is that a fully developed skill arsenal is unquestionably essential to becoming a strong player, but is insufficient because the full value of that skill can only be realized in the service of deep strategic understanding. It�s much like driving a car - technical driving skill is essential for maneuvering safely and efficiently in traffic, but useless for getting where you want to go without an adequate road map! So the focus in this book is on how to identify which fights are necessary and/or productive and which should be avoided, rather than on how to conduct a fight once it�s begun. It attempts to do what many believe impossible - to explain this essential aspect of Go to beginners and intermediates so clearly and concisely that they will thereafter think much like strong players, even if they�re still far from being able to consistently translate that understanding into fully accurate and incisive play. Of necessity, we do discuss the details of some fights, because it can be very helpful to the
reader to see the sort of complications that may result from the implementation of the ideas being studied. But even in those cases, our emphasis is on identifying plausible moves which fulfill the position�s overall strategic objectives, rather than on finding those that are absolutely best. Finally, it must be understood that although this book provides a valuable road map for Go fighting in the form of a set of simple but important strategic ideas which are generally (but certainly not always) applicable, those protocols must be viewed as neither absolute prescriptions that must be slavishly followed, nor unerring guides to the absolutely best moves! Despite that important caveat, the book�s premise is that mere exposure to these key ideas will provide the greatest increase in any beginner/intermediate�s playing strength for the least effort expended! But, as desirable as that is, it�s only a good first step. Completing the transformation into a strong player will also take much study and practice of the detailed techniques of Go, as well as lots of over-the-board playing experience - all things well beyond our present purposes, and which are therefore left for your independent effort. The Use Of Ratings In This Book Except as otherwise noted, all of the illustrations in this book were taken from actual Dan level games played on leading on-line Go servers, and that means that the stated ranks are all really equivalent to 1- 3 stones stronger on the AGA scale! So although 5D may not seem all that impressive, when you realize that it�s really equivalent to from 6D-8D AGA and therefore among its highest rated players, that player�s judgment about where to play becomes much easier to accept as valid. Acknowledgement I hereby pay my respects and acknowledge my debt to all of the many wonderful Go teachers and authors who have preceded me. Thanks are hereby offered to the vetters of this book�s original incarnation, Ray Kukol 4D, Lisa Maloney, Michael Quintero, Dale Blann, Masaaki Hamaguchi, and my son Randy, who were kind enough to review the manuscript, find errors, and offer some insights into places in which it needed clarification and/or modification. Thanks are also offered to Joanne Phipps 3D and Louis Abronson 5D, who vetted the revised manuscript, found some significant errors, and made key suggestions that helped me reedit it yet again. But in the end, because I�m a Beethoven and not a Mozart, I once more rethought and completely recast everything, so that although much of the book�s content is essentially the same as in the earlier versions, the presentation is now completely different. As a consequence, responsibility for what appears here, including any errors, remains uniquely mine . Finally, special thanks are offered to Jakob Meulengracht for his invaluable assistance in preparing the HTML coding of the manuscript that allowed its on line publication. Milt Bradley, July 2008
Chapter 1 - The Role Of Fighting In Go The financial investment model is an appropriate, if rather grossly simplified, way to grasp the essence of a Go game. Think of the stones you play as your investment capital, and the resulting territory you acquire as
the return on that investment. It�s well established that a prudent financial strategy invariably requires a judicious balance between long and short term investments. It�s much the same in a Go game, where the balance that must be struck is between profit (short term) and such relative intangibles as thickness and attack (long term). In this balancing process, it�s often feasible to cede even a large temporary lead in solid profit to the opponent, in the expectation of later recouping. But whatever the chosen strategic mix in any given game, at game�s end the sole determinant of victory or defeat is the amount of empty board space controlled by each side. Capturing more stones than the opponent, or even capturing any opposing stones at all, is essentially irrelevant except as it contributes toward that goal. Given that fact, it might seem that victory should be achievable through the simple walling off of areas by both sides. But that�s not true! Even if that primitive strategy (pejoratively termed �ground gaining Go�) could be successfully followed initially, the finite size of the Go board coupled with the fact that both sides are seeking to gain control of the same limited amount of space means that conflict is ultimately inevitable. And that�s especially true when one side or the other realizes it has fallen behind in acquiring territory and can only recoup by �stealing� a portion of what the opponent has claimed. So in well played Go games the confrontations usually begin early, and then are almost invariably crucial in determining the final outcome. As a result, perhaps the major key to making appropriate strategic decisions lies in understanding that:
Go Is A Fighting Game
This should distinctly not be interpreted as implying that fighting is all there is to Go, because nothing could be further from the truth. Rather, fighting is perhaps best understood as the essence around which all of the many subtleties and complexities of Go tactics and strategy coalesce to produce the wonderful game which has intrigued humanity for millennia. The Basic Principles Of Fighting The Life Or Death Of Groups Is The Central Issue In Fighting
Although most high level Go games are decided as a result of fights, those fights are anything but random, mindless conflict for its own sake! Quite the contrary. Fights between competent opponents occur only because both sides are unavoidably competing for control of the limited assets of space, shape and connectivity available on the 361 intersection Go board.
Only Fights Involving Important Groups Are Likely To Be Productive
How to identify important groups is the subject of Chapter 2.
Only Fights Against Weak Groups Are Likely To Be Successful
How to identify weak groups and determine when and why they are vulnerable is the subject of Chapters 3 and 4. When attacking vulnerable groups is most likely to be successful is the subject of Chapters 5 - 7. Rather
Gratuitous Fights For Their Own Sake Are Almost Always A Mistake
Fight Only In Pursuit Of Strategically Important Objectives And Only When And To The Extent Absolutely Necessary
Diagram 1 In this game between a 5D and a 7D, the atari of B1 on the marked White stone has forced the connection of W2, with (small) advantage to Black because B1 not only separates White and is potentially useful, but also because W2 only adds insignificantly to White�s already thick formation. The key question now is how Black should best continue.
Diagram 2 The exchange of the atari of B1 for W2 on the left has created useful Aji for Black to exploit at the proper moment, but continuing there immediately to support/utilize the 2 Black stones would only prematurely start a fight that would almost certainly be to Black�s detriment! As things stand, Black�s absolutely essential play is B3! This begins to sketch out a Black corner in the lower right while partially neutralizing the White thickness, and also prevents the excellent extension/kakari of W�a�, and leaves the decision regarding what to do with the 2 Black stones on the left for later. (In the actual game, the proper moment to support those stones never arrived!)
Diagram 3 In this game between two 7 D�s, White has retained Sente, so it�s his choice as to how to proceed from this point forward. Invading the wide extension between B1 and B21 seems inviting. But is it really? And if it�s not, what would be better? And why?
Diagram 4 This is the sort of position in which it�s tempting to start a fight by invading with W2! Although that might conceivably succeed, the 7D who played White in this game thought better of it. He instead opted for this calm development, which had the advantage of taking no unnecessary risks. Its detriment is that it yielded him only a minuscule overall plus. Caution! There is sometimes no reasonable alternative to initiating a fight when you�ve fallen behind, and less aggressive play is unlikely to reverse the game�s losing trend! But other than in such exceptional circumstances, avoiding gratuitous and/or potentially dangerous fights is usually sound policy. How to Distinguish between vital fights and those that aren�t is one of the major subjects of this book, so, hopefully, that important distinction will be much clearer after you�ve read it all.
Fighting Guidelines: In a fencing bout, every legal touch has the same value. So when the opponent thrusts, a fencer�s first response must be to parry! Only then does it become feasible to initiate an aggressive counter action. In a boxing match, every legal blow has the same point value to the judges, but more effective blows can not only steal the initiative from the opponent but can also serve to wear him down so that both his attack and defense become less effective. Equally important, they can also serve to instantly end the bout via a knockout! And it�s much the same in Go. A move by the opponent which intends to seize Sente by making a threat that you can�t afford to ignore may be defended against as expected, but it also may be ignored in favor of a threat of one�s own which is in fact more serious. In each case, deciding what�s appropriate strategically and then achieving their desires requires accurate positional appraisal followed by precise execution by both sides, so in the final analysis a player�s arsenal of tactical skills is the foundation upon which his strategy is both built and realized. The crucial factor in the conduct of any fight is the realization that each separate group of both White and Black stones must somehow form at least two separate and distinct eyes by the end of the game, to both remain alive and garner the territory that will count toward a win. So the more separate groups you can force your opponent to establish, the more �free� moves you gain with which to pursue your own objectives.
This is generally true because most moves made by the opponent to secure his own eyes won�t also expand his space or attack your positions! Because it�s easy for a beginner or intermediate in a handicap game to be intimidated by White�s superior skill, it�s also important to remember that
The White Stones Have No Special Powers, And Share The Same Need For Eyeshape, Space, and Connectivity As Black�s
So Black must carefully appraise and then seek to exploit any weaknesses in White�s positions, rather than reflexively playing purely defensively as though the White stones were somehow invulnerable! The following principles provide excellent guidance in most situations. Why they�re generally valid will become clearer when we discuss strong and weak stones in Chapter 3.
To Attack, Play Away. (Keep a discreet distance, inhibiting the opponent�s ability to expand and/or form eyes.)
The Nature Of Attack An attack uses threats against weak stones to create gains, either locally or elsewhere, which typically take the form of territory (profit), the creation of power/influence, or an attack on another group. Attacking plays will usually elicit a response, but won�t necessarily result in an immediate fight. Attacking scenarios are of almost transcendent importance in playing Go and among the most satisfying to implement, so it will be worth our while to briefly examine their structure and implications here, deferring fuller discussion for later. In a 2008 article in the AGA e-journal, well known American Go teacher Jim Kerwin, 1P, said the following: �The key to attacking is to start by choosing where and what you want to gain. You will find it difficult at first to see a possible gain and how to use attack to get it. The good news is that if you can�t see how to use the weak group to get what you want, you can afford to wait. The worst case is that the opponent will eventually spend a move to reinforce the group allowing you to play a profit move, so you�re guaranteed something.� This is splendid advice, as might be expected from a Go professional, but I believe that it�s still amenable to modest refinement for the beginners/intermediates who are endeavoring to learn from this book. The relevant issue is the player�s meta-strategy for playing Go in any particular game. When engaged in competition in which winning and rating are the motivation, Kerwin�s conservative strategy of staying
within the confines of the player�s current knowledge/skill base except in desperate circumstances is clearly appropriate. But in playing �casual� Go, especially when expanding your experience base is the dominant motivation, a far more adventurous and aggressive strategy will usually be more appropriate! Given that such �casual� games will almost necessarily constitute by far the majority of your early playing experience, rather than holding back unless you�re reasonably certain of success as Kerwin suggests, in those games your preferred strategy should be to assess as best you can, and then, if in your best judgment it seems at all feasible, attack! Then, especially if you later review what happened (or use a service like The Go Teaching Ladder to have a much stronger player point out your errors), by learning from your mistakes you can maximize your rate of progress.
To Defend, Play Close (Make contact as a method for creating eyeshape and/or sealing off eyespace.)
Contact plays will almost invariably result in an immediate fight. In any event
Before You Play Defensively, Always Seek An Offensive Move That Also Satisfies Your Objectives
FIGHTING CONTINUES UNTIL BOTH SIDES ARE (at least temporarily) STABLE
This may mean that both sides are safe, that one side�s stones are either unequivocally dead or temporarily abandoned, or that both are still incompletely settled. In the latter cases, the fight will often resume later, when the appearance of other stones nearby makes it profitable for one side or the other. To see how these principles work in practice, let�s examine a situation that frequently arises in both even and handicap games.
Diagram 5 The �Knight�s Move� approach of W1 (or the symmetrical point on the upper side) is the most common way for White to begin operations against the Black 4-4 point stone. Because it�s an attack, it doesn�t make contact with the object of that attack, but instead stays a discreet distance away! When Black is in a position to respond aggressively, the one point squeeze play of B2 is the strongest counterattack, also playing at a discreet distance from its target, and inhibiting W1's ability to expand down the side to make a base there. Feasible but milder squeeze plays instead of B2 which may be globally preferable in some situations are �a� thru �d�, while �e� is sometimes chosen when Black feels the top and/or center are more important than the left side. After B2, White has the choice of defending W1 immediately or playing elsewhere. (If he tenukis he will suffer a fairly serious local detriment if Black is first to play locally again, but even then W1 can�t be killed.) How each of White�s feasible responses to B2 can play out is shown next.
Diagram 6 In response to the pincer attack of B2, one common (but rather passive) continuation is for W3 to dive into the corner. After the Joseki sequence thru W11 (B�a� in place of B10 is sometimes preferable), White is not only alive with profit in the corner, but is also unconfined. In return, W1 is at least temporarily abandoned and Black has thickness. This dynamic �equality� is a fair allocation of assets for both sides for the moment, but not a fully adequate characterization of the situation. The important aspect of this position unaddressed by that assessment is that White�s profit of about 10 points in the corner is almost (but not quite) already assured, but Black�s thickness on the outside must still be sooner or later converted into an approximately equivalent gain either locally or elsewhere for this trade to be ultimately fair.
Diagram 7 �Abandoning� W1 as in Dia 6 isn�t always globally desirable, and in that case the one point center skip of W3 here is often a good alternative to entering the corner. After that, the calmest sequence is as shown, with White getting strong center influence in return for Black�s sketching out corner territory. (The contact play of B6 helps defend the corner territory in Sente by threatening to connect underneath to B2 by continuing at 7, thereby inducing W7 to prevent that.) After this, with the 3-3 point (�a�) in the corner and �b�, �c�, and �d� all still available for White if and when circumstances make them appropriate, and with the skirt at �e� also still open, the big corner territory is as yet far from securely Black�s!
Diagram 8 It�s also feasible for White to switch W5 in Dia 7 to the �shoulder hit� on B2 shown here, with this common result. B14 prevents a White enclosure, and at least tentatively assures life for the B214 group. Then, depending on what�s going on elsewhere, White may play �a� immediately to assure his connectivity (the best way to do that), or tenuki and hope that he�ll be able to get back to consolidate his position here before Black can play to cut him apart. Instead of the aggressive squeeze play of B2 in Dia 5 - 8, Black might feel it preferable to play defensively, so let�s examine next just how differently that will play out.
Diagram 9 Especially when Black already has the marked stone or one near it in place, instead of squeezing, the attachment of B2 is feasible. As earlier noted, this is not an attack! A contact play like this B2 is actually a defensive move which is intended to enable Black to both �make shape� and take some corner/side territory. Its main detriment is that it also induces White to make shape and territory as shown, thus simplifying the position while also reducing both side�s later options. (There are a number of other feasible Joseki variants beyond these few which give somewhat different results, but those details are outside our present interest and so will not be discussed here.)
Diagram 10 Relevant to this discussion is the �bang against� attachment of B2 here, which, as earlier noted and despite its appearance, is primarily an attack and not a defensive move! Since this is something that seems inconsistent and therefore may be confusing, understanding its rationale is important. The attachment of B2 is most appropriate when the triangled Black stone (or one at �a�) is already in place on the upper side, and is even more effective when (as here) the marked left side star-point stone is also present (as is true in high handicap games). The aim of B2 is to make infeasible an immediate White switch to the 3-3 point in the corner at �b�, as in Dia 8. It does this because if W3 at �b�to �steal� the corner territory, B4 at 3 would give Black excellent eyeshape while severely damaging W1. So most often W3 is considered necessary. Then B4 works perfectly, in conjunction with the triangled upper side star point stone, toward building a large Black territory in the upper left corner and adjacent upper side. (Although as noted in Dia 7, that territory is still far from completely secure, especially with W�b� still available.) After B4 White needs eyespace for his 2 stones, but the marked Black left side star point stone stands in the way of an ideal extension, leaving only the very short one point skip to W5 as really feasible. Next, B6 prevents a White slide to either �c� or �d� to expand his eyespace, after which W7 is necessary to create the beginnings of some eyespace and shape while fleeing toward the center. B8 is then often best, building Black�s strength and looking toward the lower side. What�s really important here is to recognize the fundamental difference between the almost entirely defensive attachment of B2 in Dia 9 and that of Dia 10, which is primarily (but not entirely) offensive. Once that critical difference is clearly understood, it should then be far easier for you to make the proper decisions and appropriate followup in similar situations that arise in your own games.
Whatever the situation
Don�t Act On The First Plausible Move That Solves Your Major Problem.
Always Look Further For A Better Move, Especially One Which Also Accomplishes Other Desirable Goals.
Diagram 11 This is a fairly common type of position, in which the central area to the left of the Black stones is still quite open. In most cases, when the marked White stone probes his one point skip Black will want to maintain his connection, and the first step in finding the best way to do this is to identify the feasible alternatives. Please decide on your own candidates before looking at the following diagrams.
Diagram 12 Black�s available connection options are marked from �a� to �d�. But which is best? There is no one universally correct answer because the preferred option will depend upon other stones already in place (not shown here) or deemed likely to appear in subsequent play.
Diagram 13 The simplistic choice is the hard connection of B1. Although this is the only absolutely secure, unbreakable connection, it�s also the one that creates no shape at all while offering the fewest followup alternatives. Despite these detriments there are situations in which it�s the most desirable option, so it can�t simply be dismissed out of hand. But absent special circumstances that make the other options infeasible and/or Black�s ultra-solid thickness here particularly useful, this is usually the worst choice. So an alert Black will look further.
Diagram 14 A slightly better alternative, which in certain circumstances may be preferable to the others, is the extension of B1 here. This maintains the connection because if W�a�, B�b�, and if then W�c� cuts, the atari of B�d�answers. And if W�e� then extends, B�f� is a Geta that traps the two White cutting stones. But instead of pushing at �a�, which obviously doesn�t work, if the position to the left is suitable an alert White might continue with something like W�d�, to induce B�c�, and then follow with something like W�f�, to leave the entire Black group �floating� without either eyes or shape.br> And that possibility is one of the reasons that this B1 as the way to maintain Black�s connection is not often best.
Diagram 15 A bit more stylish and versatile is B1 here. After this if W �a� pushes into the gap in the Black formation, depending on surrounding circumstances B�b�, �c� or �d� are all sufficient to maintain Black�s connection with good shape. But even this usually isn�t best because this B1 doesn�t reach far enough out from his wall.
Diagram 16 So after further reflection, the one point skip of B1 here is revealed as the move that best accomplishes all of Black�s objectives! After this, if White makes the shape-killing placement at �a�, B �b� connects efficiently because W�a� is now almost trapped. After that, playing immediately (as at �c�) to rescue W�a� would only help Black. Not only would he then have a larger White group to attack, but (assuming the relatively open center we noted at the outset) that newly formed White group will probably not seriously threaten Black because those White stones will almost certainly be weaker than the Blacks they are supposedly attacking. If after B1, instead of W�a� White pushes at �b�, with B�a� the position reverts to Dia 15 after W�a�, B�d� there. After W�a�, B�b�, if White doesn�t extend from �a�, then if and when appropriate, B�c�(or even a more distant Geta) is a further stylish play that assures that W�a�is trapped, almost certainly yielding Black one eye.
Enclosure In the big fights that decide the majority of well played games it�s important that each side retain as many options as possible, and key among those options is finding support for both attack and defense from nearby friendly stones. Groups which are enclosed not only can�t simply run away from an attack, but are also unable to connect with other friendly stones which might offer help, either to win the fight outright or to at least survive it. It�s also true that if one side is enclosed it�s almost necessarily disconnected from other friendly groups, and in many (but not all) cases that also means that the opponent is connected. The result is that when looking at the final position of games which are close enough to count, it will much more often than not be true that the side which has the fewest number of groups (= is best connected!) is the winner! Perhaps most important of all is the fact that
Only Enclosed Groups Can Be Killed
Therefore To The Extent Feasible Avoid Becoming Enclosed
Becoming enclosed almost necessarily imposes a burden that is not infrequently sufficient to swing the balance of the entire game in the opponent�s favor. The converse perspective is equally valid, so under most circumstances enclosing the opponent is an excellent strategy. For that reason, understanding the principles governing enclosure constitute a major factor in becoming a strong player.
To Counter An Enclosure Threat "If In Doubt, Run Out"
The rationale is simple. Enclosed stones: - Have no interface with or influence on subsequent play elsewhere on the board. - Must be able to make 2 eyes, or die. Caution! As the board fills up throughout the game, every group will ultimately become enclosed! So the guidelines we discuss here apply primarily during the Fuseki and early middle game. It�s also true that all such �rules� of behavior represent simplifications of often quite complex
situations, but they are nevertheless quite valuable because in surprisingly many cases they also provide the clues that can allow even beginning players to find excellent moves they might otherwise miss. Dia 17 Especially in high handicap games, this is a fairly common position, in which White has made a double kakari against a star point stone. In the absence of special circumstances Black should without fail play to prevent White�s enclosure! For this purpose, B1 as shown is usually best, but sometimes the attachment at either �a� or �b� is preferable. Dia 18 If Black doesn�t respond to the double attack and allows White to play the marked enclosing move on his key point before answering, he can still (just barely) achieve life in gote as shown, but with even a slight inaccuracy he will almost surely die! And even if he does live, White�s advantage is considerable. So, on balance, Black would be well advised not to allow himself to be forced into this kind of situation! The principle of searching beyond the obvious for the best move stated earlier generally applies, but it�s especially relevant in the enclosure context, where the sense of relief that almost necessarily accompanies a successful escape may readily blind you to the fact that a superior global result might have been obtained if only you�d looked further for a better move. Here�s a fairly �typical� situation which beautifully illustrates this scenario.
Dia 19 In this game between two 5 D�s, the 12 marked White stones are almost enclosed, with no sure eyes yet! (Although one can be easily made.) So if they don�t get out immediately they will almost certainly be in big trouble, possibly even resulting in a loss sufficient to cost White the game! So what�s the best way for White to break out?
Diagram 20 Beginning with the atari of W1 and then continuing with the forcing plays thru W9 succeeds in allowing White to escape, and in some situations would be the best way to play, but not here! The problem with it is that Black becomes too strong on both sides. So finding a better way to get out is highly desirable.
Diagram 21 Beginning with the atari on the other side is clearly better, because now Black has only been strengthened on the left, but it�s still inferior! Although many players might be satisfied with this, the 5D who played White in this game looked further, and found something better! Do you see it? Try to find it for yourself before looking at the next diagram.
Diagram 22 With the stylish �dog�s neck� extension of W1 here, White not only gets out as smoothly as before, but now is one step ahead in his race into the open center - a major difference in enabling a later connection to friendly stones or forming eyes. (W1 works because �a� and �b� are miai for it to remain connected to his group below!) Perhaps equally important, playing this way doesn�t induce Black to strengthen himself on either side! White escapes in each case, but the seemingly small difference between Dia 22 and either Dia 20 or Dia 21 can easily change the balance between victory and defeat in a close game!
Fighting Against Unenclosed Groups
Because Only Enclosed Groups Can Be killed, There�s Little Value In Playing �Inside� Moves Against An Unenclosed Group
It�s Usually Better To Play Outside Moves, And Force Your Opponent To Make Eyes And �Live Small�
Caution! This principle is not absolute! There are circumstances in which the global position makes it more advisable to strike first at the opponent�s key shape point(s) to prevent an easy two eyes, and then profitably harass the fleeing group as it struggles to either connect or secure its eyes in the center. The following shows a situation in which attacking an unenclosed group from the inside was counterproductive.
Diagram 23 This is the position a few moves after what we will discuss later as Dia 7, Chapter 2, with Black�s attention focused on the White group in the lower right center. This White group is not yet enclosed, so it�s in no immediate danger of dying no matter what happens next. But Black evidently reasoned that if he could prevent its ability to easily make two eyes that would both force it to run and make it vulnerable to later profitable harassment. So....
Diagram 24 B1 invaded to occupy the key shape point of the White formation, hoping to either cut it apart or prevent its making eyes. Allowing B2 next would enable B1 to connect out to the Black corner stones, shattering the White group�s viability and forcing it to run into the center eyeless. W2 was the best way to prevent that. Then B3 aimed at either connecting B1 to the left or allowing it to escape.
But White neatly avoided that by extending with the simple but effective W4, assuring the capture of B1 and creating one eye, with good prospects for another and/or easy escape into the center. So the result of this premature invasion by B1 was not only a tactical failure but also an important strategic mistake, because it made the White group almost invulnerable!
Diagram 25 Instead of the invasion of B1 in Dia 24, Black should simply have played on the outside like this, expanding and strengthening his own formation and aiming to seal White in, while biding his time to when an eyekilling sacrifice attack at the point of �a� might have a reasonable chance of success.
Fighting Against Large Groups
DIRECT THREATS TO KILL LARGE GROUPS ARE RARELY SUCCESSFUL
Because of the need for efficiency, the enclosure of a large group will often be more or less incomplete. So as the battle progresses and the group continues to grow, those imperfections will typically provide a number of opportunities either to break out directly or to make eyes in place by capturing some of the surrounding attackers. Consequently
THE BEST PLAN USUALLY IS TO USE SUCH THREATS INDIRECTLY, AS THE MEANS OF ACHIEVING OTHER IMPORTANT OBJECTIVES
Here�s a �typical� example. Diagram 26 In this game between a 7D and 6D, Black has secured the upper right corner and a small life on the lower right side. In return, White has secured the lower right corner, as well as eyespace on the upper right edge for his large incompletely settled but not yet enclosed group there. But it�s Black�s turn, and although there�s little chance that he can kill this White group, if possible he�d like to keep the pressure on and gain profit elsewhere by attacking it. But how to do that?
Dia 27 The Knight�s Move of B1 is the strongest way to proceed! Although White can then readily live on the edge if he acts immediately, allowing himself to become enclosed is bad strategy! So instead White tried to escape. Dia 28 With this sequence, Black deliberately didn�t go all out to try to prevent White�s escape! Instead, he cleverly parlayed enclosure threats to build center strength (note the almost captured W6 and 8),
resulting in a global advantage that ultimately enabled him to win the game.
Chapter 1 Problems
Problem 8 This position arose in a game between two 5D�s. Here, we see that White has conceded both the upper and lower right corners to Black in return for a potential attack on the 3 Blacks on the right side. These stones have nice shape, but also have almost no room to expand either above or below, so that only movement toward the center is really feasible for them. The question to be answered is how White can properly exploit this situation.
Chapter 2 - Important Stones At each turn, the player�s primary task is to find the globally best move in the current position! In doing this, appropriate tradeoffs must be made between many diverse yet complementary factors (e.g. territory vs. influence, attack vs. defense, etc.) if a good result is to be achieved. But those essential factors are really useful only after you have successfully identified: - Which stones are globally important and which are not, and - Whether the important stones are strong or weak
Important Stones Require Attention/Action! Unimportant Stones May Often Be safely Ignored.
But what makes stones important? Safe stones which enclose territory are valuable, of course, but in the sense relevant to our focus on fighting:
Stones Are Important Only To The Extent That They Significantly Influence Further Play
There are seven (7) ways in which this importance is manifested. Stones are important if they significantly affect: 1. Contesting /controlling a key board area.
Diagram 1 In this early middle game between two 5D players, the only areas now fully controlled are A (Black) and B (White). They are somewhat different because although the Black �A� group is alive and takes about 8 points of territory, it�s almost completely contained and is therefore unimportant to the future course of play! The White �B� stones are somewhat important because they impact the adjacent still unsettled marked Black stones. Although Black almost has control of the C and D areas, both are still open to a White invasion so these stones are at least moderately important. The game�s main focus from this point on will center on the fact that each side has a large (marked), still unsettled group in the lower center. Black�s group has much better eyeshape, but White has more open space available, so there�s no real advantage on that score at the moment to either side.
Diagram 2 In this early middle game between two 1D players, the marked weak White and Black one point skips in the lower center and the two not yet settled Black and White groups to their left are not only important, but will form the focus of future action until their respective fates are resolved.
2. Deciding which side wins or loses an important fight. Diagram 3 In this game between a 9D and 7D, W80 completed the enclosure of the huge Black center group, thereby making it vulnerable to attack. With Sente, Black can easily secure his group, but unfortunately he missed the potential of the marked White stone and mistakenly believed that he was safe. So ....
Diagram 4 When B81 made the territorially large move on the right side, W82 - 92 shocked him by developing the marked White stone to cut the big Black center group apart, leaving it with portions already dead and the remainder with only one sure eye. So Black resigned. Instead of B81, if Black had recognized that he was so vulnerable to being cut apart, the simple play at 83 would have trapped the marked White stone, not only creating a sure eye for Black but also essentially unifying all his local forces. After that, given his solid positions in all 4 corners, the game would have favored him.
3. Assure your own shape and/or prevent the opponent�s. Diagram 5 In this early Fuseki position between two 5D players, B5 instead of the more customary B7 was a slightly atypical conclusion to the popular Joseki in the upper left corner. br> After this, if W6 at �a� to approach the upper right corner stone, B�b� would happily squeeze while creating an ideal Black formation in the upper left. So if White wants to prevent Black from getting too much territory locally that way, he has little choice but to invade with W6 as shown.
Although this is a reasonable strategy for White, the price he must pay for it is allowing the blocking attachment of B7. This threatens to continue at 8 to make perfect shape for Black while seriously damaging W6, so it induces W8 to prevent that. But that gives Black the opportunity of making a large knight�s extension from the upper right corner stone with B9, which does double duty by also preventing White from creating his own base via the ideal 3 point skip third line extension to �a� from the 2-stone base of W6-8.
The result as shown is a newly created W6-8 group that must flee baseless into the open center, and this is a large part of the reason that the somewhat �unconventional� B5 was such a strong move! Although W10 was the move actually chosen next to flee into the center, any of W �c�, �d�, �e� or �f� might in some circumstances be preferable alternatives, the choice between them depending on the location of other nearby stones of both colors, and White�s strategy. Here�s another excellent example.
Dia 7 When B1 sealed off some eyespace and territory in the corner, a Black followup at 2 would have created a powerful pon nuki eye shape, inducing W2 to prevent that. In turn, W2 threatened to follow with at 3 to seal in the Black corner, so Black somehow had to prevent that. B�a� next would get Black safely out, but wouldn�t apply much stress to either the White position on the right or the left, nor would it also look forward to playing at 5. So, on balance, B3 here was best. Next, White would dearly have liked to play at 5 to make good shape while blocking Black�s progress, but the weakness of the lone White stone to the left made W4 necessary to provide the beginnings of a base there. That in turn allowed B5 to occupy White�s key shape point, making W6 necessary to provide the White stones on the right with their own base. 4. Expand/enclose your own territory/eyespace and/or reduce the opponent�s.
Dia 8 In this position, a few moves after that of Dia 7, whoever plays first locally has an enormous advantage! Dia 9 If it was White�s turn, W1 would provide eyespace, stabilize his stones, and also greatly diminish both the territorial and eyemaking potential of the 4 Black stones to its left. But it was actually Black�s turn, so ... Diagram 10 B1 is an ideal multipurpose move because it: - Provides eyespace for the Black stones to its left - Prevents the excellent W�a� (as just discussed). - Threatens to follow with B�c�, to seriously undercut (and attack) the still unsettled White 2-stone group to its right. B�b� instead would be a mistake because it would induce W�c�. Then if B 2, White would have Sente for W�a�and that would be bad for Black (as already noted).
B2 instead of B1 would also be wrong! Not only would that make Black overconcentrated, but, instead of defending via W�b� (which would leave White overconcentrated himself and allow B1 after all!), White would simply answer W�a�,with advantage. After the correct B1 the diagonal extension of W2 was prudent, and not strictly Gote because it not only provided White�s own eyespace while making B�b� or �c� ineffectual, but also threatened W�d� to destroy Black�s base in the corner at an appropriate later moment. 5. Ensure your own and/or prevent the opponent�s shape and/or connection.
Diagram 11 Both sides share the same key point here, although its implications are quite different for each. It would provide both shape and connectivity for Black if he can seize it, and make Black�s shape impossible if White can play there instead.
Diagram 12 If it�s Black�s turn, B1 would provide both ideal shape and connectivity, making Black very strong locally. But it was White�s turn, so ...
Diagram 13 After W1 on the key point destroys Black�s shape, it�s necessary for him to defend in order to assure the connection between the two marked stones and his main force, to prevent White from capturing them to make a big lower side territory. White�s threat is to cut via W�a�, B�b�, W�c�, or W�a�, B�c�, W�b�, so let�s see how Black should best play now to ensure his connection and prevent White�s big local gain.
Diagram 14 The first idea that might occur is to play B1, which will undoubtedly induce W2 to give White shape and some territory, while also ensuring that Black stays confined. Then B3 makes a �bamboo joint�, assuring a virtual connection, but in Gote. The problem with this for Black is that, if later B�a�, depending on what�s going on elsewhere on the board White may not feel constrained to answer at �b� in order to ensure Black�s confinement! So instead ...
Diagram 15 Best for Black is to begin with the Knight�s Move of B1 here, because now W2 is forced, else B2 connects out. Then after W4 and B5, this position is identical with Dia 14 except for the addition of B1 and W2. But that exchange favors Black, because B1 is a cutting stone which may later either cause White problems or force him to expend resources to ensure its capture, while W2 merely adds an insignificant amount of extra strength to an already very solid White formation! The difference between Dia 14 and 15 may be small and subtle, but it�s the kind of thing that not only wins close games, but also distinguishes really strong players from ordinary ones!
6. Keep your own stones strong and/or the opponent�s weak. Diagram 16 At the moment, both of the marked stones are unsettled, but whoever gets to play at �a� will instantly make his own stone strong and seriously weaken the opponent�s. So this is a key point for both sides which takes priority, and must not be missed!
7. The group contains too many stones or occupies too vital a position to afford to give up. The basic principle to be followed is:
Urgent Moves Before Big Moves
This means that you should always play to secure the eyespace/eyeshape and/or connectivity of your own important weak groups (or attack the opponent�s) before even considering making moves with �mere� territorial implications, almost no matter how large! This is a principle that strong players invariably follow almost instinctively, but which weaker ones often have yet to learn. Diagram 17 In this game between two mid-single digit Kyu players, when B1 was played White should have answered with W�a� to secure some eyespace as well as his center connection for his 4 stones at the top. Instead, he foolishly ignored the safety of this weak group to play the territorially big W2 on the right side.
Diagram 18 After the mistaken W2, B3-7 severely punished White�s failure to secure his center connection by cutting his formation apart and winning 5 stones with enormous profit, forcing White�s resignation only a few moves later.
Finally, before we leave this important topic, it�s essential to be aware that
The Relative Strength And Importance Of Stones Constantly Changes, And Therefore Must Be Reappraised Before Every Move!
To better understand the meaning and implementation of this important concept, let�s look at an example from an early middle game position contested between two 5D players. Diagram 19 As things stand now, the marked 3 stone White wall seems not only strong (it has 6 liberties and a large adjacent open area), but it�s also unquestionably considered very important by both players because it sketches out the beginnings of a huge White moyo on the lower side, in conjunction with the two Whites on the right. But watch how that appraisal changes in what follows, as both sides evaluated the evolving dynamics as they continued from this position.
Diagram 20 Black concluded that, despite appearances, the 3 marked White stones were vulnerable, so he attacked very aggressively with B1 to prevent them from readily making a base and too much secure territory on the lower edge. W2 counter-squeezed B1, because at the moment that lone Black stone is weaker than the 3 stone White group! His objective was to prevent Black�s easily making a base for that lone stone, while beginning to sketch out a substantial White territory between W2 and the lower right corner stones.
Then, after the brief sequence of B3 thru B7 that followed, White apparently realized that the influence the 3 stone wall had formerly been providing had essentially ceased to exist, with the result that his evaluation of those 3 stones had suddenly changed, not just from an important valuable asset to one that was relatively unimportant, but to an actual potential detriment! So White concluded that running out to save those 3 stones in the current global position would be counterproductive. Instead, it would be better to change strategy, and rather than trying to save those 3 stones to use them as sacrifices in order to help consolidate as much of his lower right territory as possible! So ... Diagram 21 The result: The formerly important 3 White stones have become Black prisoners, but in return White has consolidated about 30 points of territory in the lower right corner!
The key idea to grasp is that White didn�t view his 3-stone wall as a fixed asset, but rather as just another potential bargaining chip, which he was prepared to trade in at any time if sufficient compensation was available to make that transaction profitable for him. If you proceed with that kind of flexible attitude, as your skills advance with experience you won�t be confronted with the need to change your mental perspective in order to realize the rating improvement that should rightly be your due! Now let�s try a few problems to see how well you not only understand these concepts, but can recognize them as they occur in real game situations.
Chapter 2 Problems In each of Problems 1 & 2, please identify each separate group and then characterize its importance.
Problem 4 In this game between 6D and 5D, after W1 invaded on the key 3-3 point in the corner to probe Black�s response, B2 was forced. Then when W3 slid to try to create White�s own eyespace, B4 was the best response. How should White continue now?
Chapter 3 - Strong/Weak Stones
Strong Stones Are An Advantage
Strong stones require little or no defense, so they allow you to attack or play aggressively.
Weak Stones Are A Disadvantage
Weak stones require defense, so they also require more cautious play. In many real game situations, beginning or intermediate players may find it quite difficult to correctly determine, in advance of its being played through to a conclusion, whether a fully or only partially enclosed group is going to end up alive (= very strong) or dead (= maximally weak)! That in turn means that the assessment of such a group�s viability upon which the player will have to base his strategy will often be more of a �guesstimate� than a fully reasoned and reliable judgment. The only long term solution to this problem is to develop your assessment ability via the study of Tesuji and Joseki, solving many, many life-and-death problems, and watching and/or playing a lot against the strongest players you can find. Since, as earlier noted, all of that is part of the �standard� protocol for progressing in Go, it will not be further discussed in this book. Instead, our focus will be on identifying the factors that determine the strength or weakness of stones. Strength of stones comes in two disparate incarnations: - Intrinsic Strength tends to remain largely invariant as the position changes. - Relative Strength is always influenced by and is frequently extremely sensitive to even small changes in the proximity and configuration of nearby stones, so it must be continuously and carefully reevaluated move-by-move. A. Characteristics of Intrinsically Strong Stones: 1. Already Have 2 Eyes, or can make them despite any opponent attack. (Very Strong)
Diagram 1Although the White corner stones are almost completely enclosed, they�re safe and strong because there is no way that Black can directly prevent them from making two eyes! The problem with White�s strength here is that, except for the territory enclosed it�s essentially wasted, because these stones are almost completely cut off from any interaction with the remainder of the board. (So in the sense of the last chapter, these stones are unimportant!)
2. Have Good Eyeshape. (Strong) Diagram 2When W2 is distantly squeezed by B3, making contact via W4 on the 3-3 point begins several popular Joseki variants. In this variant, after the W8, B9 exchange White�s shape is good and he may safely play elsewhere, because either W�a� or �b� will assure his two eyes!
3. Enclose Sufficient Space For Eye Formation, Even Under Attack. (Strong) Diagram 3The White corner is large enough and configured well enough that it�s virtually as strong as if it already had eyeshape. As things stand, with even minimally correct play White is assured of being able to make 2 eyes despite any Black attack.
Diagram 4 The upper left corner of this Fuseki, contested in the 2006 North American Masters tournament between Ming Jiu Jiang 7P (Black) and Z Chen 6D (White), shows a not uncommon type of local resolution, in which Black has created superb thickness (and a burgeoning left side moyo in conjunction with his B5-11 stones below), in return for White�s large profit in both the upper and lower left corners.
B. Characteristics of Relatively Strong Stones: 1. Are effectively connected to a very strong group. (Strong) Diagram 5 At the moment, the virtual connection between White�s three marked stones and his two-eyed corner group is safe because if B�a�, W�b�, B�c�, W�d� connects. But this connection is not absolutely secure, because, if played as a Ko threat that White can�t afford to answer, any of B�a�, �b�, �c� or �d� will set up a cut. So this situation will have to be carefully watched by both sides until it�s definitively resolved.
2. Are in an open area, with no significant problems for the opponent to exploit. (Moderately strong)
Diagram 6 The marked White stones have the beginnings of both shape and modest territorial enclosure, plus free center access. So they are safe for the moment. But until the local situation is definitively resolved, White must be wary of their being later undercut, separated, and/or enclosed.
3. Any Significant Nearby Opposing Stones Are Weaker. (Moderately Strong) Diagram 7 The Black stones both above and below the 3 Whites are relatively strong because they have reasonable eyemaking potential at the edge. The Whites are somewhat weaker because it�s somewhat harder to make eyes in the center. But the White stones are far from being completely without resources, because they aren�t anywhere near being enclosed. They have lots of room to run (to �a�), or to make eyespace and shape if necessary, beginning with either �b�, �c�,�d�, �e�, or �f�as appropriate to the overall global position. Because these stones are currently far from being settled, White must continue to monitor this situation very carefully, especially if B�a� is played.
C. Characteristics of Weak Stones: Stones are weak because they exhibit serious deficiencies in one or more of three major areas: 1. Enclosing eyespace and/or making shape. 2. Connectivity. 3. Liberty count. The relative weakness of a group exhibiting one or more of these deficiencies is a function of the seriousness of the deficiencies, how many of them it exhibits, whether or not the group is enclosed, and whether or not it�s involved in a fight with an equivalently weak opposing group. In general, groups which exhibit deficiencies in more than one of these areas and/or are enclosed are weaker than those which are deficient in only one area and/or are not enclosed, but that�s not universally true because a even a single deficiency can be fatal if it�s sufficiently great!
Caution! Maintaining Sente is always advantageous, but is especially so when involved in a semeai with opposing stones because it not infrequently develops that winning that fight is more a function of who can strike first or most effectively at the opponent�s weaknesses, than of who can best defend his own.
Dia 8 The Black group lacks both eyespace and shape, so ... Dia 9 If White can play at 1, it would effectively rob Black of his base, leaving this key group floating and vulnerable! Because that would be disastrous for Black ... Dia 10 With Sente, the simplest and most solid way for Black to play is with B1 on that same key point, as shown here. This not only provides Black with excellent shape, but does so without inducing White to strengthen the 2 stones below, which may now be potentially vulnerable. 2. Connectivity Deficiency Dia 11 11 The two point skip between the W2 and W4 is weak because it can easily be cut if Black moves first! But it�s still joseki because doing so will not necessarily be profitable.
Dia 12 B1 is the
correct way to begin, and after the strong hane of W2 the drawbacks of B3 and W4 naturally follow. After that, the cut of B5 separates White. But after B9 and W10 the overall result is considered even, and that�s why the 2 point skip in Dia 11 is Joseki!
3. Shortage Of Liberties �The Five Liberty Criterion� There is one simple but almost transcendentally important idea that governs fights between opposing groups:
WHEN OPPOSING STONES ARE IN CONTACT, AN UNENCLOSED UNIT IS STABLE, AND A PLAY ELSEWHERE IS FEASIBLE, IF THE UNIT HAS 5 OR MORE LIBERTIES.
This is generally an excellent guideline. But as with all other such criteria it has exceptions, so every position must be judged on its individual merits. Understanding this one simple idea can completely transform your ability to properly conduct many of the fights which arise. The beauty and power of this elegant criterion is that in many cases it makes it possible to find the right move (or at least avoid a seriously wrong move) without the necessity for making a precise and detailed analysis of many complex alternative move sequences! Simply knowing that a given proposed defensive move will leave a key group with less than 5 liberties is usually an indication (but not an absolute proof) that those stones will sooner or later be in trouble and may die, and that such a proposed move is therefore not likely to be best. Conversely, knowing that a proposed defensive move will yield at least 5 liberties for a threatened group is an indication (but also not a proof) that it isn�t likely to die immediately or easily. Failure to obey this simple precept is a prime cause of many of the tactical debacles which
surprise and plague beginning and intermediate players, as the following examples demonstrate.
Dia 13 This is the beginning of a �the main line� of a popular Joseki which frequently arises in both handicap and even games. When B2 squeezes W1, diving into the corner with W3 is one feasible (and common) way to proceed. After B4 and W5 the relevant question to our present interest is what Black should play next, and the 5-Liberty Criterion provides the answer!
Dia 14 The extension of B6 is necessary, and when it�s correctly played as shown the 3 stone unit that it completes then has 5 liberties, and so is �contact stable� - i.e. able to fight successfully. After W11, White has secured the corner territory plus egress along the right side. In return W1 is temporarily abandoned, while Black has 6 liberties, thickness, plus some territorial potential along the bottom. Now let�s see what bad things can happen if B6 is played differently. Diagram 15 Here B6 is played as a �Hane at the head of two stones�, a well known Tesuji which is often the best move, but which is a disastrous error in this position! The reason it�s wrong here is that it leaves the two stone B4 unit with only 4 liberties, and therefore �contact unstable� i.e. lacking enough liberties to sustain a fight. An alert White will immediately take advantage of this via the Hane underneath of W7, followed by B8 and the two forced connections of W9 and B10. Then when W11 cuts, not only is B6 isolated, but (more important) the B4 -10 4-stone unit has only 3 liberties, and is in serious trouble!
Some feasible continuations are shown next, to give you some idea of just how badly Black can
fare after this error. Dia 16 In this variation White gets an enormous corner by capturing the 5 B14-20 stones, and B�a�to trap the 3 White stones doesn�t work! So B�b� to escape is necessary. But this allows either W�a� or �c�, and then White�s prospects in the coming fight are at least as good as Black�s. Dia 17 This continuation is somewhat better for Black, although White is not only alive in the corner with the sequence B�a�, W�b�, B�c�, W�d�, but also has tremendous thickness in the center, while Black�s position is low on both sides.
There are also many other possible continuations after the cut of W11 in Dia 15, some better than those shown and some worse, but all are inferior for Black because of his violation of the 5Liberty Criterion!
Chapter 3 Problems In each of Problems 1 & 2, identify any important weak groups.
Problem 3 This variant of a popular 3-4 point even game Joseki arose in a game between two 5D players. When Black tenukied after W13 to make what he considered to be a globally bigger move elsewhere, the key question to be answered is: As things stand, is Black thick? (and therefore strong.) If so, why? If not, why not?
Problem 4 In this game between a 7D and 5D, White has to make shape for his lower group. But how best to do this?
Problem 5 In this game between a 4D and 5D, White can play to try to prevent Black from making good shape (and thus becoming strong locally), but should he? If so, how? If not, why not?
Problem 6 In this game between two 5D�s, the 3 marked Blacks are crucial cutting stones, so retaining them is necessary. How best to do this, considering that they have only 3 liberties?
Chapter 4 - Peeps and Cuts Peeps and cuts are among the most common mechanisms by which weak stones arise. The primary differences between a peep and a cut are: - A peep�s value is often almost fully realized at the moment it succeeds in forcing the opponent�s connection, so that in many cases it may then profitably be (at least temporarily) �abandoned�, to thereafter serve primarily as Aji. - Most cuts result in the formation of a new (often weak) group, which thereafter must be watched and defended. Although there is no single simplistic �rule of thumb� that can provide unerring guidance in deciding whether it�s best to cut or peep in any given position, in general, and considering only the local situation: DON�T PEEP IF A CUT SUCCEEDS
The problem confronting the double digit Kyu player is that (s)he�s typically uncertain of whether or not any given cut should succeed ! And considering that their own play is probably going to be less than perfect, in games in which the main objective is learning and improvement rather than just victory, the best strategy is to cut, and then learn from experience both how to correctly appraise that decision in advance and how to conduct the resulting fight once you�re embroiled in it. Peeps Dia 1 In this variation of a popular 3-4 point Joseki, Black plays for thickness while conceding the corner territory to White. Dia 2 After the atari of B10, W11
connects, and then B12 makes a double �Tiger�s Mouth� virtual connection.
Dia 3 Next, the peep of W13 is a Kikashi which is answered by the connection of B14, and this is followed by the similar W15 peep, B16 connection exchange. After this, the White corner has the miai of �a� and �b� for its life so it�s safe! And, in the absence of other nearby friendly stones to help, there is no reasonable attack that White can currently expect to successfully mount against Black�s solid enclosing wall. So local action often ends for the moment, leaving this situation as is until later events make it clear what each side needs to do next locally. IMPORTANT! Just because a peep has been played (and answered), it distinctly does not imply that direct use must be made of that peep stone either immediately or ever! That may in fact occur, but at least as often a peep stone will be used indirectly to attain some other desirable goal (most often as a ladder breaker), or may even simply be temporarily �abandoned�as Aji, for possible later use. With that in mind, let�s now look again at the situation of Dia 3 and appraise the implications generated by the two peeps of W13 and 15 and their forced responses. The first thing that we notice is that W13 is a completely isolated lone stone pressed against a solid Black position, and W15 is only a bit stronger because of its assist from W3. So both of these peep stones are, by definition, more or less weak! In response to these peeps, we see that Black has not only been forced to add two stones of his own, but also has been forced into a position which, although thick, not only has absolutely no shape, but is also already partially enclosed and inhibited from expanding readily. The overall assessment of the position in Dia 3 is therefore: - On balance, Black is clearly the stronger on the outside. - If White correctly views W13 and 15 as expendable potential sacrifices rather than as essential assets which must be maintained even at cost, for the moment White stands at least equal overall because of their presence. Whether this Joseki integrates better into the global strategy of one side or the other depends on the position on the remainder of the board and is an issue beyond our present focus, so it will not be discussed here.
Figure 1 In this early middle game between two 4D players, the key issue at the moment is the fight in the upper right that has just begun between the enclosed and still unsettled B47-55 group and the enclosing W10-54 stones, which are still lacking shape and which therefore must be strengthened before he can safely attack Black. The solution to this dilemma that White conjured up was W56, peeping into the cutting point at �a� in Black�s lower right group. Because the B1- 43 stones would be forced into a dangerous (and quite possibly disastrous) fight if cut off, that gave Black essentially no choice but to connect at �a�. Having thus helped stabilize his own weak stones in Sente, White was then able to turn his attention back to the desired attack on the weak Black group in the upper right corner. So in this position the peep was the perfect move!
Cuts
The Typical Intention Of A Cut Is To Permanently Separate A Group Of Opposing Stones
and that almost invariably means that the cutting stone(s) will subsequently have to be reinforced/supported as required. A cut therefore typically initiates an important long term commitment.
Diagram 4 In this position from a game between a 9D and a 7D, the hane of B1 is a typical continuation of the Joseki in the corner. After the exchange of W2, B3, the necessary continuation thru B7 resulted in the creation of a weak Black group, in return for which White�s thickness has been effectively neutralized. Whether or not this turns out to have been good strategy by Black will depend on the followup by both sides.
Cuts Are Also Commonly Used To Make Shape Or To Facilitate Escape
Diagram 5 The cut of B8 followed by the forced sequence thru B12 sets up the capture of the marked White stone, resulting in White�s superb thickness in return for Black�s securing a large corner. Now let�s look at a position in a game between two 5 D�s in which making a judicious cut was the best way for a nearly trapped group to escape.
Diagram 7 Cutting with W1 is the way to begin.! That makes W3, 5, 7, 9 and 11 all forcing moves, sacrificing 2 stones (W1 and 5), and then moving smoothly out with W13., and leaving behind the potential for an almost certain eye at the top. Beginning instead with either W3 or W7 would allow either the connection of B1 or the extension of B10, and then White will have to flee eyeless! The outcome of a cut will frequently not only be decisive (as in these examples), but sometimes unpredictable, at least among players at less than a very high level, with the result that:
Making A Judicious Cut Is Often The Most Powerful Way To Play, And Sometimes The Only Possible Route To Victory
But Cutting Can Be Fraught With Danger
Diagram 8 This is a not uncommon position, especially in high handicap games. At first glance, it appears that a White cut at �a� will be big, so that it�s necessary for Black to protect against it. But that�s only an illusion! On deeper analysis, it becomes apparent that a White cut at �a�is actually infeasible!
Dia 9 If W1 cuts, expecting (or hoping for) this submissive B4 in response to W3, he may be in for a big surprise because ... Dia 10 After this B4 instead, if White foolishly continues as shown here, Black has this forcing sequence (a �squeeze�) with which to ruin White�s shape. Then ...
Diagram 11 After the atari of B10 forces the connection of W11 (with simply awful shape), the exchange of W13 for B14 is necessary to allow W15 to be an atari, which then forces B16 and gives White time for W17 to move out. This diagram shows one continuation after the plausible diagonal move of W17. Unfortunately for White, it fails. But there are lots of chances for Black to go wrong in the resulting fight, so White may well live instead if Black plays weakly.
White�s problem is that even if he escapes after W15, the outside strength that Black will build up while attacking his ever growing weak group should doom his overall game prospects! On the other hand, if Black isn�t a particularly strong fighter, or if this sequence is used by White as ko Aji, it might still be very dangerous for Black. So on balance, unless White is a particularly strong fighter or believes that Black is an especially weak one, W1 at �b� in Dia 9 instead of the cut is objectively the better way for White to play. The problem is that in most global situations that move won�t be Sente, so it must be timed correctly! Cuts And Ladders Cuts frequently give rise to a ladder. In those cases, wherever feasible the �rule� is
Capture Any Cutting Stone(s) As Soon As Possible
Diagram 12 When B1 ataris the marked White cutting stone, it sets up a ladder which favors Black because it runs into the Black stones in the lower right corner. Then W2 is a ladder breaker! But instead of playing the natural appearing B�a�, which would reinstate the ladder, Black�s best response is to immediately capture the White stone with B3, removing its dangerous Aji, perfecting his thickness, and thereby strengthening his now nearly complete moyo on the upper side. That this allows the excellent W4 is regrettable, but unavoidable.
Chapter 4 Problems Problem 1 In this position the key question is: Should White peep at �a�, cut at �b�, or neither?
Problem 2 Considering only the local situation, how should Black best exploit the cutting point at �a� in the White formation?
Problem 3 What should Black do about the cutting point at �a� in the White formation?
Problem 4 In this position from a 3 stone handicap game between a 6D and a 3D, W1 has just been played to secure his bottom territory. What�s Black�s necessary response?
Problem 5 What�s White�s big play here?
Problem 6 How can Black best exploit the cutting points in White�s position?
Chapter 5 - Sector Lines, Enclosure & Connectiivity In the previous chapters we discussed the principles upon which fighting must be based if it�s to be productive, and then spelled out how to identify the weak, important stones which should be the objects of any attack. In this chapter we begin the discussion of the criteria for deciding whether and when to initiate or avoid such attacks. Among the key operative themes in attack/defense are the closely related factors of enclosure and connectivity. These often become significant almost from the very earliest moves in the game as both sides maneuver for advantage, especially but not exclusively in the complex local (usually, but not exclusively corner) confrontations called Joseki. Another important issue, closely related to enclosure, is how to act against an opponent�s moyo. Moyo situations are typically quite complex, so without some simplifying concept to provide guidance the average player would find it virtually impossible to accurately assess their often subtle interactions, and then make the correct decisions. The ingenious concept known as a Sector Line efficiently satisfies the critical need for guidance in both the attack/defense and moyo situations. Although the Sector Line concept has been applied implicitly for centuries in the Orient, the first explicit description of it of which I�m aware was in a mid 1970's article by Bruce Wilcox in the American Go Journal.
But just what is a Sector Line? A Sector Line Is An Imaginary Straight Line Extending Across An Open Board Area Joining Two Stones Of The Same Color, Or Extending From A Single Stone To The Board Edge.
The Sector Line�s conceptual rationale is that a solid wall of stones of that color could theoretically be constructed along that line. The fact that such a wall will almost never be realized in practice does not affect the Sector Line�s value as a guide to making the appropriate strategic and tactical decisions. Diagram 1 When B2 approaches W1, the squeeze play of W3 is particularly effective because ... Diagram 2 Now the lone Black stone is enclosed within the indicated White Sector Lines, as both players would visualize them.
When To Use Sector Lines - Sector Lines are primarily (but not exclusively) useful in dealing with weak stones, which might be captured if they can�t make eyes or escape. - Sector Lines are most often applicable in the Fuseki and early middle game, because it is usually only then that enough of the board is still vacant to make them really meaningful. The seriousness of the situation for the enclosed stones is primarily a function of: - The proximity of the nearest Sector Line. - The spacing between the stones forming that Sector Line. In each case closer is more serious, with the effect diminishing rapidly with increasing distance. No exact criteria exist for determining this spacing/distance effect, so each situation must be individually evaluated using the player�s best judgment. How Sector Lines Function - Sector Lines act as a kind of �early warning system� to indicate which weak stones are in danger of becoming fully enclosed (and thus before the necessity of fighting a life-or-death battle for survival is thrust upon them).
- Sector Lines provide only generally appropriate action guidelines, and do not specifically identify: - the preferred strategy to be followed - the best move itself, or even an explicit identification of the set of feasible alternatives from which the best move should be selected. Caution! Although the Sector Line concept is both simple and extremely valuable, it�s not always determinative! A Sector Line is not valid if it: - Intersects an opposing stone. Diagram 3 When B1 is played, it breaks the outer Sector Line and negates it, so that Black is no longer enclosed!
A Sector Line is not valid if it: - Intersects an opposing Sector Line. Diagram 4 Here we see that W72 is within Black Sector Lines, but Black�s 69-77 group is similarly enclosed by White Sector Lines which intersect Black�s. The two B49, 59 stones are within White Sector Lines, but are also an anchor point of the Black Sector Lines which enclose W72. The result is that none of these Sector Lines are valid for determining the appropriate action to be taken in this area. This sort of situation is quite common when the board becomes relatively crowded, but in no way detracts from the general utility of the Sector Line concept.
Despite these very real limitations, the information Sector Lines provide is invaluable: A. To The Attacker, Sector Lines indicate whether or not to try to either: 1. Steal the opponent�s eyespace, and therefore drive his weak group out into the center. Or 2. Cut off flight into the center, and so force the weak group to attempt to live, either by making eyes in place or by capturing some of the attacking stones. B. To The Defender, Sector Lines indicate whether it�s best to either: 1. Run into the center to escape. 2. Try to connect to nearby friendly stones. 3. Make eyes. 4. Abandon the threatened stones (at least temporarily). 5. Counterattack. Caution! In any given position not all of these alternatives may be feasible, and choosing among those that are is a matter of the player�s judgment - a subject on which the Sector Lines themselves offer no direct help! Now let�s examine each of these Sector Line characteristics in detail. A. The Attacker�s Uses Of Sector Lines 1. Steal the opponent�s eyespace The sequence shown in the following diagrams occurred in a championship game between two 9 Dan professionals, who were then among the top 10 players in the world. Yet the simple Sector Line concept explains and helps predict their moves to a remarkable degree! Diagram 5 The position in the lower right corner begins with the same popular 3-4 point Joseki we saw earlier in Dia 1, in which White has just squeezed the lone Black stone from above, enclosing it within the indicated Sector Lines. These Sector Lines are close enough to constitute a fairly serious threat, so under normal circumstances Black would respond immediately. But because this 9P Black calculated that he can still readily live locally even if White is first to play again here, he instead chose to take Sente elsewhere. Although this was a rational global strategic decision, it gave White the opportunity to maximize his local advantage, as we see in the following diagrams.
Diagram 6 W1 takes advantage of Black�s failure to defend by blocking him from the corner, making territory for White while making it harder for Black to secure eyespace locally. If White were to be allowed to continue at 2 next , that would not only make perfect shape for his own stones but would also make it extremely hard for the Black stone to make life locally. So with little choice, B2 occupies the key shape point himself, while cutting the White Sector Line! (A strong clue that this is a desirable move!) A (slightly lesser) problem with B2 is that it also makes his unit �heavy�. W3 With this stylish Knight�s move extension, White increases the scope of his control of the corner by extending to the left, at the same time creating a new Sector line which once again encloses Black.(thereby maintaining Sente!)
Diagram 7 In order to escape that enclosure it�s necessary to break White�s new Sector Line, and in this position the stylish diagonal extension of B4 is the best way to achieve this end. An alert reader will have noticed that B4 not only broke the White Sector Line but also established Black�s own Sector Line enclosing the lone White stone on the right side. But because the Black star point stone anchoring the upper end of that Sector Line is so far away, the lone White stone is only mildly affected by this. So for the moment White can afford to ignore that Black Sector Line, to continue his own attack. White�s natural response to B4 is to extend once again on the bottom with the one point skip of W5, increasing his local territory while also initiating the new Sector Line shown, to once again enclose the 3 Black stones.
Diagram 8 When B6 breaks the latest White Sector Line, there is no further White move that will simultaneously enclose the Black stones within a new White Sector Line while also extending White�s lower side territory. That means that, for the moment at least, it is no longer profitable for White to continue playing on the lower side, because it would be Gote. On the other hand, we see that Black has now established his own Sector Line enclosing White�s lone right side stone. But because the upper anchor stone of this Black Sector Line is so distant, this lone White stone has more than ample maneuvering room to either make a base or escape into the center if attacked further. So the Sector Line analysis tells us that White can now afford to play elsewhere if his evaluation of the global board position indicates that would be more productive - and that in fact is what the 9 Dan pro playing White in this game actually did!
2. Cut off flight into the center. Diagram 9 This is a situation that frequently arises in both even and handicap games when Black fails to respond locally to the kakari of W1. W3 (which is also often played at �a�) encloses the Black corner stone within White Sector Lines as shown. But Black can still easily break out safely via a play at any of �a�, �b�, or �c�. But if he doesn�t ...
Diagram 10 Most often, White�s strongest continuation is with W1 here, to solidly enclose Black within his Sector Lines. Black can then cut these Sector Lines, but can�t forcibly break out through them. Now let�s examine why allowing W1 is usually bad for Black.
Diagram 11 Black can still live in the corner, if he either knows this sequence by heart or can find his way through its tactical complications unaided. But it�s dangerous because even a slight error in the sequence can easily result in the entire corner�s death! And even if Black lives, as here, White�s thickness usually gives him the better position globally. So playing this way is usually only advisable in special circumstances.
B. Defender�s Uses Of Sector Lines 1. Run into the center to escape. Diagram 12 Black will usually be best advised to break out of the White Sector Line, most often by occupying the key point himself via B1 as shown, but sometimes by attaching at �a� or �b�instead. After B1, W2 to seize the corner is by far the most frequent continuation, and then Black will usually (sooner or later) block at either �c� or �d�, the choice depending on the global board position.
2. Try to connect to nearby friendly stones.
Diagram 13 In this game between an 8D and 6D, the marked Black stone is completely enclosed by White Sector Lines, so it appears that all of this large territory is about to become White�s. Living in place is difficult, but Black saw an opportunity to save this stone and neutralize much of White�s potential territory in the surrounding area if he could somehow manage to connect to the Black stones below. The next diagram shows how he went about doing it.
Diagram 14 With this clever sequence, Black managed to connect underneath in the lower left and achieve life, thus neutralizing most of this formerly large White area. In return, White captured a part of Black�s former lower edge group, to sharply increase his own territory there. So Black�s gain was not without cost, and that�s a fairly common result of such confrontations. But on balance Black has profited a bit more, at least in part because he has emerged from this fight with Sente.
3. Make eyes. Dia 15 In this game between two 7D players, when the marked Black stone was played it not only prevented White�s damaging push through-andcut, but also completed the enclosure of the White 7-stone group on the right edge. In the absence of special circumstances Black should without fail play to enclose White as shown! Dia 16 If White now desires, his 7 stones on the right edge can live easily via W1, because then if B�a�, W�b� completes his two eyes. And if Black doesn�t play at �a�, it�s possible that at an appropriate later time White will be able to follow with
the profitable endgame sequence of W�a�, B�c�, W�b�, B�d�.
The problem with making life by playing W1 is that Black will then happily continue with B2 to connect his corner stones out while seriously weakening the important (and presently both shapeless and eyeless) 5-stone �L� shaped White center unit immediately below! Because that was a prospect that was unacceptable to White, what he played instead of this W1 is shown next. 4. Abandon the threatened stones (at least temporarily). Diagram 17 Because the result of Dia 16 was unpalatable, White chose instead to play W1 here, to strengthen the crucial weak 5-stone center White string! This not only undercut the Black corner while preventing Black�s connection underneath, but also isolated the lone Black stone on the upper edge. But the severe price that White had to pay for this was B2, which more or less assures the death of the White right edge group, because now White needs both �a� and �b� to secure his two eyes, and he can only manage that by making two successive moves here. (Only possible if played as a Ko threat which Black can�t afford to answer.) So after B2 White had no choice but to tenuki, and hope that circumstances would later enable him to rescue this �abandoned� 7 stone group on the right edge.
Here�s another example, arising in a position that�s not uncommon in both handicap and even games: Diagram 18 W4 is a probe intended to induce Black to fix the shape of his stones, so that White will then know how to best proceed locally at the appropriate later time. But as things stand it was too early in the game to be sure after B5 whether White will prefer to continue below, on the right, or on the 3-3 point in the corner, and W4 is enclosed within the indicated close and very threatening Black Sector Lines. So for the moment W4 was correctly �abandoned�, as White played elsewhere! (From that, it might reasonably be argued that W4 was premature and should better have been deferred until a later time. But that's an issue well beyond our present focus.)
5. Counterattack.
Diagram 19 In this game between a 4D and a 3D, when W1 was played it seemed that White had visualized the indicated Sector Lines and the huge potential moyo that they enclose. But, although appearing logical, this reasoning is actually doubly flawed! Not only are there are two Black Sector Lines running from the upper right to the lower left that intersect (and therefore neutralize) several of White�s, but, far more significant, Black can counter-attack by establishing his own far more threatening Sector Lines!
Diagram 20 A strong Black response would have been as shown, not only enclosing the 4 weak White stones within the indicated close (and therefore very threatening) Sector Lines of his own, but also simultaneously assuring that Black can move into the White moyo before it can be consolidated. (Note that the 8 marked Whites at the top are tightly enclosed with only 3 liberties, and are therefore effectively captured!) Although the outcome of the fight that would have followed isn�t entirely clear, it would have offered Black his best chance to win. When he failed to make this key play, White moved smoothly on to an easy victory!
Sector Lines As Moyo Invasion/Reduction Indicators - Playing anywhere inside the opponent�s Sector Lines will constitute an invasion. - A play on or just outside an opponent�s Sector Line will initiate a reduction. The key clues to deciding whether a reduction or invasion of an opposing moyo is the more likely to produce a satisfactory result are whether or not one or more of the following is true: - There is at least one long Sector Line operative. - One or more of the enclosing Sector Lines have significant gaps for possible ingress or egress by opposing stones, especially if - There are friendly stones fairly close outside those Sector Lines. If any of these conditions exist, an invasion will often be feasible because there will be opportunities to either connect out or to live within the moyo by placing key eyemaking stones which also threaten to connect out. To the extent that these enabling conditions don�t exist, only a reduction will usually be feasible. But it�s important to remember that there are no absolutes! Although the use of Sector Lines will go a long way toward enabling you to make the right decision, your ultimate success or failure in the fighting that ensues will still depend upon your ability to find and correctly time the right threats, and on your opponent�s ability to meet them. The following example shows the kind of dangerous tactical complications that frequently result from invasions, and why application of the indications provided by Sector Lines must always be made with great caution and forethought. Diagram 21 This is a not uncommon situation in which Black has made a 5 point skip from a 4-stone wall based on the third line to form a small moyo, against which White will often feel compelled to act. But how? And where?
Diagram 22 The best try to make a live group within the Black space is to begin with this one point third line skip of W1 from the extension stone. In response, the diagonal extension of B2 is the strongest way to prevent White�s escape to the outside, forcing him to try to live in place. This diagram shows one possible continuation, in which the invasion dies, and the next diagram shows another with the same result.
Diagram 23 The problem in this position with an invasion like this W1. is that there really isn�t room enough for the invaders to live if Black defends correctly! And if White does die, as here, that allows Black to consolidate a territory of over 30 points.
Diagram 24 This diagram shows that if Black errs, then White can escape, with a disastrous reduction to what formerly seemed a large potential Black territory. But in at least partial compensation Black now is strong on both sides while the still eyeless Whites remain weak and vulnerable!
Diagram 25 From the foregoing, it�s likely that a prudent White won�t choose to invade but will instead opt for a reduction. For that purpose, W1 as shown here (just breaking the Black Sector Line) or �a� are usually the best moves, the choice between them depending upon the location of other nearby White and Black stones and the tactical considerations they engender.
Now let�s see how Sector Line principles were applied in a complex Moyo situation. Diagram 26 In this position from a game between two 5D players, White has created a large moyo in the upper center which Black must do something to reduce before it can be consolidated into a winning territory! As usual in such situations, the question to be answered is whether Black should invade the moyo and attempt to live within its confines, or try to reduce it by nibbling away at it from somewhere on its outer perimeter. This is the kind of situation in which Sector Lines can often provide the best clue as to which of these courses of action is likely to be the most productive. The major difficulty in this position is that a White Sector Line actually covers each of this moyo�s borders, so that only an invasion is really feasible if Black wants to prevent White from consolidating too much of this vast area. At the same time, we see that there are four places, marked �A�, �B�, �C�, and �D� in which the White Sector Line is long enough and/or Black stones are near enough to it to offer support to an invasion. Such potential places of ingress and/or egress are called �doors�. Here, only doors A and B offer real potential for Black as things now stand.
A complication is that the White moyo is so large that only a player of professional strength seems likely to be able to even come close to accurately visualizing all of the invasion possibilities and their likely responses in advance. So �mere mortals�, even fairly strong
players like the 5D protagonists in this game, necessarily have to largely rely on their �gut� instinct plus confidence in their tactical skills to guide them in making difficult decisions like this. A detailed analysis of all of the complex tactics involved in the fighting that transpired next in this game is advanced material far beyond the scope of our interest in Sector Lines. So in the discussion of the actual game resolution provided below we will focus only on the main theme of the invasion. Diagram 27 Because the main A and B doors capable of exploitation are both on the left side of White�s moyo, it�s clear that Black�s best invasion point must be somewhere in that vicinity, but the choice of B81 as the starting point for Black�s invasion was a judgment call. W82 Rather than simply trying to limit Black�s incursion, White counterattacked by threatening to continue at 83, which would both restrict the expansion of Black�s upper left corner territory while making a sizeable territory of White�s own in that area in conjunction with his stones below. In addition, it blocked Black�s access to door A. B83 Given that door B is still open. and because a White continuation at 83 would be too good to allow, Black felt that he had no choice but to block here himself to seal off his upper left territory. So White retained Sente. W84 similarly blocks off Black�s flight path to door B, leaving Black with the difficult problem of how to continue to achieve life. But now Black�s chances for success are somewhat improved, because he will be able to play a second stone inside White�s moyo before White can respond there. The details of the complex fighting that actually followed in this game are primarily tactical considerations that lie far beyond our focus on learning how to use Sector Lines, so
are not presented here.
CAUTION!! As we�ve seen, with substantial amounts of maneuvering room available inside a substantial moyo, not only does the ultimate capture of any invaders become more uncertain, but the possibility of resulting external complications also increases exponentially. And even when the invaders are trapped and must be at least temporarily �abandoned�(as in Dia 23), they typically still retain considerable Aji. This may either lead to their later rescue or to an advantage elsewhere for the invader, especially if a Ko fight erupts. So both sides will have to remain alert to this potential until the situation is finally completely resolved or the game ends. As earlier noted, detailed exploration of those complications is beyond our present interest, but you might find it productive to investigate them on your own. Now let�s look at a key portion of the Fuseki/early middle game between a 5D and 4D, to see how Sector Lines provide almost unerring guidance to strong (if not necessarily perfect!) moves. Diagram 28 W1 encloses the Black lower right corner stone within White Sector Lines. Then, in the absence of any more urgent play elsewhere, it�s to Black�s advantage to respond by expanding/sealing off his eyespace to ensure his life. The defensive attachment of B2 is an excellent, time tested way for Black to achieve safety, and begins a popular Joseki.
After the necessary connection of W5 Black remains enclosed, but his formation can now make eyes against any White attack! So it�s not strictly necessary (although often desirable!) to make a further submissive play like B�a� immediately, because even if W�b� is permitted the simple B�c� gives Black an unassailable live shape. So after W5 Black can afford to tenuki with sente. But because White is now threatening to build a moyo on the lower side, it�s often globally incumbent on Black to try to prevent that from becoming a reality before it�s too solid to readily counter. Black�s problem is that, wherever he plays on the lower side now, his stone will already be within (somewhat distant) White Sector Lines! But because the end points of the upper Sector Line are so far apart, that�s not particularly dangerous. So with B6 Black makes a �standard� kakari against the White lower left corner star-point stone. Because that doesn�t enclose the White corner stone within Black Sector Lines, White need not defend but may instead counter-attack. He does that with maximum force via the squeeze play of W7, which does enclose B6 within close (and therefore very threatening) White Sector
Lines, while also making a maximum strategic extension from his W3,5 wall on the right! This leaves Black with only two viable choices - either dive into the corner and at least temporarily �abandon� B6, or run out to break the White Sector Line. Given White�s thick position in the lower right, diving into the corner would concede White too much almost secure territory on the lower side, so Black has no real option but to break White�s Sector Line! His choice to do this is the �standard�one point skip of B8, although in some global positions either �d� or �e� may be preferable. B8 is Sente because it encloses the White star-point stone within Black Sector Lines! So W9 (or �f�) to break that Sector Line and sketch out some territory is also natural. Although this also establishes a new White Sector Line enclosing B6,8, in conjunction with W1 all the way across the board, once again its anchor points are so far apart that it has almost no effect. The result is that Black is free to take sente with the strong �shoulder hit� on W7 of B10, to once again establish close (and therefore very threatening) Black Sector Lines around W7. That�s the �normal� joseki continuation in this position, but in this game the circumstances in the lower right impelled Black to deviate from the �usual� sequence would normally follow, as we see in the next diagram. Although the complex ramifications of this intensely tactical fight are well beyond our focus on the Sector Line concept itself, they�re shown below for the reader�s edification. The following material may be glossed over at the reader�s discretion. Diagram 29 Instead of continuing with the �normal� Joseki move of W11 at 14 to establish a live group along the edge, with this W11 a swap occurred, with Black destroying White�s potential at the bottom in return for White�s effectively killing the 3 Blacks on the left and almost (but not quite) securing the lower left corner!
End of material to be glossed.
The Limitations of Sector Lines The action guidelines provided by Sector Lines are necessarily incomplete because: 1. There may be several different groups affected by active Sector Lines at any given instant, so their presence alone doesn�t change the player�s overall problem of deciding which situation takes priority, and of handling any interactions between them.
2. Sector Lines only provide guidance to an appropriate local strategy! Global considerations involving a nearby corner, side, the center or even the entire board may dictate that a move other than that indicated by a Sector Line analysis is best overall. A. From the defender�s perspective, this may mean that a rescue attempt should be deferred, or that a threatened weak group should be abandoned for later use as Aji, despite the fact that it could be rescued! B. From the attacker�s perspective, it will frequently mean that pressure should be applied to weak opposing stones without any real intention or expectation of capturing them (although that outcome will be welcomed if it should present itself!), in order to build up strength for use in attaining some important objective elsewhere. 3. Sector Lines do not identify the specific move that works best in any given situation whether a tesuji, or just the most appropriate strategic play. Correctly identifying the best global move requires a high level of tactical and strategic competence, most of whose development is outside our focus in this book. Despite these limitations it�s advisable in your own games to: Look First At The Relative Strength Of The Opposing Groups And Any Sector Lines They Generate
and Override Those Indications Only If There Is A Clear And Compelling Reason For Doing So
No single simplifying idea like Sector Lines can instantly transform a beginning or intermediate Go player into an expert, but in many situations it can go a long way toward suggesting reasonable lines of play that might otherwise be missed. Although the influence of Sector Lines is often easy to see after-the-fact, things are necessarily far less clear in the heat of battle! Reacting appropriately after you�ve recognized that an opponent�s move has enclosed one of your key groups within a dangerous Sector Line is often essentially routine because there may only be a limited number of viable options, but correctly deciding what to do next when you have Sente with which to play anywhere is quite another matter! Not only is it necessary to decide whether and where you should take profit or attack, but in the latter case to also where
you might create potentially profitable new Sector Lines. And even if that hurdle is successfully surmounted, the concept still offers no automatically applicable criteria for judging which of several possible alternative Sector Lines might prove the most profitable. And then the Sector Lines in and of themselves offer little help in resolving any of the inevitable tactical complications that will accompany their creation. The result is that although full understanding of the Sector Line concept may be necessary, it�s nevertheless an insufficient condition for becoming a strong player! Finding the best move in any given position still requires an entire complex of knowledge and tactical skills that can only be developed over time as a result of much play and study - all of which are outside the scope of this book. Despite these caveats, mastering the simple idea of Sector Lines offers perhaps the greatest �bang per buck� for the effort expended in any beginning/intermediate player�s quest for improvement! Finally, it�s also important to recognize that when implementing the Sector Line concept in your own games, you will almost necessarily make some strategic errors and even more tactical ones. And those errors will in turn result in some failures in either or both attack and defense, sometimes even resulting in last minute reversals of winning games in which a long series of excellent moves is completely offset by a single egregious blunder. But such occurrences, however difficult they may be to accept cheerfully, are a natural part of the learning process and should not be allowed to dissuade you from making the strongest moves of which you are capable! With application of the key concepts provided in this book and continued diligent study and practice, sooner or later the number and seriousness of such errors will diminish, and your playing strength will then make the quantum leap upward that your new found strategic insights justify. Now let�s try some problems to see how well you�ve mastered the Sector Line concept.
Chapter 5 Problems
Problem 1 This is the early middle game
between a 6D and 5D. Your task here is to show each side’s Sector Lines as the players would visualize them.
Problem 2 Where are the operative Sector Lines here? And how significant are they? Problem 3 It was actually Black’s turn to play here, so what’s his best move? And (equally important) why? If it was White’s turn to play instead, where would be his best move, and why?
Problem 4 In this position: 1. Show any Sector Lines that are operative. 2. Answer the following questions: A. How solid/secure do you assess those Sector Lines to be? B. Based on that assessment, should Black think invasion? Or reduction?
Problem 5 This position arose in a game between two 5D players. What’s Black’s key play here, and why? If it’s White’s turn instead, what would be his best move?
Problem 6 When B1 was played in this game between a 6D and 5D, the marked 4 Whites are within Black Sector Lines and almost trapped. At the same time, the two Blacks are themselves still within a White Sector Line, so that these competing Sector Lines technically cancel each other! But the two Blacks have the outside while the four Whites are almost enclosed! So it’s clear that if these White stones don’t escape immediately they will die, because there’s insufficient room on the edge for them to form two eyes. So the key questions are: Can they escape? And if so, how?
Problem 7This position that arose in a game between a 5D and a 4D. White has constructed a vast (but still incomplete) lower center moyo which Black would much like to reduce. At the same time, Black’s own upper side position is also becoming impressive, so in playing to reduce White’s moyo Black must be careful that White’s counter play doesn’t inflict even worse damage on his own position - and that’s quite likely to be the outcome if he plunges in too deeply! So the move Black seeks is one that looks carefully in both directions, and the best answer is quite readily suggested by the Sector Line concept! Can you find it?
Chapter 6 - S.W.O.T. Analysis The themes we�ve explored in this book thus far provided the what, where, when and why of fighting. This chapter integrates those ideas and reaches their logical culmination in a technique widely applied in business management, known by its acronym of SWOT analysis, which enables the establishment of a rational and appropriate action plan. In Go, SWOT analysis begins with a global board evaluation of the importance and relative strength of the opposing groups prior to each move, just as we�ve done in the preceding chapters. Then we add to that an appraisal of our own aggressive potential, together with the converse appraisal of where the opponent can do us damage. The result is a global evaluation of each side�s:
S = Strengths W = Weaknesses O = Opportunities T = Threats This basic analysis is then augmented with an appraisal of how each side stands in terms of: - Settled territory. - Territorial potential. The combination of these factors then allows the creation of an appropriate action plan, specifying (to the extent feasible): - The main focus of play in the current position. - The most urgent immediate task for the player with Sente. - What (s)he should do to achieve that goal. - The opponent�s expected response. When properly completed and updated move-by-move, this global assessment and action plan provides the road map that guides both sides throughout the game! CAUTION! Even if the SWOT analysis is perfectly performed (no mean feat in many positions for less than strong players), finding the best moves to exploit that appraisal will frequently require both tactical and strategic skill well beyond players at the level for which this book is intended. But please don�t be discouraged by this, because it�s only a technical detail which will eventually be self correcting as your knowledge and skill improve with increasing experience. Until that high level of competence is finally attained, the result of applying a SWOT analysis may �only� be that you identify the right objectives, even if you don�t always find the very best moves to implement them! So, at worst, any resulting lack of success won�t be because you overlooked some important element of the position! Now let�s revisit the position we examined earlier in Chapter 2, Diagram 2, and see how the more comprehensive SWOT analysis enables sharpening focus beyond the simple (but essential!) identification of strong and weak stones to produce an appropriate action plan.
Diagram 1 The SWOT analysis of this position is as follows: Black: Strengths: - The upper side is very strong, but the �b� stones don�t reach out very far into the vital center, so their overall impact is only modest. - The �k� stones already have one eye and potential for another both on the edge and in the center, so they may be considered modestly strong. Weaknesses: - The �i� stones have no eyes and are pressed on both sides by Whites which are stronger. Opportunities: - The (modest) chance to exploit the weakness of the White �h� stones. - The (even more modest) possibility of rescuing the trapped �e� stone. - The chance to attack and possibly capture the White �f� stone. - The potential for attacking the White �j� stones which still have only 1 eye. Threats: - The still unsettled status of the fairly large �k� group. - The weakness of the �i� group, sandwiched between the stronger White �h� and �j� groups. Settled Territory: - 10+ points in the upper left corner.
Territorial Potential: - Almost, but not yet complete control of the entire upper side (because of the gaps between the �a�, �b�, and �c� groups, and the still open 3-3 point in the upper right corner.) which could easily total 50+ points if fully realized. - 10+ points in the lower right corner. White: Strengths: - Because of the trapped Black �e� stone, the White �d� group is very strong, and has great influence in the vital open board center. - Because of the trapped Black �m�and "n� stones, the White �l�/�o� group is equally strong, and also has great influence in the vital open board center. - The presence of both of these strong groups on opposite sides of the still open center greatly
improves the fighting prospects of White�s still somewhat weak �h� stones. Weaknesses: - The fairly large �j� group as yet has only 1 sure eye. - The White �h� stones as yet have no eyes are squeezed on both sides by Black. Opportunities: - There is good potential to invade and reduce the still porous big Black upper side, either between the �a� and �b� stones, between the �b� and �c� stones, or on the 3-3 point in the upper right corner. - There is also good potential to make territory between the �f� stone and the �d� group. - There is also modest potential to expand the left and right side groups into the center. Threats: - Mainly that either of the still unsettled �h� and �j� stones will either be captured or will lead to disaster elsewhere if they are forced to run. Settled Territory: - Essentially none at present. Territorial potential: - 20+ points on the left side. - Perhaps 15+ or so points in the �d� group. Action Plan: - The current global focus is on the interplay between the weak �h�,�i�, �j�, and �k� groups. Now let�s see how this simple but surprisingly powerful SWOT protocol was applied in a game between two 4D players. Figure 1 The SWOT analysis of this position is as follows: Black: Strengths: - A still quite incomplete lower left corner enclosure. - Good shape in the upper left corner that should allow making two eyes against any currently foreseeable attack. - A fairly thick and almost connected right side, with one almost abandoned embedded White stone (W14) and one weak White stone (W26), both within Black�s Sector Lines. Weaknesses: - The �thin�Black lower left side position. Opportunities: - The chance to exploit the weakness of W6 on the left, and W14 and W26 on the right. - The possibility for invasion into the big gap between W12 and 24 on
the upper side. - The Aji of the gap between W18 and 24. - The potential for expansion from the lower left corner, especially along the lower side. Threats: - The potential inherent in White�s possible development of W6 on the left and W14 and 26 on the right.
Settled Territory: - Essentially none. Territorial Potential: - A few points in the upper left. - Ten to 15 points in the lower left. - Perhaps 30 or 40 points on the right side, if the problem of W14 and (especially) W26 can be solved. White: Strengths: - A solid, shapely position in the upper left corner. - Solid and well coordinated positions in the upper and lower right corners. Weaknesses: - W6 is a lone White stone splitting two Black positions and within distant Black Sector Lines. But that�s not urgent at the moment, because the area is too open for a Black attack to seriously compromise the ability of the W6 to make a base and/or escape. - W14, which abuts a strong Black wall and is also nearly surrounded, so it�s clearly at least temporarily abandoned. - W26, although at the moment it�s easily able to escape. The problem with this stone is that it must be aided before Black can play again to block its easy egress to the still open center, and then capture it create a vast Black territory. - The gap between W18 and 24, and between W12 and 24. Opportunities: - Primarily to develop W26 to prevent a large local Black territory. - The chance to develop on the lower side. - The chance to consolidate the upper side by adding a stone between W12 and 24. Threats: - Mainly that W26 will be trapped and captured, and that Black will make too large a territory in that area as a result. Settled Territory: - Essentially none at present. Territorial potential:
- Ten plus points in the lower right corner. - Probably 10 or so points on the upper left side, and in the upper right corner. Action Plan: - The current global focus is on the weak W26, and the way in which both sides handle that problem will shape much of the remainder of this game! - Because the center is still so open, White does not have to support W26 immediately, but he must watch the local situation carefully! So at the moment White can afford to improve his prospects elsewhere, with the lower left as the currently most fruitful target. The following material may be glossed over at the reader�s discretion. The optimal implementation of a SWOT analysis is mainly a matter of technique, and is therefore outside the realm of our focus on the analysis itself. But briefly showing how the fairly strong protagonists in this game answered this challenge may prove illuminating to the reader, so we show that next, with minimal commentary.
Figure 2 W32 induced B33 to defend the corner territory, and then W34 not only made a base but threatened to more or less complete a large moyo on the lower side by continuing at �a� or thereabouts at an appropriate later time. When B35 strengthened Black�s upper border, it would normally induce W�b� in response to preclude Black�s strong pressing move there. But in this situation the threat it posed against W14 and 26 on the right side is far more serious, so White felt compelled to respond to that instead! W36 follows the maxim of attaching for defense (see Chapter 1), and after the natural Hane of B37 in response, the cross cut of W38 is a standard technique to �make shape�. But after the atari of B39, W40, B41, instead of playing W42 White might have been better advised to simply play W�c�, B45, and then skip out lightly (and relatively safely) into the center with W�d�. But because White was also looking at the weakness of the Black lower right
side group ... The sequence shown followed through W52, after which Black has succeeded in the first stage of his strategy by inducing White to develop the weak and isolated W26 into a group too large to give up, but which is nevertheless still ripe for attack! Figure 3 After W52 White was out of Black�s Sector Lines, so there was no good way for Black to immediately exploit that still unsettled White center group. So Black�s attention shifted to White�s threat to close off a big lower side moyo, and for this purpose the invasion of B53 was an excellent way to start! In this situation, the instinct of the typical beginner/intermediate would be to immediately aim next at the potentially vulnerable W32-34 two point third line skip in the lower left, but Black�s sophisticated plan is much deeper than that! Black�s clever idea is to use B53 et seq as a diversionary mechanism for creating thickness in that area, with which to then: - support any weaknesses in his own lower right side group, and - prevent a later flight to safety in that direction by the weak White center group! After accomplishing those objectives, Black also emerged with Sente because W78 was necessary to secure White�s eyespace and territory in the lower right corner. So Black was free to implement his plan with the cap of B79, blocking the flight of the now large and still eyeless right center White string, once again enclosing it in Black Sector Lines, and forcing it to seek safety above.
What happened after that was primarily tactical and therefore beyond our current interest, but suffice it to say that after a tense and incisive battle the embattled White center group was
unable to either make 2 eyes or escape, so White resigned. This is an almost perfect illustration of the danger that often follows when the Sector Line indications are ignored and a weak group (W26) is belatedly added to in an attempt to save it! Black�s final favorable result in this game depended upon his ability to produce the precise tactics needed to counter White�s many serious escape and counterattacking threats, so it was by no means assured after B79. But whether or not it was, the key idea to remember is that it�s best to not become enclosed and forced into the kind of desperate situation White confronted here. End of material to be glossed.
Chapter 6 Problems In each of Problems 1 and 2, perform a SWOT Analysis to determine: - Which stones are Strong and which are Weak, and why. - Each side�s Opportunities and Threats and what they imply. - Each side�s settled territory and territorial potential - An appropriate action plan.
Problem 3 In this problem you are asked to perform a SWOT analysis, and then use its results to decide where White should play. For your answer to be considered correct for our current purposes it�s not necessary to find the absolutely best move, but selecting one in the appropriate area certainly is!
Chapter 7 - A Sampling Of Major Fighting Scenarios
What we�ve done in this book thus far is to explain how to: - Identify the important weak groups which should be the focus of play. - Use the SWOT analysis technique to develop an appropriate action plan for exploiting those weak groups. In this chapter, we illustrate a select few of the more important of those action plans. As noted earlier, the first step in attacking a weak group will usually be a threat to enclose, because only enclosed groups can be killed. That threat will then typically elicit a response in which the target group attempts to flee, usually either into the open center or toward friendly stones. Our focus in this final chapter is on the methods for taking best advantage of that flight. In most cases the attacker�s only reasonable expectation should be that the attacked stones will succeed in escaping, so that any profit resulting from the attack will typically be realized elsewhere (usually, but not always, nearby). Consequently, all-out attempts to surround and kill will usually not only prove futile but unproductive as well. (Of course if the defender errs and the opportunity for a kill or other major coup does present itself, it should be seized, with alacrity and thanks!) Capping This is the commonest and most basic attacking technique - most often appropriate, but (as we show below) not always! Figure 1 In this 2004 AGA-Ing Pro Cup match between Huiren Yang 1P (White) and Mingjiu Jiang 7P (Black), B31 has capped White�s weak 3stone W12-20 group, blocking its easy path into the center. Although Black has no reasonable expectation of killing these stones, this is nevertheless the best way to exploit their weakness, aiming to profit elsewhere by harassing them.
Figure 2 This is how the game actually continued. (The details of the complex tactics involved are far beyond our present interest, and so will not be discussed here.) White resigned after B159 because the impenetrable Black lower center moyo is just too large for White to overcome.
Figure 3 in this 2005 North American Masters match between Jie Li 9D (White) and Thomas Hsiang 7D (Black), Black has just erred with B81. Instead, he should have secured his large weak group via the one point skip to �a�. Now White can exploit this oversight - but how?
Diagram 1 Capping with W1 seems like the logical move, but here it�s not best because it leads to a Ko which might involve dangerous complications. Instead, 9D Li thought through those complications, and came up with an even better idea.
Diagram 2 Instead of capping, the diagonal move of W1 here is even better, because it precludes that Ko possibility. Next, Black thought it prudent to strengthen (and expand) his corner with B2 before answering W1. Unfortunately that turned out badly because B2 induced W3, which then contributed importantly to White�s attack on the weak Black group below. After the B2, W3 exchange, Black had time to attach with B4, and at that point he must have believed that he was going to survive White�s attack relatively unscathed. But that expectation was dashed when the peep of W13 and the following W15 set up the later cut of W21, trapping the 8 Blacks on the right and leaving the rest of the big weak Black group fleeing with only 1 eye. Only a few moves later Black was forced to resign.
Diagram 3 In this 2006 Paris Open Championship Tournament game between Motoki Noguchi 7P (White) and Fan Hui 2P (Black), B79 (B1 here) was played to make it difficult for White�s two marked stones to safely connect to his friendly stones in the upper left. This put the onus on White to either break through Black�s encirclement - highly unlikely in this position - or to make life in this immediate area in the face of Black�s surrounding strength.
Diagram 4 As this game developed, instead of trying too hard to enclose and kill the weak White center group, Black instead wisely chose to make profit at the top without unduly strengthening the target group. This succeeded so well that White resigned before the weak group�s ultimate fate could even be decided! This was superb strategy, and exemplifies how such an exploitation should ideally be carried out.
Diagram 5 In this game between a 2D and 3D, Black has suffered a huge loss of 8 stones in the lower left, so his only possible chance to win is if he can somehow mange to kill the large still eyeless marked White group in the upper center. Since this group�s only realistic chance to connect with friendly stones is with the Whites in the lower right, the attachment of B1 is a fine (and typical) way for Black to try to prevent that connection. Although that strategy didn�t succeed in this game, it in no way detracts from the general principle involved.
Diagram 6 In this game between two 4D�s, when W1 invades Black�s thin lower right position, with White�s strength on both the bottom left and right side to run to, it would seem that this stone is not only quite safe, but actually may be stronger than the lone Black to its left as well. But is it really? Black�s clever response gives the answer.
Diagram 7 After the twin kikashis of B2 and 4 followed by the attachment of B6, the lone White stone has now become weak and can only run straight up into the center, where Black is already strong. The price that Black has had to pay for this is that W3 and 5 have given White a considerable profit on the right, but if Black�s following center attack succeeds (as it did in this game), his compensation there will more than make up for that loss. So this strategy is inherently dangerous, but can be very effective if adequately followed up.
The Steering Attack Unlike the Cap, which typically offers the capped player several options in response, a properly placed steering attack stone essentially constrains the opponent to running in a single desired direction. Diagram 8 In this game between two 4D�s, White�s large weak center group offers Black an ideal opportunity to begin the creation of a large Moyo in Sente by forcing White to move in a desired direction. Do you see how?
Diagram 9 B1 blocks White�s progress to the right, forcing his group to flee up into the open top, allowing B3 to begin sketching out a large moyo on the right side. Although this area is still much too large and open to all become territory, it does provide Black with considerable potential. How much of that potential territory can later be realized as solid territory is, of course, still to be determined in subsequent play, but it does provide Black with a significant winning chance.
Diagram 10 In this position from a game between two 5D�s, Black has set White up for the devastating splitting attack of B1, which is also on the key shape point of the lower White group.
Diagram 11 The choice and timing of the best splitting point and the ultimate outcome of the resulting fight are both a function of the opponents� skills, but unless gross blunders occur the end result should more often than not be favorable to the attacking player.
The Running Battle Now let�s look at the early stages of a game contested between an 8D and a 7D involving a classic running battle, in which, for many moves, almost every move can be explained by the Sector Line concept! It�s my bet that, just by using this simple concept, you will not only be able to come close to predicting these strong players moves surprisingly often, but also would probably not have made the overplay of W15 in Dia 13 that ultimately cost 8D White this game!
Figure 4 In this position W1 is the most logical (but hardly the only) way for White to play, making the fullest possible use of his upper left 4-4 point stone by making a long strategic extension from it. A squeeze play is the best way for Black to answer because Black is concerned with neutralizing White�s center thickness below, and B2 is the strongest and most aggressive pincer available. Perhaps most important, it encloses W1 tightly within Black Sector Lines, so it�s Sente! If instead Black were to passively extend at �a� to coordinate with his strong position in the lower right, W�b� would work much too well with both the White upper left star point stone and his thickness below for Black to allow.
Diagram 12 If W3 now dives into the 3-3 point to seize the corner as shown here, this Joseki will inevitably follow, and that would leave Black with both thickness which helps neutralize White�s thickness below, and Sente with which to play at either �a� or �b�in the upper left corner, again with a result White felt was unfavorable to him. So instead ...
Diagram 13 The one point center skip of W3 to break the Black Sector Line was necessary if White didn�t want to become enclosed, and that was the first key move in his strategy. It also enclosed both the Black corner stone and B2 in White�s own fairly distant Sector Lines. Most important, it was Sente because a following move at 4 would force Black into a low, nearly enclosed position in the upper right corner. So...
B4 Prevents White�s good play at this same point and breaks the White Sector Line, while
increasing Black�s space. But it�s Gote because it doesn�t establish a Sector Line of Black�s own. W5 Since Black has no enclosing move next, White is free to try to establish some eyespace, and this �slide� threatens to follow at 6 (the 3-3 point), to both steal the corner territory and provide the White stones with almost certain life. So it retains Sente. B6 Prevents White�s play on the key 3-3 point and so retains most of the corner territory. This assures Black of almost certain life, and equally important, keeps the White stones unsettled! But despite those wonderful assets it�s Gote, so White is again free to pursue his own objectives. W7 This is the second key move in White�s strategy, so it�s important that you thoroughly understand its rationale! What he intends to do is to counter Black�s strategy of negating the value of White�s center thickness below by building a compensating White moyo in the upper left! At least equally important, this stone prevents B2 from extending to the left to make eyespace, retains Sente by enclosing B2 in a White Sector Line, and also threatens to capture it by continuing with W�c�! (Pretty good for a single move!) B8 This is close to being the only logical response because B2 has no base, and attaching to W7 at �a� would only induce W�b�, B�c� to strengthen W7 in Sente and thus play into White�s moyo strategy. B�c� instead would not only be too slow in moving out into the center, but would also not threaten White in any substantive way. In sharp contrast, B8 breaks White�s Sector Line and establishes one of Black�s own which encloses W1-5, while also threatening to follow with B�d� to lock those White stones in. So B8 seizes Sente, and begins a classic running battle in which each side has a weak group in potential danger. Diagram 14 Becoming enclosed would force the White stones to either live small in Gote or die, so escaping is essential. This one point skip of W9 is the best way to do that, because it retains Sente by threatening to continue at 10, which would force Black into a low position on the right edge. B10 Prevents White�s good move at this same point and increases Black�s potential right side territory, while aiming toward making that territory really huge if he can further coordinate it with his strong lower right corner. But despite that it�s Gote because it makes no serious enclosure threat against the W1-9 group. (W9 already broke
what would have been Black�s new Sector Line.)
W11 Because the W9 group can�t be enclosed immediately, White can afford to use his Sente to play here because it encloses B2-8 within a new White Sector Line, while threatening to continue with W�a� to lock-in those two Black stones and almost certainly kill them. This is a fine double purpose move, because it also coordinates with White�s upper left corner stone, beginning to construct the large White moyo in that area White was aiming at when he played W7. B12 Black must break out of the new White Sector Line, and this is the best way to accomplish that because it in turn puts the W1-9 stones within Black�s own new Sector Line, and threatens to continue with B�b� to enclose him. So Black once again has Sente. W13 Even if White allows B�b�, after W�c� it would still be possible for his enclosed group to live, but that scenario would be bad for him. So he has no real choice but to skip out to break the Black Sector Line thus. Although W13 actually encloses the weak B2-12 group within a new White Sector Line, it�s one with a very distant (and therefore not very threatening) anchor point, so Black is really free to continue as he wishes.
Diagram 15 B�a� now to further expand his right side is both large and feasible, but then W14 will follow and that would be bad (although not disastrous) for the weak Black 3 stone string of one point skips! So instead ... B14 offers the weak Black string the most future alternatives, so it�s safest. But either B�c� or 15 is also feasible, with the choice between these options more a matter of the player�s judgment than of necessity. W15 was the key turning point in this part of the game! Unfortunately, it was somewhat overambitious, despite being the most consistent with White�s moyo strategy in playing W7 and 11. It mistakenly emphasized the creation of White�s potential upper left moyo over the safety of his weak stones on the right, and thereby violated the earlier noted key principle of: �Urgent Moves Before Big Moves�.
Instead, W�a�, �b� or 16 to strengthen his weak group were preferable alternatives, and, as with B14, the choice between them would be a matter of the player�s best judgment rather than of necessity.
Because W15 yielded Sente to Black in the running battle it was also the riskiest choice, although one it seems that White undertook willingly because he lusted after the big moyo he was trying to create on the left, and as an 8D he undoubtedly had absolute confidence that his tactical ability would suffice to rescue him from any resulting difficulties on the right. But even as strong a player as he would almost certainly have been better advised to play one of the other, safer choices noted above. B16 Because the Black string isn�t enclosed or even nearly so, Black is now free to be aggressive. Seizing the opportunity offered by White�s failure to reinforce the weak White group, this important play once again encloses those stones within Black�s Sector Lines, and forces a response. W17 Breaks the new Black Sector Line, but still leaves the White group within a more distant Black Sector Line anchored in the lower right corner, and that�s a measure of the size of White�s error in playing W15. B18 Reestablishes the more dangerous close Sector Line, and continues to force White�s response. W19 Not only breaks both of Black sector Lines, but also gives White access to some badly needed potential eyespace on the right edge. Equally important, it also threatens to play at 20 next, occupying the key pivot point in the corner. That would not only increase White�s own eyespace while reducing Black�s, but would also actually threaten the life of the Black corner because of its weaknesses at �d� and �e�. Because that would be too good to allow ... B20 This is now the key move, stabilizing the Black corner stones and destabilizing White�s, which are now no longer certain of making 2 eyes! What happened next to the weak White stones will not be shown because it�s entirely tactical and therefore outside the scope of our interest in the basic Sector Line/connectivity/enclosure themes we�re discussing. But it may be illuminating to note that despite 8D White�s exceptional tactical prowess he wasn�t able to make 2 eyes locally, and in the process of attempting to achieve life or break out of Black�s enclosure he overstepped the time limit and lost the game! A classic example of the difficulties that can follow from ignoring the indications provided by Sector Lines!
Chapter 7 Problems
Problem 1 In this position fairly early in a game between two 4D�s, the question is how Black can make best use of his Sente.
Problem 2 At this critical point in the early middle game of a 5 stone handicap game between a 7D (a really strong amateur) and one of the world�s top 9 Dan pros, a SWOT Analysis of this position shows that the focus of attention must be on the situation in the lower left center! There, both the White two point skip and the nearby Black one point skip are weak and potentially vulnerable. Almost equally important, because the Black Sector Line from the lower left corner stone to the Center Handicap stone intersects the White Sector Line from the side stone to the upper 2-point skip stone, neither is currently operative. Given those facts, with Sente where should Black play now? And why?
Problem 3 As earlier noted, our objective in this book is to help the reader determine the relevant theme(s) in any given position, rather than trying to find the absolutely best move. So in this position from a game between two 5D�s, your task is to identify Black�s most appropriate objective, and then suggest a plausible move to begin carrying it out. If you have the right plan and your suggested move plausibly advances it, your answer is counted as correct whether or not the move you chose was actually best.
Problem 4 Your first task here is to recognize what�s at issue, and then find the best way for White to succeed in fulfilling that objective.
Epilogue
Applying What You've Learned
If this book has successfully realized its design intent, a double digit Kyu reader who finishes it should have acquired a set of new ideas which provide a much improved understanding of how high level Go is played. That�s a necessary first step, but real, sustained improvement will only result when those ideas have been permanently embedded in your thinking processes, so that their application has become an automatic, almost instantaneous response, rather than requiring the conscious application of a mental checklist. To realize that goal, there is no adequate substitute for playing many, many games, getting practical experience in implementing those ideas in the face of determined and competent opposition. But that raises a serious problem for most beginners/intermediates, because they will typically be playing most of their games against �equal� or only somewhat stronger opposition. The difficulty this presents is that the caliber of those opponents is not likely to be sufficiently high to afford the opportunity to confront (and therefore learn to counter) the most incisive moves. The unfortunate consequence is that it will often be possible to get by and even prevail with inferior plays that the far stronger opponents you will encounter later in your Go career will almost certainly severely punish. And so, despite your best efforts, by playing against only equal or marginally stronger opponents you will almost necessarily be learning many �things that ain�t so�, which will therefore later have to be unlearned if you are to make the much desired advance to the higher skill levels. Fortunately, it�s relatively easy to transcend this important difficulty by watching/studying the games of professionals and amateurs who are strong enough to make few egregious errors. In earlier, less technically sophisticated times, being able to watch such strong players on any kind of consistent basis was impossible for any but the relatively few fortunate individuals who lived in communities in which there was a large local Go club with sufficiently strong members. But today, being able to do this is feasible for everyone, 24/7, through the advent of the internet! KGS And IGS are by far the largest internet Go communities in the world, and also the preferred home of many of the world�s top ranked professionals, a number of whom play there regularly, albeit mostly anonymously. For these reasons, they�re my preferred choice. But some of the ethnic Go servers (especially the Chinese and Korean) are perhaps even stronger, so for those for whom the language barrier isn�t a problem they form an excellent (or even superior) alternative. But watching the games of professionals or the very highest rated amateurs is IMHO not the best way to proceed, at least for the �average� double digit beginner/intermediate! The reason is that the highly refined technique and exquisite positional judgment of these ultra-strong players enables them to employ strategy that is often essentially incomprehensible to anyone not close to their own stratospheric skill level. So until you�ve reached at least low single digit Kyu rating you will be well advised to concentrate your watching on players in the 1d to 5d range, where the strategy employed will usually be more or less comprehensible to you, while the protagonists� technique will still be sufficiently well developed to minimize most egregious errors. But even that isn�t sufficient, because in order to really profit from your watching it must be an
active rather than a merely passive experience! What this means is that move-by-move you must mentally assume the role of each player in turn, evaluating the whole board situation, performing your own SWOT Analysis, and deciding on what you believe should be the best next move. Then as the player actually makes his move you must compare that with your own idea, and, in the many cases in which they differ, try to figure out why the move actually played was preferable to your own choice. Since this process of analyzing the differences will typically take much more time than is available between moves in real time, in order to be able to adequately conduct this kind of analysis, it will usually be necessary to save the game and then replay it later at your own pace. Although that may seem to be a lot of extra work, the payoff for going through this exercise on a regular basis can be immense! The ultimate result will be that, perhaps slowly and possibly quickly but in any event surely, you will begin noticing that your own move choices and those of the strong players you are watching will become identical more and more of the time, as your playing strength soars as well! If ever there was a �royal road� to Go mastery, this is it! And it�s fun as well - �the best of all possible worlds�. Enjoy! ~~~~~ Chapter 1 Solution 1
Solution 1A B1 to escape White�s enclosing move at this same point is absolutely essential. After this key play, the three corner Blacks are strong and the two White stones on the right are weak and threatened, so Black has Sente! Chapter 1 Solution 2
Solution 1B If Black allows W1 instead, all of the Whites are essentially safe, and it�s Black who�s potentially at risk.
Solution 2 Connecting with B�a� would not only be unnecessarily submissive, but overconcentrated as well! Instead, B2 not only indirectly defends the cutting point, is �light�, but also isolates and attacks W1. Not as strong, but still better than �a�, would be B�b�, which also attacks W1. And if Black isn�t particularly concerned with W1 but still desires to reinforce his group here while aiming at the upper Whites, then B �c� might be a good choice. Chapter 1 Solution 3
Chapter 1 Solution 4
Solution 4 W2 or �a� are the most common ways to build center thickness, and W�c� or �d� are sometimes preferable, all in accord with the principle stated earlier of avoiding contact. W�b� may be chosen when White is more interested in the lower left than the center. The appealing looking W�e� is actually a mistake because it�s too close to the Black stone! After the natural splitting response of B�f�, White will have two weak groups to manage, and will almost certainly end in trouble on one side or the other. Chapter 1 Solution 5
Solution 5 The key here is to recognize that, at least for the moment, the fight on the left side is over because both sides are stable, and the two isolated Black stones in the lower left aren�t big enough to warrant immediate action. That in turn means that White�s response to the marked Black stone must without fail be played elsewhere! (In this position, that means on the right side.) Of course it will make a major difference in the game whether or not that tenuki is played on the best point. But for the purposes of this chapter�s focus on when fighting is or is not appropriate, count your answer as correct if you recognized that a tenuki is called for!
Chapter 1 Solution 6
Solution 6A B1 here is bad on three major counts: - It garners no profit. - It makes no threat (so it�s pure Gote!) - It produces bad shape empty triangles at both �a� and �b�.
Solution 6B This way of playing is feasible, but inferior because it produces one point less for Black than the preferred (game) solution of 6E. Note that W4 is essential, because of the defect at �a�. If it�s omitted, ...
Solution 6C If W4 is omitted, the pitch of B5 on that same point will capture 5 Whites! If W6 captures, after the atari of B7 if W8 connects then B�a� will capture 11 Whites! So W8 must connect at �a� and allow B9 to replay at 5 to capture 6 Whites.
Solution 6D This B1 is best, and this diagram shows that it absolutely prevents an immediate cut with W2 because after the atari of B3, connecting with W4 would allow B5 to produce a snapback that captures 7 Whites. So ...
Solution 6E After the atari on the marked stone of B1, White saved this stone with the simple connection of W2. This forced B3 to connect, and although this produced an empty triangle, it was acceptable because it retained Sente by forcing W4 to prevent Black�s pitch and following capture as in Solution 6C.
Chapter 1 Solution 7 Solution 7 B�a� is feasible but would be painfully slow. Instead, the one point skip to B1 is tesuji. After that, if W�a�, B�b�, W�c� captures, then the simple B�d� easily gets Black out. So what actually happened was W2 as shown. Then after B3, W4 occupied Black�s shape point, keeping the fleeing Black group as weak as possible under the circumstances.
This was fine play by both sides, as would be expected from players at their relatively high level. Chapter 1 Solution 8 Solution 8A If White begins by playing on Black�s key inside shape point with W1, this shows one plausible continuation. But after B8, although White has gouged out most of the territory from Black�s underbelly, Black is quite safely led out into the center, and what might have been White�s thickness in the center, with which he hoped to compensate for the two big Black corners above and below, has been effectively negated. So playing this way would be very inferior for White. Solution 8B From the principles enumerated earlier we know that as things stand this still unenclosed group can�t simply be killed, so if White desires to attack it his only sensible option is to begin by trying to confine it from the outside. So White correctly began his attack from the outside with the capping move of W1. B2 is the best way for Black to try to expand his space, and after the expected hane of W3 and draw back of B4, W5 is necessary to prevent Black�s strong �outside hane� at this same point. When B6 cuts, W7 is necessary to prevent Black�s atari on W1 at this same point. And then Black has a big decision to make!
If Black now plays at 9 to make shape, W8 will assure the capture of B6 and connect White, while providing him with the powerful thickness he sought. ` That was unappealing to Black, so with B8 he chose to keep White separated. But in return, now that Black is enclosed, it does make sense for W9 to occupy Black�s key shape point! Whether or not Black can live after this will be a function of the respective fighting skills of the opponents. Given that Black allowed W9 it�s reasonable to assume that a player as strong as the 5D who contested this game correctly pre-calculated his chances in that regard, and in the end he did in fact live here. (Although the result of that local fight was obviously critically important to the game�s outcome, from our present perspective it�s a �detail� which lies outside our concern with the proper way to play in such situations, so we won�t go into it further.)
Chapter 2 Solution 1
Solution 1 Assessments a: Unimportant, although live, and takes a small corner territory, because it�s enclosed and therefore can�t influence subsequent play. b: Very important when formed, because the wall projected its influence over the entire upper middle of the board Much less important now that the Black �d� stones have been played specifically to negate that influence. c: Somewhat important because they prevent the �d� stones from making a base on the edge, but not very important because those same Black �d� stones effectively cut them off from the center. d: Vitally Important! These stones prevent White from making a massive, winning territory between his two powerful (b and J) walls on either side! e: Important because it helps capture W�f�, and thereby unites the B�g� and �h� units. f: Important, as just noted. g: Moderately important because they reach out toward the center and therefore potentially aid the vital but still unsettled B�d� stones. h: Moderately important because they will almost certainly connect to the B �t� stones below to secure a large Black territory on the edge. i: Almost worthless! If capturing this stone was the only way that Black could connect his �g� and �h� stones, it would be at least moderately important. But given that Black can also connect by capturing W�f� (which is already in atari!), the importance of W�I� sinks to just the 2 points that its capture would bring. j: Fairly important, because they form a thick, powerful wall which casts its influence over the entire upper left middle! But not really important because that influence is already partially negated by the Black �d� group.
k: Valuable because it takes the corner territory, but unimportant because it�s enclosed and therefore can�t influence subsequent play!
l: Potentially important, because the possibility exists that this stone can be used to seal off the left side and then also capture B�m� to form a large White territory there. m: Quite Important because the fate of this stone will probably determine whether or not White can make a big territory in this area. n: Moderately important, partially because of the potential noted above, but mainly because of its potential for preventing Black from making a very large territory in the lower center. o: Moderately Important because they coordinate well with the B �q� stones to form a nice territory in the lower left, with a threat to make more just above. p: Unimportant because this stone is effectively captured. (But its presence paid off for White earlier, because the threat to connect it out allowed the W�n� stones to secure their eyespace.) q: Moderately important because of their coordination with the B�o�group and the territory that provides, as well as the fact that they help seal off the W�s� stones from the center. r: Unimportant. This was a Kikashi to induce White to connect. Once that was accomplished, it�s now worth only the 2 points its capture would bring the opponent. s: Moderately important because they have some center access, so that they may be able to participate in later action there. t: Moderately important because the large territory they enclose in conjunction with the B�h� stones may induce a White invasion, with subsequent fighting there. They will also almost certainly play a role in any later center fighting. Chapter 2 Solution 2 Solution 2 Assessments a: Important because they control the corner and have expansion potential along the upper side, and together with the �c� stones trap (and effectively capture) B�b�. b: Marginally Important, because if it can escape that would neutralize the large White edge territory around it. c: Important because together with the �a� stones they not only trap B�b� to take a large territory, but also project influence toward the open upper middle of the board. d: Important because together with the �f� and �g� stones they trap (and effectively capture) the two W�e� stones, to both assure life and take a modestly large territory. Equally significant, they�re not enclosed and can therefore influence subsequent play nearby. e: Important because their demise will ensure the connectivity and safety of the B�d� and �f� stones, to yield a large Black territory. But that�s not yet certain,
so this situation will have to be watched closely until it�s definitively resolved. f: Important because they are not only essential to the capture of the W�e� stones, but the weak link in that process. They also make an essential contribution to the W�h�, B�I� potential Seki below. g: Important primarily because of their impact on both the fight against the B �d� stones and the W�h�, B�I� Seki to their right. h: Important because of the very large number of points the difference between their life or death represents. At the moment they�re embedded in a Ko fight with the Black �h� stones which will probably result in Seki when the Ko is filled, but (although unlikely) that might conceivably change before the game�s end. i: Important. Similar to the �h� stones because of the fight involving both. j: Quite Important, because the Ko it�s involved in will determine whether or not the fight between the W�h� and B�j� groups becomes Seki. k: Overwhelmingly Important. If this group should die the Seki to its left would collapse and then the W �h� stones would die as well, leading to White�s instant resignation. l: Unimportant, except for the fact that its capture provides the W�k� group with its lone eye. m: Vitally Important. Similar to the W �k� stones, but without an eye. n: Quite Important. This group is crucial to both the Seki below (because of its impact on the B�m� group), and the W �e� fight. o: Very Important, because in conjunction with the other nearby Black stones it helps contain the crucially important W�k� group. p: Important, primarily because of their effect in trying to enclose the W�k� stones. q: Important, primarily because of the potential aid they may offer to the escape of the W �k� stones. r: Intrinsically Important because as the lone 4-4 point stone in a corner, this stone�s territorial and influence possibilities are at present almost unlimited. But the current focus of this game must be the key fight now underway on the lower side, so the realization of any potential here must wait until that urgent issue is resolved. Chapter 2 Solution 3
There�s no time now to protect the cutting point at �a�, nor is there time to make the excellent splitting placement of W�b� on the right side, because either would allow B�c� to attack the still baseless 3 White stones in the lower left. The urgent play is for White to immediately stabilize those 3 weak stones by providing them with a base via the two point third line skip of W1, even though that allows the strategically big B2 on the right side, with global advantage to Black.
Chapter 2 Solution 4 Solution 4A By trying to hang onto W1 with this W5, White would make the serious error of allowing B6 to enclose him, thus forcing him to try to live in the corner! But that would lead to this easy to read out in advance sequence, in which White can�t make 2 eyes, and so is dead! (If W7 at 8, B8 at 7,
Solution 4B By playing this W5 to run away on the outside, White abandoned W1 as having served its purpose of forcing Black�s response, allowing Black to secure the corner. Then, in this sequence (there are feasible alternatives which lead to similar but somewhat different results), White succeeded in his real purpose of gouging out and �stealing� much of what otherwise would have been a
and White is still dead!)
very large Black territory.
Instead ... Chapter 3 Solution 1 Solution 1 The marked 10-stone Black group as yet has neither eyespace or shape, and that�s a serious detriment. But it�s offset by the fact that Black has the lower left corner, a live (twoeyed) group in the lower right, and unopposed stones in both of the upper corners. White has safe groups in the lower left and lower right corner, while his center group is strong (if not yet absolutely safe) because of the 3 trapped Blacks. On balance, if Black can save this large weak group without suffering too much damage to his positions above, both side�s overall chances are about equal.
Chapter 3 Solution 2
This situation is a complex fight in which each side has 2 unsettled groups. In such cases, even a minor slip by either side can lead to disaster, so extreme caution is required. The status of each group is as follows: a: The lone Black stone on the upper left 4-4 point is strong. b: This live Black group is very strong. c: This live White group is very strong. d: This live Black group is very strong. e: This large White group is marginally weak. It is sure of only 1 eye on the edge, but as things stand can either connect to the �c� stones or escape. But that connection/escape is not yet certain, and therefore must be watched carefully as the game progresses! f: This Black group is marginally strong. It can almost certainly make at least one eye, and has free center access at the moment. g: This White group is weak! It has no sure eye, no real shape as yet, and only center access to provide viability. h: This Black group is also intrinsically weak, but a bit stronger than the W�g� stones because its shape is better and it already is further out into the center. i: This White group is strong because it�s almost certain to be able to make 2 eyes in the corner.
Chapter 3 Solution 3 Black�s thickness is imperfect because W �a� to cut him apart might (in some global positions) be feasible. But even if that isn�t true, there still remains the annoying and potentially dangerous peeps at �b� or �c� to worry about. And in the current position �d� is also open, so a later W�e� at the right time (with potential to connect underneath) will reduce the value of this Black formation by a major amount. So the unavoidable conclusion is that as things stand Black�s thickness here is at best incomplete, and these Black stones are not strong! Chapter 3 Solution 4
W1 is the best way to make shape. Then if later B�a� with atari, W�b� traps that stone and makes the needed second eye. W�c� instead of W1 seems superficially equivalent, but although it�s exactly the same as the correct W1 insofar as assuring the life of the White group is concerned, the correct W1 has the potential followup of W�d�, while W�c� has no such followup potential because after the White group becomes safe the 6 Blacks to their left are just unequivocally dead!
Chapter 3 Solution 5
Solution 5A W1 on Black�s key shape point is intrinsically OK, provided that it�s followed up correctly! Solution 5B After W1, B2 will make a Bamboo joint to strengthen his weak stones while threatening to connect at 3.
But if W3 is then played to prevent that connection, the simple B4 traps the 2 Whites to connect Black after all, making his stones strong! Solution 5C After B2, instead of futilely cutting with W�a� to produce the bad result of Solution 5B, depending on the nearby and global position White will be much better advised to run away at either �b� or �c� if he intends to fight, or to simply tenuki and leave W1 behind temporarily as having fulfilled its purpose, until such time as it becomes clear that utilizing it further will help him more than Black. Chapter 3 Solution 6 B1 is the best way to proceed, because of the threat it makes to atari next at 2. W2, B3 and W4 are then forced, after which Black has 5 liberties and is technically �contact stable�. But here that�s not adequate, because if Black tenukis, the turn of W5 will be too good for White to allow. So B5 is necessary, yielding 6 liberties. And because a following B6 would be bad for White, W6 is equally necessary. So Black retains Sente, allowing him to safely tenuki if he desires.
Chapter 4 Solution 1 Solution 1A Cutting would be a major mistake that would only increase Black�s thickness, because the cutting stones would be easily caught in Geta as shown.
Solution 1B Correct is for W1 to peep into Black�s cutting point, forcing B2 to connect. After this, W1 may later turn out to be a useful aid to any weak White group below, while B2 has only trivially added to an already strong Black formation. In some situations, it�s best to leave the decision to cut or peep for later when circumstances might make it clearer which course of action is preferable. But in the game in which this position arose, as is frequently true, getting W1 on the board in Sente immediately was highly desirable. Chapter 4 Solution 2
Solution 2A The cut is clearly infeasible, because W2 easily captures. Solution 2B This peep is inferior, because after W2 connects White has good shape, while B1 has only 3 liberties and no good followup. Solution 2C This is the best peep, because when W2 connects B1is not only on White�s shape point but also still has all 4 of its liberties, and this can make the difference between winning and losing any later fight involving this Black stone. Of course if White should mistakenly answer at �a� instead of 2, then B�b� is available as a big Ko threat to force W2 after all, and that�s worse for White than this diagram. If W�b� in response to B1 it may be feasible and/or best to simply tenuki, leaving B1 behind as Aji, or it may be productive to reinforce it. But in any event, it was still ideally placed. Chapter 4 Solution 3 Solution 3A Peeping with B1 here or at �a� would be simply awful for Black, because the connected White stones are then very strong, while B1 becomes an almost worthless stone plastered against a strong opposing formation. Such moves mainly help the opponent, and so are called �thank you� moves! Solution 3B Correct is to cut with B1, provided Black has assessed that it will have good prospects in any resulting fight! W2 or W �a� to follow is almost mandatory, but in either case White is separated. What will develop next will depend on other nearby stones of both colors, the full board position, the strength of the players, and their strategy.
Chapter 4 Solution 4
Solution 4A The threat of the cut of W1 here is extremely dangerous for Black, and cannot be permitted! If this cut is allowed, after the sequence thru W7 Black�s entire position here would be in serious trouble! So ...
Solution 4B Black must play immediately to prevent that dangerous cut!. The solid connection of B�a� obviously works, but is inferior not only because it doesn�t extend Black�s position, but because it also lacks eyeshape. And making a �Tiger�s Mouth� at either �b� or �c� is also not best because it would only serve to induce a White peep on the complementary point, with (slight) advantage to White. So B1 here is the ideal answer, both extending and defending. After this, if W�a� cuts, B�b� will capture the cutting stone. Chapter 4 Solution 5 Solution 5A Beginning with the push of W1 is correct! The only conceivable response is the block of B2, but that leaves Black with the two dangerous cutting points at �a� and �b!
Solution 5B In the game from which this position was taken White�s choice (based on the global position) was to cut with W3 at �a�. If Black then gives atari to W3 via B7, that would allow the counter atari of W6, followed by losing the corner to White. So Black played B6, allowing W7 as shown. Then with the second cut of W11 followed by the sequence thru W19, White makes a nice profit, while Black
has to go back to secure his life in the corner with B20 while leaving his 7 outside stones with bad shape and uncertain prospects. So White stands much the better here. Chapter 4 Solution 6 Solution 6 A There are twin cutting points on the second line available for Black to exploit. If B1 here, then the atari of W2 on the outside is to be expected. After the counter atari of B3, the capture of the sacrifice B1 by W4 is natural and necessary. Then B5 virtually assures the capture of the two marked Whites. After that, with the sequence thru W10 the bulk of White�s force is essentially safe because White not only has free access to the open center, but �a� or �b� are miai to secure two eyes.
Solution 6 B Since that variation takes profit but doesn�t apply much pressure to White, Black will undoubtedly prefer to cut on the other side with this B1 instead.>br> Next, if W2 here, the atari of B3 is to be expected if Black has enough favorable Aji elsewhere on the board. Then W4 will induce the capture of B5 to create a big Ko.
Solution 6 C But White need not become involved in that Ko fight if he prefers not to! Instead, with the sequence thru W8 shown here, he can move smoothly out into the open center with good shape, with the miai of �a� and �b� left behind to assure his connectivity to W2 and 4. And if and when the connection of W�a� gets played, B�c� will be necessary to assure that the two marked Whites remain Black�s captives. On balance, this would seem to be the preferred way for White to play, but...
Solution 6 D In the actual game in which this position arose, White followed this variation instead, opting for the profit his live group took, and leaving for later the problem of what to do with his now classically weak 3 stone string after B9 capped it! Although B9 was both big and very threatening, the likely outcome of the center fight that will follow if White plays to save the 3 stones isn�t clear, so it�s hard to accurately evaluate which alternative Solution would ultimately have been globally best for both sides.
Chapter 4 Solution 7 Solution 7 W48 was a Ladder Breaker! Consequently, preventing the cut of W �a� became absolutely essential, and B1 is a much safer way to do that than via a Geta move, and much better shape than a hard connection! And it�s not Gote, because once B1 makes Black safely connected and strong, the White corner is vulnerable! Then if Black is allowed to continue with B2, W�b�, B�c�, the corner is dead! So White must defend immediately. White could expand his corner slightly via W�c�, B�d�, W2, but although that would nominally be Sente it was nevertheless unpalatable because B�d� would then have undercut the not too strong White formation to its right. So White instead prudently chose to live in the corner in Gote via W2.
Chapter 5 Solution 1
Solution 1 The key Sector Lines for White are shown above, those for Black below.
Chapter 5 Solution 2 Solution 2 The two main Sector Lines of interest here are those shown above the weak 3 stone Black group in the lower center, and both are White�s. The longer Sector Line encloses much more territory, of course, but its upper anchor point stone is so distant from the target Black group that if it were the only Sector Line operative here Black could safely ignore it for the moment, if that was globally appropriate. But the shorter White Sector Line�s right anchor stone is close enough that Black must pay attention!
Chapter 5 Solution 3
Solution 3 Black�s one point skip with the marked stone is the necessary play, breaking both of the White Sector Lines and getting the Black group safely out into the open board center. If it was White�s turn, the very same key point is also correct for him, and in this position, given the thickness of the White formation anchoring the left end of the White Sector Lines, that would put the 3 Black stones in considerable trouble!
Chapter 5 Solution 4 Solution 4 Black has three territories, but nothing even vaguely resembling a moyo, so the only significant operative Sector Lines are White�s. As shown, it�s quite apparent that, especially in the left center area, they�re very long and quite porous, with Black stones to support any invasion very near. Based on those facts, plus the observation that the lower left corner is still wide open, an invasion rather than a reduction clearly seems appropriate. Invading on the 3-3 point in the corner would be absolutely safe, but would almost certainly leave Black confined there and White thick outside, with a result that would be too good for White. So Black reasoned that he would almost certainly be better served by instead invading on the lower left side with a Knight�s move Kakari against the White 4-4 stone. After that, the resulting fight could develop in many different ways, with details far outside our present interest, so we won�t go into those various possibilities.
The key idea that the reader should bring away from this discussion is that the information provided by Sector Line analysis is valid, and the resulting decision to invade that it suggested is generally correct, even if you don�t choose the very best invasion point! And that judgment isn�t substantively changed by the fact that Black�s invasion ultimately does or does not succeed. The overall lesson that this conveys is that the application of Sector Lines is highly useful in making the correct strategic decisions is necessary for success in Go, but it is by no means foolproof! Accurate tactical followup is the other essential ingredient for success, and, as we�ve earlier noted in the Introduction, that vital skill can only be developed over time with much study, and then honed to perfection via extensive play against competent opposition. Since all of that is beyond the scope of this book, it is therefore left to your independent study. Chapter 5 Solution 5 Solution 5 B1 is the key play! Although the White corner stones were already within Black�s Sector Line, with W1 (or �a�, �b�, or �c�) White could easily have cut that Sector Line and thus put the baseless (= weak) Black 7- stone group on the left in danger. Instead, the simple B1 completely encloses the White corner stones within essentially unbreakable Black Sector Lines, so with still incomplete eyeshape White must do something about that immediately or die! The key White shape point in the corner is �d�, and a weak player would be well advised to play there immediately to assure White�s eyes.
But 5D White has calculated that after W2 he can still live even if Black plays at �d�. (You might want to experiment with this position and prove this for yourself.) White also recognizes that the Black group to the right isn�t yet completely settled, and that the territory at the top isn�t yet sealed off either. This combination of assets means that W2 with its aggressive potential is considerably better than the purely defensive �d�, so that�s what White played! For its part, B1 does far more than merely enclose the White corner, important as that is. By preventing W1 (or W�a�. �b�, or �c�), B1 strengthens his own eyeless 7 stone group on the left so that there isn�t an immediate need to support it - and that gives Black Sente to play a big point elsewhere after the necessary W2 defends in the corner. On the other hand, if Black were to neglect to play at 1, a White play there would happily seize Sente by splitting Black, and thus completely reverse the flow of this game! Although B1 superficially seems innocuous and slow and is the type of (actually essential) play that can
easily be missed by the novice, it�s also a move whose need and power are readily revealed by application of the Sector Line concept! Chapter 5 Solution 6 Solution 6 Var 1 By now you should already know that if White is to escape from Black�s enclosure his first move must break the enclosing Black Sector Line! In this position the one point skip to W1 is the key play, not only breaking the Black Sector Line but also establishing one of White�s own that encloses the 2 Blacks. But this B2 in response is far too ambitious! After the sequence thru W7 it�s clear that the 3 Black stones will be captured, and with that White�s four stones will have escaped, with at least one sure eye. So instead ...
Solution 6 Var 2 The atari of B2 here is forced. The connection of W3 is then necessary, forcing the capture of one White via B4 to save the 3 Blacks. Then W5 completes White�s escape with a good shape �Bamboo Joint�.
Chapter 5 Solution 7
Solution 7 White has one long Sector Line here, and by playing to just break it (a reduction, rather than an invasion), Black satisfied both of his objectives as well as possible in this position. And although it�s not known whether either of these players explicitly used Sector Lines in deciding upon their moves, it�s apparent that B39 was played precisely as though they had! More important, I�m betting that you, the reader, although perhaps little more than a beginning player, was also able to find this exact move or one very near it, just by applying the simple yet powerful Sector Line concept!
Chapter 6 Solution 1 The SWOT Analysis of this position is as follows: Black: Strengths: - The Black upper left corner is not fully enclosed, and can easily make 2 eyes if needed. (Although B53 might be ataried and captured by White, doing that would be Gote and wouldn�t affect the main Black group�s viability, so it�s not important enough to be played any time soon.) - The B3-45 lower right side/corner can almost certainly make 2 eyes if needed, although all of the territory there isn�t Black�s yet because it�s still quite open to a White invasion. - B25 can either connect to the strong Black group above or to the one on the right, so it�s safe for now. - The B5-49 group has good shape,
easy center access and some territorial potential, so it, too, is safe for now. - B1, B51 are in the corner, with no nearby opposing stones. - B27 has good relationship to B1, B51, plus room to extend on either side or jump to the center if needed.
Weaknesses: - No real weaknesses! Opportunities: - Attack the still unsettled White center group from the right, in order to build moyo/make territory on the right side. - Expand/consolidate the B1,27,51 area. - Extend on the third line to the left from B27. - Enclose some territory in the lower left center. Threats: - Black: - A White invasion is feasible in both the upper and lower right corners. - The B5-49 group is still unsettled. Settled Territory: - Perhaps 10 points in the upper left corner + 10 points in the lower right. Total = 20 points. Territorial Potential: - Another move in the upper right corner will nail down at least 15-20 points immediately, with prospects of still more to follow when White tries to prevent Black�s further expansion. - A move near the star point on the right side should bring substantial profit either above or below. - White: Strengths - The W2-54 group is very thick and has good shape. - The W4-32 lower left corner is almost absolutely secure. Weaknesses - The 11 stone W28-50 center group has only rudimentary shape and is only open above and to the right, although it technically isn�t enclosed within Black Sector Lines. Opportunities - Invade between B1 and 27. - Invade the right side and use the center group to hopefully make a significant White territory in that area. (Dangerous!) - Try to build moyo in the lower right center, using the W28-50 group. - Create a moyo by extending from the upper left group to its right. - Expand into the open area in the left middle, making some White territory there while minimizing Black�s. Threats - The big lower right center group has no eyes and is less than solidly thick, so it needs the most careful watching! - The W2-54 group�s thickness might be neutralized without adequate compensation.
Settled Territory - About 15 points in the lower left corner + about 3 points in the upper left. Total = 18 points. Territorial Potential - Extending from the upper left group could net about 15 points. - Making proper use of the center stones to invade the right side should net some profit, but at the moment it�s hard to estimate how much. The main focus of play now will be on White�s twin major detriments: - The big weak W30-50 lower right center group. Black will at least harass these weak stones and attempt to kill them if possible (highly unlikely, as things now stand), or use that attack to either make territory elsewhere (especially on the right side) and/or prevent White from so doing. - White is far behind in settled territory, and must redress that balance before it�s too late! Chapter 6 Solution 2 The SWOT Analysis of this position is as follows: Black: Strengths: - Three almost certainly secure groups in the upper left, upper right, and lower right. - In the lower left there are only Black stones thus far, but that�s only a minimal advantage because that area is still so open. Weaknesses: - The three B39, 45 stones are almost certainly �captured�. - Although the three B11 - 21 stones have excellent shape and center access, they are still unsettled. - The three B25-51 stones are also somewhat weak, and that�s compounded by their proximity to the B11-21 stones. This gives White the potential for driving them toward each other, and then setting up a potentially devastating splitting attack. Opportunities: - Black�s only really significant attack potential exists against the W30 - 52 group. - There is also some limited potential for an attack against the W10 - 22 upper right stones, whose shape is still incomplete. - There is a significant territorial potential on the left side, where there are only Black stones at the moment. Threats: - The 3 B25 -51 stones are still insecure.
- So are the 3 B11 -21 stones, albeit to a somewhat lesser degree.
Settled Territory: Strictly speaking, none as yet although at least some will almost certainly be realized from each of the first 4 items below. Territorial Potential: - Less than 10 points in the upper right corner. - About the same in the upper left corner. - A bit more in the lower right corner. - Possibly 10 or so points in the lower left. - A presently unquantifiable amount on the left side, which will depend on who is first to play there, and where. White: Strengths: - The big lower right group on the edge is secure and stable because of the 3 �captured� Blacks. - The upper left corner formation has excellent shape and space. - Although the six W10-22 upper right stones have incomplete shape, at the moment they�re relatively strong because the 3 Blacks immediately below are somewhat weaker. Weaknesses: - The 5 W30 - 52 stones are solidly connected and have a high liberty count (6), but no shape or eyespace, only limited center access, and are already enclosed within Black Sector Lines! But White has Sente, can lean on B53 to make Sabaki if needed, and has the at least equally weak B25-51 stones to fight with, these stones aren�t in any immediate danger. Opportunities: - The potential exists for: - an attack on: - the B11 - 21 stones - the B25 - 51 stones - An invasion in the left bottom. - Most of the lower left side is still virgin territory. Threats: - The 5-stone W30 - 52 string is in grave danger of being enclosed, with little eyemaking potential! - The W10 - 22 upper right group still has very incomplete shape. Settled Territory: - About 10+ points on the lower right side. Territorial Potential: - A possible 10 or so points on the upper right side. - Perhaps 10 points on the upper left edge. - Perhaps 10+ points in the lower left corner. The main focus of play now: Both side�s major weaknesses are in the same area - the interface between the W30 - 52 group and the B 25 -51 group on the lower side, so that must be the immediate focus of play! That situation involving two weak groups is necessarily quite tactically oriented, albeit with a
strong strategic component. And those tactics must necessarily dominate at least until the fate of the opposing weak groups is established, it�s not feasible at this early stage of the fight to lay out a definitive plan for how to proceed after it�s been resolved. But once the fate of those opposing groups of stones is better defined, a new SWOT analysis will not only be necessary but will then also be able to better specify the path the game should take from that point on! In that, the possibility for aa splitting attack against the two weak Black groups mentioned earlier may well become significant. Chapter 6 Solution 3 Solution 3 Your SWOT analysis should have indicated that Black�s lower side moyo was not only the largest structure on the board but also the one nearest completion. So your inescapable conclusion should have been that White�s immediate action to reduce it was essential! If that was your conclusion, consider your answer correct even if you didn�t find the specific starting point or sequence shown, which is more or less �standard� in similar (and not infrequently occurring) positions. Chapter 7 Solution 1 Solution 1 Capping the weak White one point center skip with B1 is the most forcing way to play here, but certainly not the only conceivable one! One plausible alternative is to begin with the jump to B�a� to strengthen Black�s corner below while threatening to enclose the White stones. But that will almost certainly induce the response of W1, to which B�c� will then be an essentially forced reply, leaving White with Sente. It�s also not inconceivable to play elsewhere, especially the right side, but B1 gives Black control of at least the next few moves of the game, and therefore on balance will be the most satisfying to an aggressive player.
Chapter 7 Solution 2
Solution 2 The key point for both sides here is clearly at �a�. If B�a�, the two Black one point skip stones are led out into the open center, and are then quite secure because they should be easily able to connect above or to the right. Almost equally important, after B�a� Black threatens to continue with B�b� to induce W�c�, then follow at either �d�, �e� or even �f� to initiate a serious attack on the baseless White group. So the defensive W�d� would most likely follow, leaving Black with Sente to use as he sees fit because White would then have no really serious local attack available.
But if Black should mistakenly play elsewhere, the cap of W�a� would completely reverse the local dynamic by leaving the two Black stones almost enclosed within White Sector Lines, and in serious difficulties! So if Black wishes to keep things simple, as he should when taking 5 stones, there really is no sensible alternative available to B�a�! But, surprisingly, that�s not what Black actually played, and by allowing the dangerous and unnecessary fight that followed W �a�, unquestionably hastened his demise in this game.
Chapter 7 Solution 3
Solution 3 For our present purposes, count your answer as correct if you recognized that an attack intended to keep White�s weak stones in the left center from connecting to his strong upper side stones was called for, and you suggested a move near the actual game�s B1 as shown.
Chapter 7 Solution 4 Solution 4 White�s objective here must be to prevent Black from easily saving his weak group to the left by connecting his forces. W�a� would also do that successfully, but W1 is superior because it also looks forward to saving the marked stone, and thus making it difficult for the upper Black group to make its needed second eye!
~~~~~ Glossary Of Japanese Go Terms
AJI (ah�-gee): Potentially exploitable threats remaining in a position. AJI KESHI (ah�-gee keshi): A bad move which needlessly neutralizes the potentially exploitable weaknesses in the opponent�s position. ATE (ah�-tay): A move that gives atari. ATARI (ah-tah'-ree): A condition in which one or more units has been reduced to only a single liberty, and is therefore subject to capture on the opponent's next play. ATSUMI (atsumi): Thickness. BOSHI (bo-shee): �Cap�. Usually, a one point skip above an opposing stone. DAME (dah'-may): A neutral liberty shared by safe White and Black groups. Does not count as a point for either side. DAN (dahn): "Step". The designation of playing strength for those of master level. Ranges from 1-Dan to 9-Dan, but professional ranks are separate and much stronger. DANGO (dan-go): �Dumpling� = A shapeless mass of stones with little eyemaking potential. DE (day): A move which pushes between two opposing stones. FUSEKI (fuh-say'-key): The full board Opening. GETA (gay-tah): A trap or snare which can effectively capture opposing stones even when they still have several liberties. GO (goh): The name of the game. (Called Wei Ch�i in Chinese, and Baduk in Korean.) GOTE (goh-tay'): The converse of Sente. A move which makes no significant threat, and which therefore doesn't require an immediate response by the opponent. GOTE NO SENTE (goh-tay no sen-tay): A Gote move which contains (often hidden) aggressive potential. HANE (hah'-nay): A Diagonal attachment against an opposing stone. HASAMI (hah-sah�-mee): A pincer. HIKI (hee�-kee): �Draw back�. HORIKOMI (hori-koh�-mee): A �throw-in� sacrifice which kills an eye and/or whose capture reduces the opponent�s liberty count. JOSEKI (joh-say'-key): An analyzed sequence of plays which theoretically leads to a dynamically equal local result for both sides. KAKARI (ka-kah�-ree): An approach move against a corner stone to prevent a Shimari. KATA (kah�-tah): �Shoulder�. The point diagonally above a stone. KATACHI (kah-tah�-chee): �Shape�. Usually, good shape. KATATSUGI (kah�-tah-tsoo�-gi): The solid connection. KATATSUKI (kah�-tah-tsoo�-kee): A shoulder attack. KEIMA (kay-mah): The �Knight�s Move�. KESHI (keshi): "Reduction�, or "minimization�. When played to reduce an opponent's Moyo (Sphere of Influence), Keshi consists of "light" moves, not too deep within the area of the opponent's strength. KIKASHI (ki-kah'-shee): A forcing move which must be answered, and which therefore necessarily retains Sente, but which is incidental to the main flow of play. Such stones are typically abandoned after they have served their purpose of forcing the opponent's response, serving only as Aji thereafter. KIRI (kiri): �Cut�. KO (koh): "Eternity". An important, oft recurring tactical situation in which a single stone is captured and THE NO REPETITION RULE applies. KOMI (koh'-mee): The points added to White's final score in �even� (no handicap) games to compensate for Black's first move advantage. KOSUMI (ko-suh�-mee): The diagonal extension.
KYU (kyu): Rank. The designator of playing strength for players of less than Dan (master) strength. For amateurs, ranges from 35 Kyu (beginner) to 1 Kyu (just below master strength) MIAI (mee-iy): Two complementary points of approximately equal importance in a given situation, such that whichever one a player occupies, the opponent can (and usually must) occupy the other. MOYO (moh-yoh): A large Sphere Of Influence or Potential Territory. NAKADE (nah-kah-day): The placement of stones inside an opposing group to reduce the shape to one eye. NADARE (nah-dah�-ray): The �Avalanche� Joseki. NIDAN (nee�-dahn): �Two Step�. NI-REN-SEI (Nee-Ren-Say): A Fuseki pattern in which a player occupies both 4-4 points on a single side. NOBI (noh�-bee): Extend. NOZOKI (noh-zoh�-kee): A peep which threatens to cut. NUKI (nookee): A capture. ONADARE (oh�-nah-dah�-ray): The �Large Avalanche� Joseki. OKI (oh-kee): A placement, usually intended to steal eyes. OSAE (oh�-sah-ay): A blocking move. OSHI (oh�-shee): �Push�. Usually along a line atop (or alongside) an opponent�s stone or line of stones. PONNUKI (pon-nuh�-kee): A powerful shape created when 4 stones capture a single opposing stone. SABAKI (Sah-bah'-kee): "Disposal". Light resilient shape which allows a group to be easily settled, or to be partly or totally sacrificed if necessary without significant penalty. SAN-REN-SEI (San-Ren-Say): A Fuseki pattern in which a player occupies all 3 handicap points on one side. SEMEAI (semi-eye): A life-or-death fight (= race to capture). SENTE (Sen'-tay): The initiative. A move central to the major strategic and/or tactical motifs of the game, which therefore requires the opponent's response, and which cannot be ignored without significant penalty! Such stones typically have long term implications, and must therefore be watched and defended. The converse of Gote. Closely related to Kikashi. SHICHO (shih'-cho): The Ladder. SHIMARI (shih-mah'-ree): A Corner Enclosure. SHINOGI (shih-noh�-gee): A sequence of moves to provide a weak group with either escape or good eyemaking shape. SUBERI (soo-beh�-ree): �Slide�. A Knight�s Move toward the edge, usually from the third line to the second line. SUJI (soo'-gee): "Style" or "skillfulness". Clever, artistic play. See Tesuji. TAISHA (tie-sha): The �Great Slant� Joseki. TENUKI (teh-nuh�-kee). �Play elsewhere�. TESUJI (teh-soo'-gee): A Suji which raises the overall efficiency of the player's local (and sometimes global) stones to their highest possible level. TOBI (tobi): A jump (= skip). TSUGI (tsu�-gi): A connection. TSUKE (tsu�-kay): An attachment to an opposing stone. TSUME (tsu�-may): An extension which inhibits the opponent�s extension. TSUME GO (tsoo�-may GO): A life-or-death problem. UCHIKOMI (oo�-chee-ko-mi): An invasion. WARIKOMI (wah�-rih-koh�-mee): A placement between two opposing stones intended to
set up cutting points. WARIUCHI (wah�-rih-oo�-chee): A wedge (placement) which has room to expand on both sides. WATARI (wah-tah�-ree): A connection at board edge. YOSE (yoh'-say): The Endgame. YOSU-MI (yoh�-suh mih�), formerly Yosu-miru : �Wait And See�. A probe intended to retain sente while inducing the opponent to fix the shape of the stones.
ooOoo
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