THE ENDGAME by Tomoko Ogawa, 4 dan and James Davies
THE ISHI PRESS, INC. Tokyo
PREFACE In this book we have tried to do two things: to cover the basic moves and rinci!es o" the endgame# and to show how they are a!ied in act$a! game sit$ations. %o is an inte!!ect$a! $rs$it, so we ass$me that yo$ wi!! want to try to think thro$gh as m$ch as yo$ can on yo$r own, and not &$st take o$r word "or it that s$ch'and's$ch is a correct move. (ccord' ing!y, more than ha!" o" the "o"!owing ages are given over to rob!ems. )orking them o$t may re*$ire some atience, b$t it sho$!d make yo$ stronger in a very tangib!e way. The rimary resonsibi!it resonsibi!ity y "or the "ive chaters chaters is divided as "o!!ows. Chapter Ogawa Chapter ! Davies Chapter " Davies Chapter 4 Ogawa Chapter # Ogawa
)e cons$!ted, however, thro$gho$t the book. +ne o" $s -avies dra"ted the entire te/t, and the other o" $s +gawa assed &$dgement on a!! the diagrams. +$r thanks go to the Nihon 0iin "or the $se o" their "aci!i' ties whi!e working on this book, and to 1ames 0erwin, who roo"read the man$scrit and s$ggested a n$mber o" modi"i' cations. Tokyo, 1aan Tomoko +gawa 1$ne, 2345 1ames -avies P$b!ished by The Ishi Press, Inc. CP+ 6o/# 7275 Tokyo,1aan 8 Coyright 2345 in 1aan by the Ishi Press (!! rights reserved according to internationa! !aw.
C$APTER %ntrod&'ing the Endgame The endgame co$!d be ca!!ed the sma!!'sca!e stage o" the game o" go. -$ring the oening and midd!e game the board is oen and the "ighting tends to range a"! $ and down and across it. 6y the endgame the board has been more or !ess di' vided $ into searate territories, and most o" the "ighting tends to a""ect on!y two o" them, occ$rring at a m$t$a! bo$nd' ary. The oening and midd!e game are m$ch !ike a sing!e !arge batt!e between two armies# the endgame is !ike a n$mber o" sma"!er batt!es going on in di""erent !aces sim$!taneo$s!y. In a way this makes the endgame easier, beca$se the !oca! en' gagements, being sma!!er, are easier to read o$t, b$t in a way it makes it harder beca$se one9s attention m$st be "oc$sed on severa! areas sim$!taneo$s!y. )hether yo$ "ind it easy or hard, one thing can be said abo$t the endgame: it is decisive beca$se it comes !ast. Tr$e, there is sometimes no endgame'one !ayer !oses a !arge gro$ o" stones and resigns ear!y'b$t in a!! other cases the endgame dete determ rmin ines es the the victo victor. r. Reve Revers rsa! a!ss o" the the !ead !ead are are "re* "re*$e $ent nt.. )atch a ro"essiona! game: yo$ wi"! see the !ayers most tense and serio$s d$ring the endgame. The endgame may be !ess e/citing than the midd!e game, b$t there is a great amo$nt o" satis"action to be gotten "rom !aying it we!!, no sma"! art o" which comes "rom winning. It is not s$rrising that strong ro"essiona! !ayers are genera!!y strong in the endgame. Sakata, 3'dan, is a bri!!iant endgame !ayer. Rin, 3'dan, is noted "or his abi!ity to s*$eee 2
the !ast dro o" ro"it "rom an endgame sit$ation. Ishida, 3' dan, considers his greatest strength to !ie in the endgame. It wo$!d be hard to "ind any ro"essiona! or strong amate$r who was rea!!y weak in the endgame. )hat makes "or strength in the endgame; +ne9s reading abi!ity and one9s eye "or tes$&i are imortant, &$st as they are in the midd!e game. (nother "actor is one9s abi!ity to co$nt and determine the re!ative sies o" di""erent moves. These tactica! matters, however, are not everything.
ing and go back to them !ater, erhas a"ter "inishing chater 7. Severa! o" the bo/es show how the va!$es o" certain moves can be co$nted, and this genera! method o" co$nting wi!! be e/!ained "$!!y in chater 7. The game, which begins on the ne/t age, was my +gawa9s third game in the 2342 +teai the ro"essiona! rank' ing to$rnament.
'dan, is *$ite strong. I had a rematch against him recent!y and !ost.
?ig$re 2 shows the "irst "i"ty moves, and as yo$ can see, my oonent concentrated on b$i!ding $ a !arge territoria! "ramework on the !e"t side and in the center, giving me a!! "o$r corners. 6y the end o" the "ig$re, the weakness o" the white gro$ on the !ower side had become the imortant "actor in the game. @
Aooking back at the $er !e"t corner, I wonder i" yo$ wo$!d have been ab!e to resist the temtation to cat$re at a, instead o" !aying )hite 7B or 6!ack 7>. This is recise!y the sort o" move that can and sho$!d be saved "or the endgame. S$ose 6!ack !ays 2 and @ in -ia. 2, instead o" 7> in the "ig' $re. Her two'stone cat$re is certain!y big, b$t the corner was a!ive even witho$t it and )hite B, as comared with a b!ack !ay in that direction, is big too.
I attacked )hite9s weak gro$ with >@, and he sent the ne/t twenty moves or so de"ending it. )hite 55, to oint o$t &$st one stone in this se*$ence, was a we!!'timed "orcing !ay. I" I answered it by giving atari at 2 in -ia. 7, )hite wo$!d !ay 7, and i" I !ost this ko, I wo$!d stand to !ose "o$r more stones to )hite 9a9. I" I !ayed sa"e by answering at 2 in -ia. @, however, then a"ter "orcing me with a in sente as he did at 4 in the "ig' $re, )hite co$!d connect at 7 to get a !iving shae. I re&ected B
these two diagrams and answered )hite 55 at 54, b$t that made 4B sente, so )hite was ab!e to !ive by !aying 4B and 45. He was not abso!$te!y a!ive, beca$se I co$!d sti!! "orce a ko with DaD, b$t he had so many ko threats to escae, starting with b, that the ko was not ractica! yet. )hat I had to do now was invade his thin osition on the right side with 6!ack 44 and wait "or a chance to start the ko !ater.
Invading the right side with 44 to > was e/treme!y !arge# a "air amo$nt o" what might have been white territory was now b!ack territory. in -ia. B. It is hard to say which is better, -ia. B or the "ig$re, b$t -ia. B wo$!d !eave )hite a big move at 5. I" )hite had answered 6!ack @ at a, then I wo$!d have carried o$t -ia. B. ("ter whitt!ing down the !ower !e"t corner in sente )hite >
e/changed 3B "or 3>, advanced to 35, bent aro$nd me at 3, and c$t at 2, "orcing me to connect at 2@. 6!ack 3> and 2@ occ$ied ne$tra! oints, whi!e )hite 3B not to mention )hite 3, 2, etc. was in a $se"$! osition "or making territory, b$t I had comensation in that )hite had !ost most o" his ko threats, so the ko on the !ower side was now a serio$s matter.
)hite co$!d not a""ord to !ose this ko, so he ignored my "irst ko threat and cat$red at . The e/change in this "ig$re marked the c!ose o" the midd!e game, and whi!e my oonent was thinking over the "irst move o" the endgame, I s$rveyed the board and made a ro$gh co$nt o" the territories to see who was ahead. This is something that ro"essiona!s do again and again thro$gho$t the co$rse o" a game, even in the oening, and I wo$!d !ike to show yo$ how we do it. The b!ack territory in the !ower right was a!ready retty we!! sett!ed, so I co$!d get an e/act "ig$re "or it. ?irst I had to make some ass$mtions abo$t what its "ina! bo$ndaries wo$!d be. I had to ass$me that event$a!!y )hite wo$!d be ab!e to !ay 2 in -ia. > on the ne/t age in sente# i" I did not 5
answer at 7, he co$!d s!ide a!! the way in to a. Simi!ar!y, I had to ass$me )hite @ and 6!ack B. To com!ete the bo$ndary on the right edge I $t in )hite FG and 6!ack F () Note that I menta!!y added e*$a! n$mbers o" b!ack and white stones.
Ne/t I co$nted the amo$nt o" territory !e"t. I can do this acc$rate!y in $nder "ive seconds by co$nting airs o" oints, as in -ia. 5. There is a neat co!$mn o" airs going down the right edge, two oints "or the white risoner at 3, a air at 2, "o$r more airs going across the bottom edge at 22 to 2B, a air above them at 2>, and "ina!!y a air !e"t over at 25. That makes @7 oints, and adding on a oint "or the stone I cat$red at D/D, I saw that I had @@ oints here. Taking the rest o" my territories, I estimated the !ower !e"t corner at a g!ance as > oints. I estimated the $er !e"t corner essimistica!!y as 2 oints, and the $er right corner oti' mistica!!y as 2> oints. That gave me @@>22>5@ oints o" sec$re territory. Now why don9t yo$ try estimating )hite9s territory; (ss$me 6!ack a and )hite DbD on the !e"t side, and don9t co$nt anything "or him in the ne$tra! area in the !ower right center. See i" yo$ don9t agree with me that even with the ne/t move, it is hard "or )hite to get 5 oints overa!!, and so my rosects in the game right now were good. Seaking o" )hite9s ne/t move, can yo$ g$ess what it was be"ore yo$ t$rn the age; 4
)hite started the endgame with 27, the !argest move since besides seiing the oen sace between the two marked stones on the $er side, it threatened to invade the $er right cor' ner. I knew "rom e/erience that my three'stone "ormation was v$!nerab!e at either a or b, so a"ter reco$nting to make s$re that it wo$!d reserve my !ead, I de"ended with 6!ack 2@. )hite had th$s ket sente and co$!d roceed to the ne/t !argest oint. Can yo$ g$ess where it was; The si/ diagrams at the to o" the ne/t age show what co$!d have haened i" I had not de"ended with 6!ack 2@. %iv' en the contin$ation shown, )hite 2 in -ia. 4 is the most dam' aging invasion. It may be ossib!e to ki!! this invasion by de' scending at B in -ia. , b$t 6!ack r$ns a risk in trying to do so beca$se o" the c$tting oints at a and b. In any case, i" )hite is a"raid o" 6!ack B in -ia. , he can "a!! back on )hite 2 in -ias. 3 to 27. That invasion is $nsto' ab!e.
)ith 6!ack 2@ on the board, FJ in the two diagrams be' !ow, )hite9s invasions no !onger work. He is $nconditiona!!y dead in -ia. 2@ (a and b are miai, and a!so in -ia. 2B, where 6!ack F makes 6!ack B ossib!e.
3
The time had come to cat$re at 2B. In terms o" the !e"t edge a!one, this move was worth si/teen oints, as is shown on the ne/t age, and it gave )hite additiona! ro"it on the $er edge by making )hite 2 in -ia. 2> sente. I" 6!ack "ai!s to answer at 7 and B, )hite B ki!!s her. Comare -ia. 2> with -ia. 25# the di""erence is !arge. Since, a"ter 2B, )hite gets to !ay -ia. 2> "ree, witho$t giving $ his t$rn, it sho$!d be consid' ered a art o" the va!$e o" )hite 2B, which th$s rises "rom si/' teen oints to we!! over twenty oints.
2
It may !ook temting to !ay )hite 2B in the center. The tro$b!e with that was that i" )hite !ayed 2B at a in the "ig$re, 6!ack co$!d sti!! move toward her three abandoned stones with DbD. I" )hite !ayed 2B at b, however, 6!ack co$!d &$m to the !e"t at DcD. )hite, there"ore, wo$!d rea!!y need two moves to de"end this area, whi!e he needed on!y one at 2B. Here is how the "ig$re si/teen oints "or the va!$e o" )hite 2B on the !e"t edge was arrived at. S$ose "or comari' son that 6!ack !ays 2 in -ia. 24. That is big in itse!", and ne/t she can $sh o$t at a to red$ce )hite9s territory "$rther, as in -ia. 2. )hite cannot b!ock 6!ack 2 in -ia. 2 direct!y at @, or 6!ack c$ts at 7, !eading to a bad ko "or )hite. 6!ack 2 to > in -ia. 2 are sente, so they sho$!d be co$nted as art o" 6!ack9s ro"it in -ia. 24. Simi!ar!y, given 2B in the "ig$re, )hite can !ay 2 and @ in -ia. 23 !ater in sente, and they sho$!d be co$nted as art o" his ro"it. To "ind the va!$e o" )hite 2B, then, what one does is to comare -ias. 2 and 23. In -ia. 2 6!ack9s territory is seven oints !arger than in -ia. 23: three airs and the oint marked D/D . In -ia. 23, )hite9s territory is nine oints !arger than in -ia. 2: "o$r airs and the oint marked / . The tota! di""er' ence is 4 325 oints.
22
Now I had sente and co$!d take my ick o" the big oints !e"t on the board. I chose the two'oint &$m to 6!ack 2>, and be"ore answering it, )hite made his sente moves at 25 and 2. They were very big, and i" he did not make them at once, I might emerge "rom the "ighting in the center with sente and !ay on the $er side be"ore him. Ne/t )hite came $ with a co$nterattack at 7 and 77 that I think m$st have ca$ght me by s$rrise. )hite 7B !e"t a and b as miai, so 6!ack 2> was going to get c$t o"". Aooking back, I don9t know why I didn9t !ay 2 in -ia. 7 instead o" 6!ack 2>. I m$st have had some reason "or re&ecting it, b$t I do not rem' cmber what it was. Ret$rning to the "ig$re, how wo$!d yo$ connect a"ter )hite 7B; 6!ack a wo$!d not be good, !etting )hite c$t o"" everything with b, b$t wo$!d yo$ !ay DbD, or make a diagona! connection at the oint above or be!ow it; Think abo$t this be' "ore yo$ read on. 27
6!ack 7> was the right way to connect. (!tho$gh )bite immediate!y gave atari at 75 and "orced me to "i!! at 74, the 7>' 75 e/change was imortant in red$cing his !iberties. )hite9s co$nterattack, however, had been a s$ccess# with @7 he had de"ended both the area on the !e"t and the area aro$nd the three stones marked FG. 6e"ore making my ne/t move, I co$nted the territories again. ?or myse!" I got: @@ !ow' er right> !ower !e"t2 $er !e"t7 $er right 7 risoners taken in the center4. ?or )hite I got abo$t 5 !e"t and $er sides2 !ower side4. )e were e/act!y even# "or the remainder o" the endgame, both o" $s wo$!d be going a!! o$t. 6!ack @@ and @> were "orcing moves that aimed at attack' ing the white gro$ in the !ower right, b$t I stoed short o" act$a!!y c$tting it o"" with 2 in -ia. 72, which wo$!d &$st ro' voke )hite into !iving and making territory with 7, whi!e gaining nothing in ret$rn. Ne/t I went back to the area aro$nd 7>'@7. I had a very !arge move !e"t thcre. Can yo$ see what it was be"ore t$rning the age; 2@
6!ack @4 took the two stones marked F o$t o" atari and cat$red the "o$r stones marked FG. )hite co$!d not connect at a; 6!ack b wo$!d answer that. The va!$e o" 6!ack @4, as com' ared with a white !ay there, was "o$rteen oints: two oints "or each o" the si/ stones cat$red or !iberated, and another air beca$se the oints marked D/D were now rea! territory "or me instead o" being "a!se eyes. (nother way o" !ooking at it is that my territory had gone $ by ten oints the FG9s and the D/D9s, whi!e )hite9s had gone down by "o$r the F9s. )hite @ and B, however, gave )hite abo$t e*$a! com' ensation, so the game was sti!! neck'and'neck. I robab!y censidered !aying @ myse!" instead o" @4, as in -ia. 77 on the "acing age. Ne/t I co$!d !ay a in that diagram in sente and make some ro"it in the center, b$t there is something more satis"ying in a move !ike 6!ack @4 in the "ig$re, that gives yo$ "o$rteen oints o" so!id cash in the ocket, than in a move !ike 6!ack 2 in -ia. 77, that may give yo$ abo$t the same amo$nt, b$t is comarative!y vag$e. 2B
)hite @ threatened an invasion o" the $er right corner again, so I de"ended at @3. )hite B threatened )hite c, which wo$!d c$t o"" my three stones in the center. 6oth )hite @ and B $t very e""ective ress$re on my weak oints, "orcing me to de"end, and th$s made ro"it in sente.
To ret$rn to 6!ack @3, this was the correct de"ensive move. I" 6!ack tries to de"end at 2 in -ia. 7@, )hite has the hitting' $nder tes$&i at 7. 6!ack cannot very we!! cat$re )hite 7 with @, beca$se then )hite breaks thro$gh her de"enses with B, 5, and . She has to de"end at @ in -ia. 7B, b$t then )hite can draw back to B, !eaving the threat o" )hite a in the corner. )hite a is )hite 2 in -ia. 7>. I" 6!ack descends to 7, )hite can !ive in ko with @, >, and 4. 6!ack @3 in the "ig$re revented KKhite 7 in -ias. 7@ and 7B, and at the same time threatened simi!ar contact !ays at DdD or e against the white stone.
2>
I !ayed B2, which stoed the c$t and threatened a hane at DaD, b$t )hite ignored my move and robed at the corner with B7. Since I answered at B@, the e""ect o" )hite B7 was to increase the va!$e o" )hite BB. That may be obvio$s witho$t any diagrams, b$t !et9s !ook at a "ew anyway. S$ose )hite !ays FG in -ia. 75 witho$t "irst robing in the corner, and I ignore him. Ne/t he can &$m in to 2, b$t I can sto him with 7 and B and ho!d the damage to reasonab!e roortions. In -ia. 74, by contrast, with the stone marked FG in !ace, I cannot !ay 6!ack B at DaD. Simi!ar!y, i" )hite !ays 2 in -ia. 7 on the ne/t age I can b!ock him at 7, and witho$t the robe, whether or not he can contin$e at a is a bit rob!ematica!. In -ia. 73, however, a"ter the same 2 and 7 there is no arg$ing with )hite @. ( good robing move !ike )hite B7 in the "ig$re oens $ weaknesses in the enemy9s osition no matter how he re!ies. Instead Instead o" 6!ack B@, I co$!d have !ayed 6!ack 2 in -ia. @, b$t that wo$!d have !e"t )hite s$ch ossibi!ities as 7 to 5. 25
In site o" )hite B7, my "irst inc!ination was not to answer )hite BB. I" I !ayed 6!ack 7 in -ia. @2 and !et )hite de"end the the cent center er with @, then then !ater !ater on )hite )hite a, 6!ac 6!ack k b, )hite DcD, 6!ack d wo$!d be his sente on the $er edge, and he wo$!d have made ro"it in two !aces. Comare this with -ia. @7, where )hite de"ends the center with 2 and !ets me !ay 7. Now 6!ack a, )hite b, 6!ack c, )hite d wo$!d be my sente, and I wo$!d be si/ oints better o"" than in -ia. @2. This was a c!ose game, and i" )hite was going to take the ro"it on the $er edge, I did not "ee! !ike sitting back and !et' ting him de"end the center, too. I wanted to !ay 6!ack 7 in -ia. @2 at @ instead. 6e"ore making $ my mind I er"ormed the ca!c$!ation on the ne/t two ages, b$t it on!y bore o$t my int$itive "ee!ing that -ia. @2 wo$!d be a !osing !ine o" !ay, making my ne/t move inevitab!e.
24
Co$!d I !ay 6!ack 2 in -ia. @@ and sti!! win; I worked this *$estion o$t in my head as "o!!ows. I imagined )hite making a "orcing move at 7, then taking the big oint in the center at B. Ne/t I co$!d cat$re with > and 4 in sente, since i" )hite omit' ted , 2 co$!d c!am him with 2 in -ia. @B. He co$!d not c$t me o"i with 7 beca$se the stones marked F wo$!d make the c$t at @ work. He wo$!d have to connect at 7 in -ia. @> and !et me !ink $ at @, b$t then he wo$!d !ose a !ot o" territory. The c!aming move at 2 is a $se"$! endgame tes$&i to remember. ("ter )hite in -ia. @@ I co$!d either !ay 3 and have )hite !ive and make some territory territory with 2, or !ay 2 myse!" myse!" and have )hite !ay 3. The "ormer choice !ooks better, since 6!ack 3 wo$!d enab!e me to red$ce the center with 22 and 2@. I" )hite tries to $sh thro$gh and c$t 6!ack 2@ o"", his own stones get cat$red. It is not hard to vis$a!ie the rest o" the endgame "rom here. ("ter )hite resonded to 6!ack 2@, I co$!d red$ce his !ower right center territory in sente with DaD, and then I wo$!d 2
have a choice o" severa! gote !ays, o" which b !ooks !ike the bigges biggest. t. )hite co$!d !ay DcD, DcD, d, `eD, and f in sente, and then take gote at g. I" I tried to cat$re )hite DgD, I wo$!d !ose my center stones. The !ast !arge oint, at DhD, wo$!d "a!! to me. In detai!, this works o$t to the se*$ence "rom )hite 2B to 6!ack B> in -ia. @5. I com!eted the bo$ndaries in my mind9s eye by $tting in the e/changes marked FG and F. Taking into consideration the stones cat$red at the oints marked D/D , I co$nted the territories as shown in the tab!e, and I came o$t "ive oints behind. ?or ractice, yo$ might !ike to try veri"ying veri"ying my co$nting. co$nting. +" co$rse co$rse this who!e se*$ence se*$ence was on!y my "irst oinion o" how the game wo$!d go, so the end res$!t I arrived at might be o"" by a !itt!e, b$t not by as m$ch as "ive oints. That meant that, as I had s$sected, 6!ack 2 in -ia. @@ wo$!d be a !osing move. *+a'k
Aower right
@@
Aower !e"t
5
Center
27
=er !e"t
2
=er right
2>
T+T(A
45
hite
Ae"t and $er sides Aower side
5@
Right center and right side 2 T+T(A
2
23
I !ayed 6!ack B>. )hite B5 to > h$rt, b$t 6!ack >2 was my sente, icking $ the c$tting stone F and "orcing )hite to !ive with >7. ?rom B> and >2 I was ab!e to &$m o$t to >@. How wo$!d yo$ have answered 6!ack >@; I s$sect that many amate$rs wo$!d a$tomatica!!y !ay )hite 2 in -ia. @4, !etting 6!ack make a !arge'sca!e cat$re o" )hite FG with 7 and B. Aook ahead to ?ig$re 27 and see how )hite resisted with >B. I !ayed 6!ack >> to kee the otion o" c$tting o"" the white stone with a, b$t o" co$rse 6!ack a in ?ig' $re 27 wo$!d not be as nice as 6!ack B in -ia. @4.
7
)hite did not have to "ear 6!ack 7 in -ia. @. In "act, be' ca$se o" )hite FG, a"ter @ and B he co$!d take sente and !ay e!sewhere.
)hen )hite answered 6!ack >> at >5, I $shed o$t at >4 in the center, then took my sente !ays at >3 and 52. )hite 57 was necessary to revent 6!ack DbD L see -ia. @B on age 75. How m$ch did I gain by this one'stone cat$re; It en!arged my corner by three oints, two "or the risoner !$s one at D/D, and red$ced )hite9s territory by "o$r oints, as yo$ can see by comaring the "ig$re with -ia. @3. That makes on!y sev' en oints, b$t I got them in sente, and as a r$!e o" th$mb we co$nt do$b!e va!$e'"o$rteen oints'"or anything gained in sente. I hoe yo$ areciate the timing o" these two moves. I" I !ayed them too ear!y, they might not be sente# )hite might be wi!!ing to to!erate being c!amed at b. I" I waited any !onger, however, )hite wo$!d connect at 2 in -ia. @3 and I wo$!d !ose my chance. 72
2 )hite 2 in -ia. B. ?irst o" a!!, this adds si/ or seven oints to )hite9s territory: three airs and ossib!y the oint marked D/D. In addition, it weakens 6!ack9s corner. I" 6!ack !ays bere, his best move is 2 in -ia. B2. )hether )hite sho$!d ignore 6!ack 2, answer it at a, or answer it at b is a hard rob!em, b$t !et9s ass$me tbat he ignores it and that -ia. B7 "o!!ows in 6!ack9s sente. This adds at !east "o$r oints to 6!ack9s territory, as comared with -ia. B, and strengthens his corner. )hite 2 in -ia. B is th$s worth at !east 5B2 oints in gote, and a!most certain!y more. 7 )hite 2 in -ia. B@. ("ter connecting here, )hite can $sh o$t in sente with DaD, 6!ack b, )hite DcD, 6!ack d. (ccord' ing!y, i" 6!ack !ays 2 in -ia. BB, she has gained eight oints: the risoner and the three airs indicated. She may we!! have gained more than that, too, since in -ia. B@ )hite b or d, instead o" a, is high!y robab!e.
7@
@ )hite 2 in -ia. B>. This is the hardest o" the three !ays to "ig$re o$t. 6!ack wo$!d answer it at 7, and )hite wo$!d an' swer that at @. How m$ch territory )hite gains this way is hard to say'6!ack can sti!! hane at a L b$t at !east he has saved three stones "rom being cat$red. I" 6!ack !ays 2 in -ia. B5, )hite can answer with 7 and B. (gain an e/act ca!c$!ation is di""ic$!t, b$t i" we think o" a and DbD as 6!ack9s sente, then besides the three risoners, she has taken "ive more oints o" territory. In addition, she has !inked her gro$s together, which strengthens her overa!! board osi' tion. The tota! va!$e o" a!! this m$st e/ceed ten oints. The com!e/ities mo$nt when we try to eva!$ate di""erent combinations o" these three !ays. S$ose )hite starts with 2 in -ia. B4, "or e/am!e. ("ter 7 and @, 6!ack wi!! !ay B and )hite wi!! connect at >. I" 6!ack descends to 5, )hite 4 !ooks bigger than )hite DaD.
7B
How does that comare with the sim!er se*$ence shown in -ia. B ; In both diagrams )hite has gotten two o" the origina! three !arge !ays. In -ia. B4 he has made siab!e gains in the center, b$t at a heavy cost in the corner. ?or a recise comarison it wo$!d be necessary to read o$t the !ays that wo$!d "o!!ow each diagram, taking the who!e board into ac' co$nt, an e/ercise which we sha!! "orgo.
It is worth taking a c!oser !ook at the midd!e right side, not to see how big it was, b$t to see how sma!! it was. S$ose 6!ack went "irst. The e/change o" 2 "or 7 in -ia. B3 wo$!d en' !arge her $er territory, b$t $ndermine her !ower one, since "rom 7 )hite co$!d s!ide in to a. Aikewise, the e/change in -ia. > wo$!d $ndermine her $er territory. I" she !ays here at a!!, then 2, @, and > in -ia. >2 wo$!d be better, b$t most o" what they gain disaears when )hite hanes at 5. I" the three !ays considered in the bo/ above were in the ten'oint c!ass, then a b!ack, and there"ore a white, !ay here wo$!d be on!y in the "ive'oint c!ass.
7>
6e"ore !aying )hite 55, 0amim$ra m$st have tested o$t many di""erent se*$ences, and he robab!y tried to work o$t what the rest o" the endgame wo$!d come to a"ter each one, to see whether it wo$!d !eave him ahead, or at !east in con' tention. Pro"essiona!s do that constant!y. There was more to this osition than I co$!d ossib!y e/!ain, b$t one thing to note is that in the se*$ence 0amim$ra chose, )hite 55 and 4 rein"orced each other, combining to romise "$rther deredations against what was !e"t o" my corner. 6e"ore c$tting at 53, I made a "orcing move at 6!ack 54, and I wo$!d !ike yo$ to remember )hite9s answer at 5. )o$!d yo$ have !ayed there, or wo$!d )hite 2 in -ia. >7 on the ne/t age have come nat$ra!!y to yo$; )hite9s territory is abo$t two oints sma!!er in -ia. >7 than in -ia. >@, and i" 6!ack !ays 7 at @ in -ia. >@, )hite can sim!y c$t her o"" by wedging in at 7. I" yo$ don9t a!ready know it, !earn the c!am' ing move at )hite 2 in -ia. >@. It is a "re*$ent!y $sed endgame tes$&i in the center.
75
Ret$rning to the "ig$re, notice that )hite did not give atari at DaD and "orce me to connect at DbD. The reason was that he was saving himse!" the other atari, at DbD# it is standard ractice in a osition !ike this to !eave both otions oen. )hite b wo$!d not accom!ish anything in the "ig$re, b$t s$' ose I had gone on a"ter )hite 47 to !ay 6!ack 2 in -ia. >B. Then )hite 7 and B wo$!d have made a bea$ti"$! combina' tion. I needed to add one more stone to $t my new!y'won cen' ter territory in order, b$t as !ong as )hite was keeing a and b oen, my hands seemed to be tied. ?ina!!y, however, I "o$nd a move that wo$!d "orce )hite to e/change a "or b and enab!e me not on!y to com!ete my own center territory, b$t to red$ce his a !itt!e as we!!. )o$!d yo$ !ike to try to g$ess what it was be"ore t$rning the age;
74
I !ayed the hane at 4@. ("ter )hite had taken the two big oints in the $er right corner, this was a saving move "or me. )hite co$!d not c$t me o"" with 2 in -ia. >> beca$se o" the nose tes$&i at 7. I" he tried to go to the right with @, he wo$!d s$""er a rea! tragedy, and i" he tried to go to the !e"t with @ in -ia. >5, I wo$!d !ink $ with B to 2.
7
?irst )hite had to give atari at 4B, and then he co$!d c$t at 45. I came back with 6!ack 44, however, and he co$!d not c$t me o"" at 43, b$t had to give way with 4. I made a nice ro"it o$t o" these !ays, thanks to my sacri"ice at 4@. I "o!!owed them $ with 6!ack @ to 4, which red$ced )hite9s territory by three oints ass$me 6!ack a, )hite b) as comared comared with )hite9s !aying 2 in -ia. >4. Three oints oints may seem sma!!, b$t in the "irst !ace, )hite 2 in -ia. >4 wo$!d have bcen sente# I wo$!d have had to answer at 7 to kee the "o$r stones marked FG cat$red. 6!ack @ to 4 were what are ca!!ed reverse sente !ays# they were gote, b$t they stoed a sent sentee !ay !ay by the the enem enemy. y. 1$st 1$st as sent sentee !ay !ayss ha have ve do$b do$b!e !e va!$e, so do reverse sente ones, so the thrce oints here were e*$iva!ent to si/ oints in $re gote. In the second !ace, 6!ack @ to 4 created weaknesses in )hite9s osition that were to have reerc$ssions a!! the way over on the $er edge, as we sha!! short!y see. 73
)hite made a series o" sente moves at to 3B, in the midst midst o" which I s!ie s!ied d in an imortant sente move o" my own at 3. Ne/t he "o$nd a good combination at 35, 3, and 2 in the $er right, )hite 3 made s$re that )hite a wo$!d be sente, and now I abandoned what !itt!e I had !e"t there and !ayed 22. Even i" I had de"ended at 2 in -ia. >, I co$!d on!y have saved abo$t "o$r oints o" territory. ("ter "orcing me with 7, )hite wo$!d craw! "orward to B, and with a his sente, I wo$!d have to !ay > and !et him escae with 5. Considering the ris' oner taken at 4, the !oss s$""ered at 7, and the "act that )hite co$!d ne/t $!! o$t his stone at DbD, I wo$!d not have made any ro"it. +n the other hand, i" )hite had started with 2 in -ia. >3, I wo$!d have answered at 7, threatening 6!ack a, which in t$rn wo$!d threaten 6!ack DbD and DcD.
@
)hite 7, B, etc. in ?ig$re 2 destroyed a!! my territory in the $er right, even taking a risoner. This was a consider' ab!e setback, b$t then came 6!ack 2@ and 2> and my revenge. These two moves were what I had been aiming at when I !ay !ayed ed 6!a !acck @ in ?ig$r ig$ree 25 25.. )hit )hitee co$! co$!d d no nott conn connec ectt at a witho$t r$nning the risk o" the h$ge ko shown in -ia. 5. +nce he got into this ko he wo$!d $!d have to ignore any ko threat I made, ar d I had one or two good ones. I s$sect that 0ami 0amim$ m$ra ra over over!o !ook oked ed this this se' se' *$ence, with its s*$eeing combination at 2 and 27 and throw'in at 2B, or he might have !ayed di""erent!y ear!ier. @2
)hite !ayed 25 and 77 to make me $se $ two ko threats, b$t he had to give give way and connec connectt at 7 and 75, !ettin !etting g me cat$re cat$re at 74. (t the end o" o" this "ig$re "ig$re it was my t$rn t$rn to !ay, !ay, and there were three !arge oints on the board, at 25, a, and b. The ana!ysis ana!ysis is com!icate com!icated, d, b$t a was the !argest, 25 the sec' ond !argest, and b the sma!!est. The "irst ste in ana!ying the three !ays is to e/amine each individ$a!!y, as "o!!ows. 2 6!ack 2 in -ia. 52 is worth si/ oints in gote. Comare -ia. 57, where )hite 2 cat$res three b!ack stones.
@7
7 6!ack 2 in -ia. 5@ is worth "o$r oints in reverse sente, or $ to 32M7 oints in gote. ?or comarison, "irst I ass$me that )hite !ays 2 in -ia. 5B and I answer at 7. )hite @ and > destroy "o$r oints o" my territory in sente: the two oints marked / and the risoner marked O in -ia. 5@. Ne/t I try ignoring )hite 2, as in -ia. 5>. )hite carries on with @, >, and 4. (gain my territory is "o$r oints sma!!er, and now )hite9s is "ive oints !arger than in -ia. 5@. In -ia. 5> I wi!! !ater e/change a "or b. In -ia. 5@ I can !ay a, )hite b, 6!ack c, )hite d. That !eaves me a ossib!e oint at e, which I co$nt as ha!" a oint since I may or may not get it. The tota! di""erence between -ias. 5@ and 5> is there"ore B>2M732M7 oints.
@@
@ 6!ack 2 in -ia. 55 is worth three oints in reverse sente. I" )hite !ayed I in -ia. 54, he wo$!d immediate!y en!arge his territory by the oint marked / on the !e"t edge and red$ce my territory by the two oints marked D/D on the !ower edge. ?$rthermore, i" I did not answer )hite 2 in -ia. 54, he co$!d contin$e with 2 in -ia. 5. In -ia. 5, i" I gave atari at a, then )hite b wo$!d threaten a sna'back, whi!e i" I !ayed b, then )hite a wo$!d be an atari, and either way I wo$!d end $ with a!most nothing on the !ower edge. Now that we have seen what these three !ays have to o""er individ$a!!y, we can $t together s$ch ossib!e com' binations as the "o!!owing, the !ettering comes "rom -ia. 53 on the ne/t age: I. I take A; )hite takes B; I take C, ending in gote. This is the sim!est se*$ence, and we sha!! $se it as a oint o" re"erence. II. I take D !$s 5# )hite takes A, I answer at E, and )hite !ays ?in sente min$s B then % min$s @. I end in gote beca$se I sti!! have to de"end the !ower edge against )hite 2 in -ia. 5, a!tho$gh "irst I wi!! !ay H and ca' t$re )hite A in sente. Comared with se*$ence I, I have come o$t !$s 5 on the $er edge, b$t min$s 4 e!se' where, or one oint worse o"" overa!!. III. I take D !$s 5# )hite takes A; I take C# )hite takes ? then E min$s 32M7. This time I come o$t @2M7 oints worse o"" than in se*$ence I. I end in sente, b$t there is nothing !e"t "or me to take to get those @2M7 oints back. Perhas any o" these se*$ences wo$!d have been good eno$gh to win, b$t the "irst se*$ence was the best. This was the !ast hard rob!em o" the endgame.
o$ may be wondering what the signi"icance o" the ko in the !ast "ig$re was i" I was going to !et )hite !ay 6 in -ia. 53 and cat$re my three stones. That makes an inter' esting st$dy. I" I had sim!y !ayed 2 and @ in -ia. 4, then )hite wo$!d have gotten si/ oints, three airs, in an area where he gets on!y "ive a"ter !aying 6 in -ia. 53, three b!ack risoners min$s one oint "or the white stone !ost between B and D).
6!ack 73 to @4 in ?ig$re 7 went according to !an, and the game was now essentia!!y over. )hite took sente !ays at B, B7, and B5, each o" which red$ced my territory, or en!arged his territory, by one oint. )hite BB gave him some otentia! ko threats in connection with the stone marked a!b, and i" I had not answered at B>, a white atari at B> wo$!d have red$ced my territory by one oint in sente. There was a two'oint gote !ay at a "or me on the !ower edge, b$t one oint in sente is worth two oints in gote, and that is why I answered at B>. Th$s )hite got to !ay > in ?ig$re 72, en!arging his territory by one oint and red$cing mine by one oint as comared with 6!ack a, )hite b, and 6!ack c in ?ig$re 7. ("ter this two'oint !ay a!! the rest o" the moves in ?ig' $re 72 were worth on!y one oint. I cat$red )hite B with >4, b$t )hite won it back in the ko there, the moves o" which, i" we act$a!!y !ayed them o$t, are not recorded. Now !et9s ca!c$!ate the "ina! score. (t the beginning o" the endgame I co$nted my !ower right corner as @@ oints. I" yo$ remember the bo$ndaries I ass$med then, yo$ wi!! see that it had grown by the one oint at the right o" 6!ack 52, so it was now @B oints. I had > oints in the !ower !e"t
corner and 2 oints in the $er !e"t'recise!y my revio$s estimates. I had ac*$ired a !ot o" new territory in the center, however# "or ractice, why don9t yo$ see i" yo$ can co$nt it yo$rse!"; ?ig$re two oints, or one air, "or every oint where a risoner has been cat$red'these oints have been marked wiih D/D9s'and one "or every other oint, inc!$ding the oint $nder 6!ack >3. Ne/t see i" yo$ can co$nt )hite9s territories, noting that he wi!! have to connect at a, and remembering to ded$ct one oint "or the risoner he !ost at b and add one oint "or the risoner he cat$red at a!b. The three b!ack and three white stones taken in the kos cance! o$t. *+a'k
hite
Aower right
@B
Ae"t and
Aower !e"t
>
$er sides
=er !et I
2
Aower side
Center T+T(A
Right center T+T(A
The correct "ig$res are: *+a'k
hite
Aower right @B
Ae"t and $er
Aower !e"t
>
sides
>
=er !e"t
2
Aower side
Center
74
Right center
5
T+T(A 45
T+T(A 47
I had won by "o$r oints. Reviewing what had haened, I think I came o$t o" the midd!e game with a !ead, b$t then I made that *$estionab!e two'oint &$m in the !e"t center, 6!ack 2> in ?ig$re 4 that )hite was ab!e to c$t thro$gh, and the game became very c!ose. 6oth sides !ayed aggressive!y in the $er right *$arter o" the board, which !ed to )hite9s tak' ing territory in what had been my corner and my taking terri' tory in what had been his center. ("ter this e/change, I "o$nd the hane at 4@ in ?ig$re 2>, which gave me a tidy ro"it, and a!tho$gh !ater on )hite came $ with a se*$ence that de' stroyed a!! my remaining territory in the $er right corner, I came $ with an e*$a!!y good ko se*$ence on the $er edge. Perhas )hite9s "ai!$re to notice this !ast is what !et me win. I have tried to show yo$ the aroach that ro"essiona!s take to the endgame and to give yo$ a taste o" the di""ic$!ties it invo!ves. Perhas I have overdone it# I am a"raid that yo$ may be "ee!ing a !itt!e dismayed right now by a!! the se*$ences and ca!c$!ations. +n the other hand, erhas yo$ have no' ticed a "ew things that I had to g!oss over. (t any rate, be"ore !eaving this game behind, I wo$!d !ike to s$mmarie what I think are the main oints to be drawn "rom it. ?irst o" a!!, yo$ have to araise the sie o" individ$a! moves in the endgame. That means reading and co$nting, as was done severa! times in the bo/es on the revio$s ages, and it is not a!ways easy. +ne imortant rinci!e invo!ved is to take into consideration not on!y the move itse!", b$t a!so the s$bse*$ent moves that it enab!es yo$ to !ay. (nother imor' tant rinci!e is that a sente, or reverse sente, !ay has twice the va!$e o" a gote !ay.
Second!y, besides thinking abo$t di""erent moves in iso!a' tion, yo$ have to think abo$t them in combination. Idea!!y yo$ sho$!d test o$t di""erent se*$ences and ca!c$!ate to see which gives yo$ the most ro"it, b$t even witho$t going to those !engths, yo$ can get in the habit o" thinking not in terms !ike, D%ee, this is big'I9d better !ay here,9 b$t in terms !ike, DI" I !ay this way I can get two o" the three big oints, b$t i" I !ay that way I9!! get on!y one o" them,9 or !ike, D( moment ago there were two big !aces to !ay# my oonent has &$st taken one o" them, so instead o" answering his move, I9d better take the other,9 or !ike, D, >2, 5@, etc. in ?ig$res > to 2@, and yo$ wi!! see that this is what both sides were doing a!most constant!y. I" yo$ can' not "ind any weaknesses in yo$r oonent9s osition, try to create some, as )hite did by robing at B7 ?ig$re 2 in my $er right corner and as I did by !aying @ ?ig$re 25 on the !e"t side. ?o$rth!y, yo$ have to !earn to recognie areas that !ook big, b$t are !arge!y worth!ess. +ne s$ch area in this game was on the right edge, where i" I !ayed "rom one direction, I wo$!d on!y be h$rting myse!" in the other direction, -ias. B3 and >. ?i"th!y, it he!s a great dea! to know whether yo$ are ahead or behind. I" yo$ know where yo$ stand in the game, yo$ wi!! know whether yo$ can a""ord to re!a/, or whether yo$ m$st $t "orth some e/tra e""ort, or even take risks. I" I had gone thro$gh this endgame on the ass$mtion that my midd!e'game !ead was ho!ding $, I might never have both' ered to h$nt "or the !ays that event$a!!y enab!ed me to win. To "ind o$t how yo$ stand, yo$ have to co$nt or estimate the territories on the board. 2 have shown yo$ how I co$nt by airs, and I recommend this method, a!tho$gh some ro"es' siona!s co$nt direct!y by two9s instead o" co$nting by airs and do$b!ing the res$!t, and some others co$nt by $nits o"
"o$r. Territories that are on!y vag$e!y de"ined can be estimat' ed in m$!ti!es o" "ive, which makes adding them $ easy. The imortant thing is to co$nt the territories individ$a!!y and remember them, instead o" trying to co$nt a!! yo$r territory together and then having to reco$nt everything whenever one territory changes in sie. Si/th!y, esecia!!y when the game is c!ose or yo$ are behind, yo$ m$st not accet the ordinary move too readi!y, b$t !ook "or the move that gives yo$ a !itt!e bit more. 6!ack 24@ ?ig$re 2> and 6!ack 72> ?ig$re 2 were two !aces where I did that. ?inding s$ch tes$&is is, above a!!, what makes the endgame interesting. In the ne/t chater we sha!! take $ co$nting and ca!c$!a' tion again, which cover the "irst two o" these si/ oints. In the third chater, we sha!! cover the !ast oint by s$rveying endgame tes$&i. In the "ina! two chaters we sha!! !ook at some more games, and give yo$ a chance to try yo$rse!" o$t on them by resenting them as who!e'board rob!ems.
CHAPTER 2 Counting Frequently during the endgame you are faced with a choice of two or three or four moves and must count to find which is the biggest. That sounds simple, but you know by now that it is not-that there can be all sorts of follow-up moves, combinations, and other complications involved. Most important is the question of sente and gote; it is often correct to make a small sente play before a larger gote one. n the basis of sente and gote relationships it is possible to classify moves into four types-gote, sente, reverse sente, and double sente-and we shall begin this chapter by e!amining each type from a theoretical point of view. Then you will have a chance to apply the theory to some problems. ". #ote #ote means gote for both sides, so we are dealing here with situations in which neither player could play in sente. $ia. " shows an e!ample from the game in chapter one. %s you will recall, a move by one side or the other on the lower edge is worth two points.
"
&f 'lack goes first, he will hane at " in $ia. (, and after )hite*s answer at (, he will have to connect at +, ending in gote. &f he does not connect at +, there is no point in his playing " ; he would be better off not playing it at all than playing it and letting )hite capture it. &f )hite goes first he will do the same thing, as in $ia. +. omparing $ias. ( and +, we see that )hite*s territory is one point marked x bigger in $ia. + than it was in $ia. (, and 'lack*s territory is one point x bigger in $ia. ( than in $ia. +, so the total difference is " / "0( points.
$ia. 1 shows another gote situation-do you know how much this one is worth2 The side that plays first here will make a hane on the second line, as 'lack does in $ia. 3. )hite answers at ( and 'lack connects. &n general the solid connection at + is better than an open connection at a or b, because it gives 'lack essentially the same amount of profit and does not leave )hite any ko threats. $ia. 3 does not completely finish the situation. "t ends it for the time being, but later on either 'lack will return to play " in $ia. 4 or )hite will return to play " in $ia. 5.
(
&n evaluating $ia. 3, how do we cope with these two possibilities2 &t would be unfair to )hite to assume $ia. 4; 'lack plays two stones in $ia. 4 to )hite*s one, so assuming it would be akin to giving 'lack an e!tra move. n the other hand, it would be unfair to 'lack to assume $ia 5. )hat we do is to strike the mean and assume 'lack " and )hite ' in $ia. 6. That gives a value e!actly halfway between $ias. 4 and 5, and since both sides have been assumed one added stone, neither can complain. &f )hite goes first, he will play " and + in $ia. 7, and again we assume " and '. The difference between $ias. 6 and 7 is si! points8 three points of black territory and three points of white. )hite " in $ia. 7, or 'lack " in $ia. 3, is thus worth si! points in gote. )hat we did in $ia. 6 was to take the mathematical average of $ias. 4 and 5, a procedure that is often needed to get a fair numerical value for a move. )e will have to use it, for e!ample, in finding the value of a white connection or black capture at a in $ia. "9. :ow much do you think this will be worth2
+
First let*s suppose that 'lack captures at " in $ia. "". %fter 'lack +, a black hane at a would be gote, so it is fair to assume that )hite " and 'lack ( in $ia. "( will finish off the lower edge. &n fact, at the proper time, )hite*s descent to " should be sente, since it threatens an atari at (. e!t let*s suppose that )hite connects at " in $ia. "+. This is where the averaging comes in, because there is a fairly large hane left for someone in 'lack a or )hite b. There is no special reason to assume that either side will get to make it, so we have to take the average. The easiest way to do this in practice is the following. First assume that 'lack answers )hite*s connection, by playing ( in $ia. "1, and count to see how much )hite has gained. 'lack*s territory is three points larger in $ia. "(-a pair for the prisoner plus the point marked x < than in $ia. "1, and )hite*s is one line two points smaller. That makes five points, and tells us that in the unlikely event that 'lack really does answer )hite " in $ia. "1 immediately, )hite has gained five points in sente.
1
e!t determine the value of )hite*s second move, the hane at " in $ia. "3. This is also a move that we met in chapter one, and you may remember the value three points; it enlarges )hite*s territory by one point and reduces 'lack*s territory by two points, all marked ! , in comparison with $ia. "1. )hite " is worth a little more than that, however, because )hite may be able to make the further hane at " in $ia. "4 and reduce 'lack*s territory by one more point. f course he has to win a ko to keep this e!tra point, and )hite " in $ia. "4 is gote to begin with, so we cannot add on too much for it, but at least we can count )hite " in $ia. "3 as being worth + / points in gote. Finally, to take the average of $ias. "1 and "3, add half the value of )hite " in $ia. "3 to the figure obtained in $ia. "1. :alf of + / is ""=(/, or ( -, so the sum is8 3/(-05-. That is the value of )hite " in $ia. "+ or 'lack " in $ia. "". $uring actual play you are not going to have to go through a lot of computations like the above before you put down every stone, thank goodness, but there are times when it would be very helpful to know the value of a move like " in $ia. "" or "+. )ith a little practice, you should be able to make the necessary calculations quickly and easily, and even if you get a slightly wrong answer, going through the process will have forced you to think about the moves in a logical way, and that in itself will be valuable. >ou will learn shortcuts, too, such as ?)hite " in $ia. "+ is essentially like the hane and connection in $ias. 1 to 7, which was worth si! points, e!cept that the hane in $ia. "3 is a point or two bigger than an ordinary hane on the first line, so &*ll add on one e!tra and call it seven. )hen the following move is made in sente instead of gote, you count in its full value instead of only half. >ou should understand that fact from the previous chapter. &n light of it, let*s take another look at a hane and connection on the second line. 3
)hat is the value of 'lack " and + in $ia. "52 &f 'lack plays these two moves, we can make the standard assumption of 'lack " and )hite ' to finish off the edge. &f )hite plays " and + in $ia. "6, however, we cannot assume 'lack a and )hite b, because now )hite can play a in sente. The correct assumption is )hite " to 'lack 1 in $ia. "7. &f 'lack does not connect at 1, )hite will cut at " in $ia. (9, and because of the stone marked ', 'lack will be in a lot of trouble. @ince 'lack and )hite have played two stones apiece in $ia. "7, this is fair. omparing $ias. "5 and "7, you can see that $ia. "5 makes 'lack*s territory five points larger, two pairs plus the point marked × , and )hite*s three points smaller. 'lack " in $ia. "5 is thus worth eight points &n general, the value of a hane and connection on the second line varies from si! points on up, depending on what the follow-up moves are and whether they are sente or not. For future reference, notice that in a gote situation, there is a difference of two stones between one side*s playing first and the other side*s playing first. &n $ia. "5, for instance, 'lack has played two stones and )hite one, while in $ia. "6 'lack has played one stone and )hite two.
2. Sente &n this section we shall be dealing with one-sided sente situations, where one side has a sente move, but the other side has only a gote move. $ia. " shows one such. 4
The side with the sente move here is 'lack; when he hanes at " in $ia. (, )hite must answer as shown to save his corner. :e cannot play ( at a, or 'lack will step over him by playing ( atariA and kill him. :ow much is 'lack ", which reduces )hite*s corner territory to three points, worth2 &f )hite gets a chance to play here, his move is the descent to " in $ia. +. ow his corner territory is five points, two points larger than before. )hite " is gote, but )hite can presumably push out at " and + in $ia. 1 in sente, so we have to count that in when figuring the value of $ia. +. $ia. 1 reduces 'lack*s territory by three points, making the total value here (/+03 points. Moreover, the difference in the number of stones played in $ias. ( and + is only one; in both diagrams )hite has played one stone, while 'lack has played one stone in $ia. ( and no stones in $ia. +. This is why a sente play is considered to have twice the value of a gote play. 'lack " in $ia. (, five points in sente, would be worth more, for e!ample, than 'lack " in $ia. "5 on the previous page, eight points in gote. )e can even put this in mathematical terms8
5 points 8 points 1 stone 2 stones The problem with a sente move is not so much its e!act value as the proper time to play it8 too early, and it may not 5
be answered; too late, and the chance may be lost. >ou will recall several e!amples from chapter one, including the position shown in $ia. 3. )hite had two sente moves there8 a small one at a and a large one at b. :e played the latter )hite " in $ia. 4-as soon as he could, and 'lack had to answer it because it threatened to kill the corner. :e saved the former-)hite " in $ia. 5-for much later, because it was relatively small and because the threat that it involved was only to destroy about four points of 'lack*s territory, not enough to make it sente if played too early.
Taking into consideration the siBe of the move itself and the siBe of the threat behind it, we can identify four cases8 ". 'ig move, big threat $ia. 4, for e!ample. Clay these early they are important. (. 'ig move, moderate threat. Clay these as early as the bigness of the move warrants, but don*t count on your opponent answering the threat. +. @mall move, big threat $ia. (, for e!ample. :ere you have a lot of leeway; you can play the move early and your opponent will answer the big threat, or you can leave it for later and he will not give up his turn to take the small move away from you. >ou should leave such moves unplayed for a while at least-they make good ko threats-but remember that they are worth as much as gote moves twice their siBe, and don*t leave them so long that your opponent plays them instead of you. 6
1. @mall move, small threat $ia. 5, for e!ample. @ave these, of course, until the appropriate time. ccasionally you will make what you e!pect to be a sente play and be surprised to have it ignored. This does not mean that it was a mistake. >our opponent may be going to answer it, but after making some forcing moves of his own first, or he may have decided to try for some kind of e!change. % good player knows that if he answers all his opponent*s moves, he will be taking one loss after another right through the whole endgame, so he is constantly on the lookout for chances to ignore them, play elsewhere, and make some profit of his own.
3. Reverse Sente % reverse sente play is, as the name says, the reverse of a sente play8 one made by the gote side in a one-sided sente situation. )hite " in $ia. " is worth five points in reverse sente. &t is gote, but it stops 'lack " in $ia. (, which would be sente.
% reverse sente play has the same double value as a sente play, and for the same reason-that there is a difference of only one stone between it and the enemy*s playing in sente. )hite " in $ia. " has, in theory, the same value as a ten-point gote play8
5 points 10 points 1 stone 2 stones This means that, in theory, )hite should prefer it to any gote play worth less than ten points 7
The opportunity to make a reverse sente play usually arises when the enemy*s sente move is not backed up by a very big threat. &n the game in chapter one, you will remember that 'lack made the reverse sente play at " to 3 in $ia. +.
)hite would have liked to play " in $ia. 1 in sente, but the threat behind it, to connect at a and rescue the four stones marked ', was worth only about eight plus one or two, say ten points, which would not have been enough to make 'lack answer it early in the game. )hen the endgame reached the ten-point level )hite was busy in the upper half of the board, and 'lack emerged from there with sente to play $ia. +. Deverse sente opportunities like this are a common occurrence. Even though reverse sente moves are gote, you should not think of them as gote; they really are about twice as valuable as ordinary gote moves, a fact which the problems in the second half of this chapter will support.
4. Double Sente % double sente situation is one in which either side can play in sente. &n $ia. " on the ne!t page, for e!ample, )hite can hane at " and connect at +, and if 'lack does not answer at ( and 1, he loses a large amount of territory. @imilarly, 'lack can hane at " and connect at + in $ia. (, and if )hite "9
does not answer at ( and 1, his corner group is in danger. &f he plays ( and omits 1, he cannot be killed unconditionally, as $ia. + shows, but the ko is still a siBable threat. omparing $ias. " and (, we see that the difference is two points of black territory and two points of white territory, or four points in all.
&f we compare the number of stones played, however, we find no difference at all. &n both diagrams 'lack and )hite have played two stones apiece. &f we try to divide the number of points gained by the number of stones difference, as we have been doing so far, we get8
(?)
4 points 0 stone
=∞
)hat this means is that whoever makes the hane, )hite in $ia. " or 'lack in $ia. (, is getting something for nothing. $ouble sente moves are the priBe points on the board, and both players try to take them as early as possible. :ow early can they be taken2 That depends, of course, on the siBe of the threats that follow them. The bigger the threat, the earlier the move can be made in sente.
""
:ow early the move should be made is another question. &n $ia. 1 we have the same double sente situation at a-b on the upper edge, e!cept that now )hite still has a lot of scope for activity in the stone marked '; consider )hite c, for instance. &t would be a crime for him to play " and + in $ia. 3; he would only be hurting his chances to do something bigger in this area. :e should abstain, therefore, even if it means enduring 'lack b in $ia. 1.
@till, the competition to take double sente points tends to be rather intense. &n the game in chapter one, you will remember, a double sente point arose at a in $ia. 4. &f )hite played there he would be threatening to ump into 'lack*s corner, and if 'lack played there he would be threatening to ump into )hite*s upper side. &t was )hite*s turn, and although there was a larger gote move at b, he felt he could not put off a, so he played it before it was really sente, and the e!change in $ia. 5 followed. @uch e!changes are natural in close games.
"(
5. Problems ow you can apply what you have learned to the following problems. &n each one three possible moves are marked A, B, and ; assume that there is nothing else worth considering on the board and try to figure out the best sequence in which to play them. >our first step should be to e!amine the moves one by one and determine how much each is worth and whether it is gote, sente, or whatnot. e!t you should e!periment with different sequences and try to find the one that gives you the most profit. Finally, in order to score yourself, identify the largest move-not necessarily the largest in absolute value, but the one you should play first in the optimal sequence and the smallest move-the one that comes last of the three in the optimal sequence < and try to assign a numerical value < 1 points in double sente, for e!ample < to each move. %fter turning the page and reading the answer, give yourself ten points if you correctly identified the largest move and ten points if you correctly identified the smallest move, then subtract the total amount by which your numerical values were off the mark. Twenty points is thus the perfect score for each problem, and there is a scoring chart at the end.
Gargest moveHHHHHHHH smallest moveHHHHHHHHHH A:____ pts. inHHHH B:____ pts. inHHHH 8HHHH pts. inHHHH "+
Lr!est move8 <( points in sente. Dia. 1. &f )hite does not answer at (, 'lack ( kills him. Dia. 2. )hite " would enlarge the corner by ( points.
2n" lr!est move8 ' < + points in gote. Dia. 3. %lthough gote, this move has hidden value. Dia. 4. e!t 'lack can play " and + in sente. The reason he cuts at ", instead of ust playing + and letting )hite connect at ", is to leave a ko threat for himself inside )hite*s territory. Dia. 5. )hite " is gote, but it promises + in sente. 'lack*s territory is now " point smaller than before, and )hite*s territory, assuming "<', is ( points larger. %n easy way to visualiBe )hite*s gain is to take 'lack " in $ia. 1 mentally off the board, one prisoner point, and move )hite ( over to occupy its place.
"1
Smllest move8 %-"I points in gote. Dia. 6. 'lack " saves a prisoner, and ne!t 'lack a would make one point of territory. Dia. 7. )hite " takes a prisoner, but without making any territory.
ombination figure. 'lack takes his two points in sente at ", then goes to +. )hite*s connection at 1 leaves 'lack 3 and 5, at two points in gote, as the largest plays on the board, so 'lack makes them and )hite gets 6. 'lack has taken ' and , worth a total of five points. &f he had started with ', or + in the figure, followed by )hite " and 'lack 7, he would have picked up only four and a half points, which shows how two points in sente can be more valuable than three points in gote. )hite 1 at 3 would give the same net result, but from the standpoint of not leaving ko threats, 1 is best.
Gargest move HHHHHHHH smallest move HHHHHHHHH A:____ pts. inHHHH B:____ pts. inHHHH 8HHHH pts. inHHHH "3
Lr!est move8 ' < 1 points in gote. Dia. 1. $escending to " means that )hite will not have to connect around a, and ne!t he can push out at + in sente. &ncidentally, if )hite played " at +, 'lack could make a throw-in at ", and then )hite would have to connect around a. Dia. 2. 'lack " is gote, but + and 3 follow automatically. %fter mentally removing 'lack + and moving )hite 1 over, we see that )hite*s territory is three points smaller, and 'lack*s one point larger, than in $ia. ".
2n" lr!est move8 %<+ points in gote. Dia. 3. onnecting at " gives )hite one point of territory at ! and two at " # or three in all. Dia. 4. &f 'lack plays " and +, )hite immediately loses two of those three points, being left with only the prisoner point at ". )hite will ignore 'lack +, making it gote, but< Dia. 5. Then 'lack trades one prisoner for two and takes )hite*s third point away from him.
"4
Smllest move8 < ( points in gote. Dia. 6. &f 'lack has his eyes open he will not connect against )hite ", but play ( and make )hite connect. )hite has reduced 'lack*s territory by one point in gote. Dia. 7. @imilarly, 'lack can reduce )hite*s territory by one point in gote. The total value here is two points.
Comb$nt$on %$!ure. %ll three moves are gote, so the players take them in order of absolute value, from largest to smallest. The only possible variation in this sequence is that )hite could play 5 at 7, threatening 6. 'lack would defend at 5, and then )hite could connect at ". T&$s would give him one more point in the upper left corner, but one less point in the upper right corner. Either way, )hite ends the e!change in gote.
Gargest move HHHHHHHH smallest move HHHHHHHH A:____ pts. inHHHH B:____ pts. inHHHH 8HHHH pts. inHHHH
"5
Lr!est move8 '<+ points in reverse sente. Dia. 1. )hite " makes )hite*s territory two points larger, and 'lack*s territory one point smaller, than if 'lack got to play here first. Dia. 2. Thus the value of a move here is three points, but the important thing is that 'lack can play " and + in sente. &f )hite omits 1, then 'lack 1, )hite a, 'lack b, )hite c, and 'lack can capture )hite ( and a. That makes )hite " in $ia. " a reverse sente play.
2n" lr!est move8 < 3 / points in gote. Dia. 3. )hite can reduce 'lack*s territory and take a prisoner, but in gote. Dia. 4. 'lack*s connection saves him the four points of territory marked ! 8 add on the prisoner, and the value of 'lack " is five points. This is assuming that 'lack eventually descends to a in $ia. +. Dia. 5. %ctually, the value is a little more than five. 'y making the hane at " and winning the ko, )hite may be able to reduce 'lack*s territory by one more point, which adds a ?plus* to the five points counted in $ias. +-1.
"6
Smllest move8 %<1 points in gote. Dia. 6. 'y connecting, )hite keeps the one point of territory marked x . Dia. 7. 'lack " takes two prisoners. Dia. 8. %nd after connecting at ", 'lack has one point of territory at x . :e has made one point of territory, destroyed one point of territory, and taken two prisoners for a total gain of four.
Comb$nt$on %$!ure. %fter )hite takes the important reverse sente point at ", he and 'lack split the two remaining plays, 'lack taking the larger at 1. The absolute values of )hite " and 3 are three and four respectively, for a total of seven. &f )hite had started by cutting at 1 and carrying out $ia. +, 'lack would have played + in sente and captured at 3, getting two of the three plays. )hite*s gain would only be 3 / points.
Gargest moveHHHHHHHHH smallest moveHHHHHHHHH A____________ B____________ C____________
"7
Lr!est move8 <( - points in double sente. Dia. 1. )hite will answer 'lack " at ( to keep 'lack from continuing at a and gaining 1 / points in sente. Dia. 2. @imilarly, 'lack answers )hite " at ( to stop )hite a. &f we assume that )hite eventually descends to b, and that 'lack does so in $ia. ", the difference between 'lack " and )hite " is two points. )e have to degrade these two points somewhat for the possibility of 'lack b, but as double sente, they still have top value.
2n" lr!est move8 %<1 points in gote. Dia. 3. 'lack " is gote, but it makes + 'lack*s sente. Dia. 4. ow + is )hite*s sente, )hite has a point at x , and 'lack will eventually have to connect at two additional points around '. That adds up to four points in all.
Smllest move8 '-+I points in gote. Dia. 5. 'lack " saves " and captures ', but does not make any territory because a and b are miai.
(9
Dia. 6. )hite " saves ' and captures ", which makes a
difference of two points so far, and there is a further play left at a. Dia. 7. That play is worth three points < two at " and one at ! < but it is gote, so only half its value should be added on. )hite " in $ia. 4, or 'lack " in $ia. 3, is worth8 (/I ! +0+I points in gote.
Comb$nt$on %$!ure. 'lack plays " in sente, then +, and answers 1 at 5, so all )hite manages to get are the two points noted in $ia. 4. &f 'lack had begun at +, )hite would have gotten both " and 1, gaining 1- points. )orse yet, if 'lack had begun by playing at the right of 5, )hite would have gotten " and +, gaining 4- points.
Gargest moveHHHHHHHH smallest moveHHHHHHHH A________ B________ C________
("
Lr!est move8 % < 5 points in gote. Dia. 1. %ssume 'lack a and )hite b later. Dia. 2. 'lack " and + are gote, but they leave two white stones in atari. To compute their value, first imagine that )hite connects at ". %ssuming a-b at the edge, 'lack*s territory is two points larger than in $ia. ", and )hite*s is three points smaller, at b, ", and (. That makes five. Dia. 3. e!t, if 'lack captures at &, he gains another four points in gote. %dding in half of this, we get8 3/I ! 105 points in gote.
2n" lr!est move8 ' < 4 points in gote. Dia. 4. @ince )hite cannot hane at a in sente, we can assume 'lack a and )hite b. )hite has gained three points of territory8 two at " and one at x . Dia. 5. 'y connecting at ", 'lack also gains three points of territory, so the total value is si! points.
Smllest move8 < 1 points in gote. Dia. 6. %fter )hite ", assume 'lack a and )hite b.
((
Dia. 7. 'y playing ", or a < )hite ignores either move,
'lack can destroy the three points marked ! in $ia. 4. Dia. 8. Toward the end of the game the e!change from " to 1 is reasonable, so 'lack has augmented his own territory at ! , bringing the total value of 'lack " in $ia. 5, or )hite " in $ia. 4, to four points.
ombination figure. :aving the first move, )hite gets two of the three large plays. 'lack*s only gain is si! points for connecting at 1. &f )hite began at 1, 'lack would take $ia. (, gaining five points, and ne!t $ias. + and 5 would be miai, so 'lack would get one of them, bringing his total to nine points.
Gargest moveHHHHHHHHHH smallest moveHHHHHHHHHH A__________ B__________ C__________
(+
Lr!est move8 < 3 points in reverse sente. Dia. 1. 'lack " saves four points of friendly territory, and later on 'lack can play a in sente to rob )hite of ! . Dia. 2. )hite " to 3 are sente. 'lack cannot afford to answer " at +, because he would be risking considerably more than )hite in the ensuing ko fight.
2n" lr!est move' % < 6 points in gote. Dia. 3. &f 'lack played ", )hite would probably not defend at a. which would save only three points. Dia. 4. @o 'lack could keep on in sente as shown. Dia. 5. omparing this diagram with the last, we see that )hite " saves eight points8 two at " plus three more pairs.
(1
Smllest move8 ' < 4 - points in gote. Dia. 6. 'lack " may look bigger than it really is. Dia. 7. Even if 'lack connects at ", he only gains seven points8 four prisoners and three points of territory. Dia. 8. &f )hite recaptures at ", 'lack*s gain drops to five points, or four if )hite also gets to play a. 'oth $ias. 5 and 6 are gote, so we8 average them to obtain 4- as the value of 'lack " in $ia. 4.
Comb$nt$on %$!ure . 'y starting with the reverse sente play, 'lack is able to take two of the three large moves for a total gain of about eleven points. &f he had started with (, )hite would have played " in sente, then +, and 'lack*s gain would have been only eight points.
Gargest moveHHHHHHHHHH smallest moveHHHHHHHHHH A__________ B__________ C__________
(3
Lr!est move8 % < 1 / points in double sente. Dia. 1. )hite can play " and + in sente. Dia. 2. @imilarly, 'lack " threatens to kill the corner. The difference between these two diagrams is the four points marked x , plus a little more since in Dia. 2 )hite may have to give up another point to avoid a seki.
2n" lr!est move8 ' < "" points in gote. Dia. 3. )hite " rescues three white stones, and if 'lack plays elsewhere )hite can follow with +, capturing two black stones. &f 'lack tries to connect at a, )hite plays b.) )hite + is worth si! points in gote, as compared with 'lack + followed by 'lack c, )hite d. Dia. 4. %ssuming 'lack a, )hite b in this diagram, the total difference between it and $ia. + is fourteen points8 nine points of black territory, three prisoners plus the x*s, and
(4
five points of white territory, two prisoners plus c in $ia. +, but since )hite + in $ia. + is gote, only half its value, three points instead of si!, should be counted. )hite or 'lack " is therefore worth "1-+0"" points in gote. Smllest move8 < "9 points in gote. Dia. 5. )hite " means five points of territory for )hite8 two for capturing " and three for the ! *s. Dia. 6. 'lack " likewise means five points, so the value of a move by either side here is ten points.
Comb$nt$on %$!ure. )hite gains four points at " and +, then fourteen points at 3 and 5, making eighteen in all.
Gargest moveHHHHHHHHHH smallest moveHHHHHHHHHH A__________ B__________ C__________
(5
Lr!est move8 < 4 points in gote. Dia. 1. 'lack must answer )hite ( at +, or a white throw-in there is fatal. %fter this 'lack a, )hite b, and then )hite c, 'lack d are a fair assumption to make. Dia. 2. @uppose )hite plays l. &f 'lack replies at (, he has to keep on at 1, 4, and 6. )hite has erased two of the points marked x in $ia. " and been able to play both + and 3 instead of ust one of them, so his total gain is three. Dia. 3. &f 'lack ignores )hite ", )hite continues with +, 3, and 5 in sente and 'lack loses the other three points mark ma rkeed x in $ia. ", bringing the total difference between $ias. " and + to si! points in gote. 2n" lr!est move 8 % < 3- points in gote. Dia. 4. 'lack " promises 'lack +.
(6
Dia. 5. )hite*s territory is now two points larger than
before, 'lack ack*s is two points sma malller, er, and )hi hitte has captured a prisoner, making a total difference of five points. @ince 'lack may be able to recapture the prisoner, we count this as 3<. Smllest move8 ' < 1 points in gote. wi thout +, so it is gote. Dia. 6. 'lack " gains nothing without Dia. 7. )hite ", also gote, saves four points.
Comb$nt$on %$!ure. &n the best sequence 'lack takes the largest and smallest plays. onsider these alternatives8 i 'lack 1, )hite ", 'lack 3 and 5, )hite plays $ia. +. 'lack has gained 3 - on the left but lost 4 on the right. ii 'lack 1, )hite ", 'lack plays $ia. (, )hite 5. 'lack has gained 3 - on the left but lost 1/+05 on the right.
Gargest moveHHHHHHHHHH smallest moveHHHHHHHHHH A___________ B__________ C__________
(7
Lr!est move8 ' < 4 points in double sente. Dia. 1. )hite cannot afford to ignore 'lack ", and 'lack + and 3 are also sente. )hite a, 'lack b will come later. Dia. 2. )h )hit itee coul could d perfo perform rm th thee same same ma mano noeu euvr vree in sente. The difference is three points of territory on each side, or si! in all.
2n" lr!est move' %-"9 points in gote. Dia. Dia. 3. 'lack has gained five points of territory8 two for ' and three others. Gater, a will be )hite*s sente. Dia. 4. )hite also gains five points of territory if he plays first, so the total value here is ten.
Smllest move8 < ( points in double sente. Dia. 5. @ince 'lack cannot play a in sente, assume )hite a, 'lack b, and, of course, )hite c, 'lack d.
+9
Dia. 6. Making assumptions similar to those in $ia. 3, we
find that the difference between $ias. 3 and 4 is only one point of territory on each side, or two in all. Dia. 7. 'lack " is not necessarily sente, either. &f )hite igno ignore ress it, it, th thee +-1 e!ch e!chan ange ge cost costss hi him m on only ly th thre reee addi additi tion onal al points, averaging 'lack a and )hite a. That is, 'lack " and + put together gain only (/+03 points.
Comb$nt$on %$!ure. 'lack takes both big points with " and 5 while )hite gains only a small amount on the right edge. @ome alternatives8 i 'lack plays 5 at "(, )hite "9, 'lack a. 'lack has given up ten points on the left sside ide to get only five on the right. ii 'lack plays " at 5, )hite plays ", 6, "9, and "(. 'y letting )hite play ", 'lack has lost si! points. iii 'lack plays " at "(, )hite plays " and "9, 'lack plays a. :e has given up 4/"90"4 points to gain only five.
Sor$n! C&rt Croblem
" ( + 1 3 4 5 6 7 total
>our score Total
39
Dank
6 kyu
4 9 5 9 6 9 7 9 " 99 " " 9
"(9
"+ 9 " 1 9 " 3 9 " 4 9
"5 9
5
" kyu
" dan
3 dan
4
3
1
+
(
+"
(
+
1
CHAPTER 3 Endgame Tesuji The endgame has its own special brand of tesuji, mostly concerned with the edge of the board. Many of them are only one or two points better than the more obvious alternative plays, but if you go through the endgame losing one point here, two points there, and so on at every turn, your losses can quickly mount up. On the other hand, if you can outplay your opponent by just a couple of points in half a dozen places, you can overtake a tenpoint lead.
Defending Territory Dia. 1. !hite has just come sliding into "lack#s upper right corner with '. $o you know the correct response% Dia. 2. &our first reaction might be this diagonal play, but !hite can jump in front of it with ' and do plenty of damage.
Dia. 3. (ne)t page* +n aggressive player might try this contact play, but it leads to an e)change, !hite living with ' to . The question is how much "lack can do in return to the white territory to the left. $epending on the answer, "lack could be the best move, and !hite might have to draw back to instead of bending out at ', but the odds are that "lack has taken a loss. Dia. 4. /f there were 0a0 black stone at a, this inside contact play would be a tesuji!hite would have to reply at 0b0 and
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"lack could then play 0c0 1 but as things stand !hite can play ' and "lack#s position has worsened considerably.
Dia. 5. The correct move is frequently to confront !hite on the second line, one space away. !hite cannot get anywhere with ', because he runs into the stone marked ". Dia. 6. !hite ' here is better, but "lack can complete his defense with 2.
Problem 1. !hite to play. 3ow can he defend the largest amount of corner territory% Problem 2. !hite could capture two stones by wedging in at the point, but he has a better way. Problem 3. "lack to defend the corner.
'
Answer to problem 1. /f "lack 2, !hite '. Dia. 1a. /f !hite plays - here, he lets "lack push him around with ' and 4 and comcs out about four points worse off.
Answer to problem 2. The clamp at - makes ' and 2 miai, and no doubt you have already verified that "lack 2, !hite ', ends badly for "lack. Dia. 2a. +gain, the wrong answer is four points worse.
Answer to problem 3. "lack - should be the first move that occurs to you in this shape. Dia. 3a. "lack#s territory may be the same as before, but !hite#s is two points larger.
Extensions $uring the opening, e)tensions are generally made on the third or fourth line, but during the endgame, they are often made on the second line. 2
Dia. 1. $uring the opening, a would be the natural e)tension point for both sides in this position. Dia. 2. /f !hite e)tended to - during the endgame, however, "lack could reply immediately at ', and on the edge, at least, !hite would have gained no profit. Dia. 3. /n the endgame, the correct e)tension is likely to be the large knight#s move on the second line to -. /f "lack replies at ', !hite can defend at a for a large profit, or he can leave this as a forcing e)change and turn eleswhere. Dia. 4. /f "lack presscs at ' he can make !hite reply at 2, but this leaves his corner open to !hite a, b, etc. Problem 1. "lack to play. !hat should he do on the lower edge% Problem 2. !hite to play% 3ow should he e)tend toward "lack#s very strong corner position%
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Answer to problem 1. "lack can keep on with a or b after !hite ', but even if he leaves the corner as it is, he has gained something from the e)change. Dia. 1a. 5or e)ample, suppose !hite later clamps him at -. 6eaving aside the possibility of drawing " out at 2, "iack can play ' and then 4, which threatens "lack a while preventing !hite 4. /f he had somehow played " after !hite - and 2, !hite would have answered at a, not ', and "lack 4 would not have worked.
Answer to problem 2. !hite - is the best e)tension. "lack cannot invade behind it7 "lack cr, !hite 8, for e)ample. Dia. 2a. /f !hite e)tends on the third line, "lack can invade at '9 after "lack , if !hite connects at a, "lack cuts at b. /f !hite plays - too conservatively at ' or 4, "lack can countere)tend to 2.
The Hitting-Under Tesui Dia. 1. !hen two stones oppose each other like ' and " the diagonal move at - is a common endgame play, but it is well to remember that about half the time, as here, there is an even better play.
Dia. 2. !hite should hit under the opposing stone with -. 3e still keeps sente, and his result is at least two points better than in $ia. -. Dia. 3. -f "lack captures !hite -, !hite can break through with 2, , and :, and "lack is going to lose more in the center than he has gained on the side. Problem 1. !hite to play. !hat use can he make of his two stones in the corner% Problem 2. "lack to play. !hite might make the diagonal play in this position, but "lack has a better move.
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Answer to problem 1. !hite - threatens to revive the two stones in the corner, and "lack has to defend with ' and 4. Dia. 1a. /f he plays ' here, !hite lives with 2 to ;.
Answer to problem 2. "lack should clamp at -. 3e can connect at a after !hite 4, or he can leave the position unconnected. /n the latter case he has still gained, because now a would be gote for !hite instead of sente. Dia. 2a. /f !hite wants sente badly enough, to make some other big play, he can connect solidly with ', but then "lack draws back to 2. This means a big local loss for !hite.
!n the "irst #ine Dia. 1. (ne)t page* "lack has an opportunity to make a fourpoint reverse sente play in the corner. !hat should it be%
:
Dia. 2. This hane is wrong. /t lets !hite make the throwin at ', which will force "lack to connect eventually at 0a0. =ote that "lack cannot play b, and that if !hite plays b, "lack cannot connect at '. Dia. 3. The correct move is to descend straight to the edge with -. Dia. 4. 6ater "lack can make this e)change in sente, so !hite#s territory is the same as it was in $ia. ', and "lack#s is from one to three points bigger. This has been one e)ample of defensive firstline technique. The ne)t four problems are concerned with offensive firstline technique. Problem 1. "lack to play on the left edge. /t would be wasteful of him simply to hane. Problem 2. !hite to play. Problem 3. "lack to gain three points in sente. Problem 4. !hite to play. /t takes some reading out, but he has a much better play on the left edge than the hane.
Answer to problem 1. "lack can connect either up or down the edge. Answer to problem 2. /f "lack plays ' at 2, !hite cuts at '. Answer to problem 3. This is two points better for "lack than playing - at 2. Answer to problem 4. !hite can jump all the way in to l. /f he haned with - at 2, "lack would answer at -. Dia. 4a. /f "lack wants to try to cut !hite off, he can only play ' and 4 like this, but !hite and : trap him in a shortage of liberties.
$l%&ement Tesui Dia. 1. (ne)t page* /n this position !hite can hane at a in sente, but we are interested in what "lack can do if he gets a chance to play first. Dia. 2. 3e has an interesting placement tesuji at -. Dia. 3. /f !hite blocks at ', "lack comes around with the hane at 2. /f !hite tried to stop that at , "lack would cut at 4, so !hite connects at 4 and "lack plays . 3e need not connect at a (three points in reverse sente* after !hite
;
8. >ven after !hite a, he has still gained about four points in comparison with !hite a in $ia. -.
Dia. 4. +ctually !hite ' in this diagram is slightly better than ' in the last diagram, but "lack links up with 2 and . Once again, even without connecting (five points in gote* after !hite 8, he has made a profit. Problem 1. !hite to play in the corner. The hane is the obvious move, but it gains in effect if preceded by a placement tesuji. Problem 2. "lack to play on the right side. Problem 3. !hite to invade "lack#s territory.
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Answer to problem 1. !hite - and 2 are a standard combination. "lack could reduce the damage somewhat by playing 4 at , (followed by !hite 4, "lack 8*, but then he would end in gote. Answer to problem 2. /f !hite plays ' at , then "lack 4, !hite 2, and "lack ' mean a disaster. Answer to problem 3. !hite - threatens !hite 0a0, which would save the three white stones and kill the three black stones in the corner. "lack has to prevent this with ', and !hite can link up with 2 and . !hite - at ', followed by "lack a and !hite 2, would be a failure, since "lack could capture the invaders with a hane below 2.
'(uee)ing Tesui Dia. 1. !hite has a spectacular way to make use of the stone marked '.
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Dia. 2. 3e starts with this diagonal move, which is the eyestealing tesuji with respect to both !hite ' and the coming white hane at 0a0. Dia. 3. "lack#s only answer is to give atari at '. !hite gives a counteratari at 2, squeezes with , and connects at :. "lack loses most of his territory and may even be in eye trouble.
Dia. 4. @laying the hane at !hite - would let "lack take the key point with ', and after that !hite could not do quite the same damage as in $ia. 2. Problem 1. "lack to play. /f he uses his stranded stone to carry out a squeezing maneuver, he can reduce !hite#s territory by a huge amount. Problem 2. !hite to play. !hat can he do on the lower edge%
-'
Answer to problem 1. "lack sacrifices - in order to squeeze !hite with 2, , and :. /f he played / at , !hita would answer at 2. Answer to problem 2. This sequence is clearly better than playing - at 2 and letting "lack answer at -.
The *on+ey ,ump Dia. 1. !hen !hite has "lack#s territory undermined by a stone like ' on the second line, he can reduce it by sliding in to l. This move is called the monkey jump. There are various ways to answer it, but the one thing "lack should not do is to give way and play 0a0.
Dia. 2. /n this particular position, the contact play at "lack - is his best reply. Dia. 3. The monkey jump in $ias. -' gained nine points in sente as compared with "lack - here. /t reduced "lack#s territory by si) and, since a is "lack#s sente, increased !hite#s by three.
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Dia. 4. !ith the position changed, "lack - no longer works, but "lack has a whole arsenal of other responsesat a, b, c, d, and even ' 1 to choose from. Aee problem -. Dia. 5. 3ere is a case where if !hite draws back at 2, he ends in gote, but this is wrong. Bnless the enemy ignores it completely, the monkey jump should never lead to gote.
Dia. 6. To keep sente, !hite should jump back to - and ignore "lack ', leaving a and b as miai. 3is profit is only slightly less than in $ia. . Dia. 7. 3e can also treat !hite ' as a forcing move and abandon it. /f "lack captures it, his profit is still two points less than1 Dia. 8. — if he had been allowed to play - here. Problem 1. 3ow should "lack answer !hite#s monkey jump% Two of the five moves suggested in $ia. 4 are correct. Problem 2. !hite to answer "lack#s monkey jump. This one is harder to stop9 only one move does the job properly.
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Answer to problem 1. "lack - and the throwin at 2 fit this shape nicely and keep !hite under control. Dia. 1a. The order of "lack - and 2 is reversible, and !hite can save the connection at - as a sente play for later.
Answer to problem 2. !hite - halts "lack in his tracks. /f "lack ' at 2, !hite would leave "lack with gote. Dia. 2a. "lack cannot press forward with '9 his whole group dies. "etter than the Monkey Cump The monkey jump is such a good move that it is easy to get into the habit of playing it automatically, but there are lots of times when another move is even better. Dia. 1. (ne)t page* 3ere it would definitely be a mistake. "lack bas a good reply to it at 0a0, but he can also ignore it, since !hite has no very e)citing followup move.
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Dia. 2. The better play is to jump in on the second line to -. !hen possible, this onepoint jump is superior to the monkey jump nine times out of ten. /f "lack ignores it, !hite has a very big followup move at 0a0. Dia. 3. 3ere is one likely continuation. >ven if "lack has enough ko threats to play 8 at a, !hite still gets a better result than with the monkey jump because he more definitely ends in sente. Dia. 4. /f !hite has enough ko threats, he can also play this way. /f "lack descends to : with 8, !hite a catches him in a snapback. Problems. /n each a monkey jump on the first line would be possible, but there is a better move. Aee if you can find it. "lack is to play in problems -D', !hite in 2D4.
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Answer to problem 1. "lack can play at a or, if he has the ko threats, at 0b0. Answer to problem 2. +dding to the effectiveness of "lack - is the fact that !hite a, "lack b, !hite 0c0, "lack d puts two vhite stones in atari. Answer to problem 3. !hite 2 at a is a possible variation. Answer to problem 4. This sequence works out to be two points better for !hite than the monkey jump.
Defending the Edge / Dia. 1. 3ow should "lack answer !hite#s hane at '% 3e would like to give atari at a, but !hite would then give a counteratari at b and the result would be disastrous. "lack is suffering from an empty triangle compounded by a shortage of liberties, so he must be prepared to retreat a little.
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Dia. 2. The ne)t move to consider is drawing back at -, but this makes horrible shape without really stopping !hite, who can jump out to '. "lack has to answer !hite ' at 0a0. !hite ' is not the worst he has to fear, however, for !hite may play a instead of ' and use that to attack his eye shape or mount an invasion of his entire upper side. Dia. 3. The correct move is the diagonal connection, which makes e)cellent shape. =ow "lack is ready to block at 0a0, if !hite lets him.
Dia. 4. /f !hite can do so in sente, he will carry on with ' and 49 barring the unlikely case of his being able to play 2 at 4 and win the ko, "lack cannot help giving up this much territory. +t least he has kept his position strong and avoided getting into more serious trouble. Problem 1. !hite to play.
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Answer to problem 1. !hite - at ' is impossible 1 "lack cuts at - 1 and !hite - at would let "lack play 2 and cause an unnecessary twopoint loss. Answer to problem 2. !hite - is the only way to stop "lack. +fter "lack 0a0 and !hite 0b0, !hite has twelve points left, counting a prisoner at the '4 point.
Defending the Edge / Dia. 1. Once again the question is how to answer a white hane on the edge. "lack cannot help giving way, but if he plays correctly, he can stop !hite from following up his hane in sente.
Dia. 2. This "lack - is a mistake, since !hite can play ' and 4 in sente. Dia. 3. The right move is this "lack l, the eyeprotecting tesuji.
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Dia. 4. True, !hite can jump to ' and reduce "lack#s territory by one more point than in $ia. ', but !hite ' and 4 are gote. Dia. 5. More than likely !hite will not take gote to play as in $ia. 4, and "lack will be able to block at - in sente. =ow his corner is two points bigger than in $ia. '. Problem 1. "lack to play and defend thirteen points of territory in sente. (3e has captured one prisoner.* Problem 2. !hite to play. Eecall what "lack#s move would be in this position. Problem 3. !hite to play. The obvious blocking move lets "lack hane and connect in sente, so look for an alternative.
'?
Answer to problem 1. "lack -, threatening 4, is the right defense. /t is also the point to which !hite would e)tend if "lack failed to defend. Dia. 1a. Fiving atari at - and then playing elsewhere is the same as making no defense at all. Answer to problem 2. !hite -, taking the same point that "lack would take, is the correct dcfense, although !hite a would be about equally good. Dia. 2a. !hite - here is a mistake 1 !hite cannot connect after 4 because of "lack aand !hite - at ' would be unthinkable.
Answer to problem 3. +fter !hite 2, "lack a would be gote. Dia. 3a. Thus !hite gets to play - and 2 in sente. Dia. 3b. /f !hite plays - here, "lack ' and 4 are sente.
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The 0ext *oe Dia. 1. There are times when you have to hold yourself to a smaller than possible immediate profit in order to prepare for a large ne)t move. That is the case with !hite in this position. Dia. 2. /f he descends at -, "lack descends beside him at ', then at 4, both times threatening to wedge in at and capture.
Dia. 3. 3e can do better if he holds himself to this !hite initially. /f "lack connects at a after 2, !hite has sente. Dia. 4. /f "lack does not connect, !hite can make this capture, which threatens a further move at a or b. The initial play in $ia. 2 was small, but the bonus it made possible in $ia. 4 is huge. Problem 1. "lack to play. /f he restrains himself, he has a nice reversesente play on the lower edge. Problem 2. !hite to play. 3ow should be handle the lower side 1 with a large knight#s move, a small knight#s move, or a diagonal move%
''
Answer to problem 1. "lack should descend to -, preparing for the tesuji at 2. Dia. 1a. /f he hanes with -, he has no ne)t move, and !hite#s territory is two points larger.
Answer to problem 2. !hite - must precede !hite 2. /f !hite played 2 first, "lack could capture it by playing -. Dia. 2a. /f !hite makes this small knight#s move, he ends in gote with about five points less than in the correct answer.
Tesui to T%+e 'ente Dia. 1. /f "lack neglects the left edge, !hite will hane at 0a0. "lack would like to prevent that, and if he plays correctly, he may be able to do so in sente.
'2
Dia. Dia. 2. Food for you if you spotted the descent to "lack -, which is better than the hane at a because it gives "lack the following jump to 2. /f !hite wedges in between - and 2 at a, "lac "lack k b starts a big ko. The only trouble with this is that if !hite simply ignores "lack, both - and 2 are gote. Dia. 3. "lack#s tesuji is to play - first. /f !hite ignores that, "lack can play 2 in sente. Dia. 4. +ccordingly, !hite will be more likely than in $ia. ' to answer "lack -, allowing "lack to descend to 2 in sente. /f !hite tries to play ' at 2, he runs afoul of the ko again. Problem 1. !hite to defend the left edge in sente. Problem 2. "lack to defend the corner in sente. Prob Proble lem m 3. !hite to play. 3e gets his largest profit by capturing the black stone, but that is gote. There is a way for him to handle the left edge in sente instead.
'4
+nswer to problem -. !hite - and 2 are hard for "lack to ignore, and they make the descent to an atari. /f "lack plays 4 at 0a0, !hite can turn elsewhere and "lack cannot hane at . !hite - at would threaten -, but "lack could ignore it, and then both !hite and - would be gote. Answer to problem 2. !hite 4 at 8, followed by "lack 4 and !hite l, is a possible variation. "lack - at 2, followed by !hite - and "lack 0a0, would give "lack more profit, but in gote.
Answer to problem 3. !hite - yields only three points less than capturing at ' would do, so when sente is worth more than three points, it is correct. Dia. 3a. /f "lack ignores !hite -, !hite will not capture his stone but leap into the corner with 2. This is much bigger9 ne)t !hite can play 0a0.
'%&rifi&e Tesui /n th thee prev previo ious us sect sectio ion n we saw saw th thre reee e)am e)ampl ples es of sacrifices made in order to take sente. /n this section we shall see some sacrifices that actually yield profits as well as sente. Dia. Dia. 1. (ne)t page* !hite has to save two of his stones from being cut off. '
Dia. 2. The obvious way to do this is to connect at -. "lack draws draws straight back with ', instead instead of playing on the third line, so as to be able to hane at a in sente. "y allowing this, !hite has not done his best. Dia. ia. 3. !hite#s tesuji is to sacrifice -, so that after 4 "lack can no longer longer hane at 0a0. That makes makes !hite#s corner two points bigger than in $ia. ', but the surprising thing is that "lack#s territory is also one point smaller. "lack has been given one prisoner, but he has to play twice inside his own territory 1 at 4 and, a nd, later, 0b0 1 to capture it. Problem 1. "lack to play on the right edge. Problem 2. !hite to play on the right edge. Problem 3. "lack to play. Problem 4. !hite to play. /f he starts with a hane on the right edge, he loses one point.
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+nswer to problem -. "lack - is a profitable sacrifice. hite te is allo allowe wed d to conn connec ectt at ', then then a Dia. ia. 1a. /f !hi becomes his sente and his territory is two points larger. l arger.
Answer to problem 2. !hite begins by playing - so that "lack will have to capture two stones instead of just one. Dia. 2a. /f he blocks with -, then since a is "lack#s sente, the corner is the same size as before, and "lack#s territory is two points larger. Answer to problem 3. "lack - at :, !hite - would mean a twopoint loss for "lack.
Answer to problem 4. "lack 4 at a, !hite b would be a bad ko, and if "lack omits 4 1 Dia. 4a. !hite - and 2 gain three points in sente. Dia. 4b. Aince a is his sente, "lack#s territory is one point larger than in the correct answer.
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edging Tesui The sacrifice tesuji of the previous section worked by forcing the enemy into a shortage of liberties. The tesujis of this section work in the same way.
Dia. 1. !hite to play. Dia. 2. /t would be rather thoughtless of him to treat this as a onepointinsente situation and push up with -. Dia. 3. /nstead, he should wedge in at -. "lack would be putting himself in atari if he played ' at 2, so he has to give way with ' and !hite gains three points in sente. Problem 1. "lack to play. 5ind his tesuji and !hite#s best answer to it. Problem 2. "lack to play and defend his corner. Problem 3. !hite to play. Problem 4. !hite to play and reduce "lack#s territory by two points.
'
+nswer to problem -. !hite should answer at ', not a, so as to end in sente. Dia. 1a. /f !hite cuts "lack off with ', he risks a big loss in a ko.
Answer to problem 2. "lack at a (ko* is worth considering, but even if "lack has to give way with and on through the ne)t diagram, !hite is still haunted by a shortage of liberties. Dia. 2a. 3e could not connect against "lack 0a0, for e)ample. Answer to problem .3. !hite - and 2 gain two points in sente. /f "lack does not connect at 4, !hite has a throwin. Dia. 3a. !hite - gains another two to four points. Dia. 3b. This !hite - would gain only one point.
Answer to problem 4. !hite - threatens a. "lack will have to connect at a later.
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%pturing
Dia. 1. 3ow should "lack capture the three white stones so as to get the greatest profit% Dia. 2. This way gives him only seven points of territory7 three prisoners plus the point marked ). Dia. 3. "lack - and 2 are the right combination. They may be played in either order. Dia. 4. +fter both sides have connected "lack need make no further moves, so he has two points more than before. Problem 1. "lack to capture the two white stones. Problem 2. "lack to play. /f he leaves this position alone, !hite can start a multistep ko. Problem 3. !hat is "lack#s best way to capture% Problem 4. !hite to play and make seven points of territory by capturing three stones.
2?
Answer to problem 1. +fter 2, "lack will not have to fill any more liberties. Dia. 1a. This hane gives him one or three points less profit, depending on whether !hite lets him capture ' or not. Answer to problem 2. +fter -, if !hite opens the ko, "lack makes an eye with 2. "lack - also prepares for "lack 0a0.
Answer to problem 3. "lack#s eye is safe. /f !hite descends to 0a0, "lack 0b0 holds him in check. Dia. 3a. This sequence loses "lack four points. Answer to problem 4. !hite - confronts "lack with the choice of being captured at ' or having !hite descend to 2, which makes !hite a destructive. Dia. 4a. This hane gives !hite one less point of territory, and !hite 0a0 loses some of its force.
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Du%l-$urpose *oes
Dia. 1. 3ow should "lack defend the left side, where !hite is threatening both a and, more seriously, b? Dia. 2. /f he plays the obvious -, !hite can later capture with ' and 4. =e)t !hite a is possible. Dia. 3. The right move is this dualpurpose diagonal connection, which defends against both threats. The linkage between it and "lack " is unbreakable7 !hite 0a0, "lack 0b0, for e)ample. Problem 1. !hite to play on the left side. Problem 2. "lack to defend the left edge. Problem 3. "lack to play. 3ow should he connect% Problem 4. !hite to play on the left edge.
2'
Answer to problem 1. !hite - links across to ' and enables !hite to play 2 to : in sente. Answer to problem 2. "lack - is two points better than "lack 0a0, one point because he can push out at b in sente and one point because he has not filled his territory unnecessarily at 0a0. Answer to problem 3. +fter !hite a and "lack b, "lack will be in just the right place, giving "lack the ma)imum amount of territory. Answer to problem 4. !hite - threatens ' while protecting !hite ' from capture. /f "lack connects at ', !hite can hane at 2 in sente.
n%sions Dia. 1. (ne)t page* Occasionally the enemy makes a mistake and gives you the chance to reduce one of his territories more than just slightly. This diagram shows a good e)ample. "lack is trying both to guard the cutting point at a and keep !hite from playing b in sente, and "lack - would be an e)cellent dualpurpose move if it worked, but it does not. Dia. 2. "lack has seen that if !hite drives him down the edge, even the jumpingahead tesuji at cannot stop him from linking up with 8.
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Dia. 3. "ut he has forgotten about the throwin at :. /f he catches himself in time, he will answer !hite - in $ia. ' at the point between 2 and , but he still loses nearly half his territory. Problem 1. !hite to invade "lack#s corner. The sequence involves a ko. Problem 2. "lack to invade !hite#s corneranother ko. Problem 3. "lack to invade !hite#s corner.
24
+nswer to problem -. /f "lack connects with 8, !hite : makes a living group. "y playing 8 at 0a0, "lack can get a ko, but what he should have done befere all this started was to draw back with " at 2. Answer to problem 2. The ko is direct9 "lack can win it by connecting.
Answer to problem 3. "lack 2 at works, too. !hite should play ' at 4, followed by "lack ' and !hite 2 or 9 then at least he can live. Answer to problem 4. /f "lack plays ' at 2 or , !hite e)tends to ', gaining three liberties, then captures the two corner stones and kills the whole group. =ote that !hite at 2 would fail, "lack answering at .
2
Tesui th%t Att%&+ Eye 'h%pe
Dia. 1. >ven when an enemy group cannot be killed, it may be possible to earn a large profit by attacking it in the right way. That is certainly the case here. !hat should !hite do% /t would be a bad mistake for him to give atari at 0a0. Dia. 2. 3e should steal the eye at ' with - and 2. "lack can still live, but !hite trims him down to three points of territory in sente. Dia. 3. &ou can get an idea of the size of the moves in the previous diagram by comparing it with this one. =ow "lack has eight points of territory, and !hite has the cutting point at a to worry about. Problem 1. "lack to play. "y threatening the group in the corner, he can make a tremendous invasion of the area to the left. Problem 2. !hite to play. /f he attacks the group on the lower side in the right way he can capture part of it in sente.
28
Answer to problem 1. "lack - threatens ' and a ko9 if !hite connects at ', "lack can jump all the way in to 2. Answer to problem 2. /f "lack plays ' at 2, !hite a, "lack 4, and !hite ' kill him, and "lack ' at 0a0, !hite 2 would mean a lifeordeath ko. !hite - at 0a0, "lack 4, !hite ', "lack -, and !hite a is another possibility, but it ends in !hite#s gote.
*is&ell%neous Tesui There are many, many other positions in which the right tesuji will yield a little e)tra profit. 3ere are a few of them.
Dia. 1. !hite has lost two stones, but he can use them to squeeze "lack in sente. 3ow should he start% Dia. 2. /f he turns in at -, "lack can block with ', then answer !hite 2 by descending to 4. 6ater, as !hite connects, he will capture with a and b. Dia. 3. !hite can get a bigger share of the corner if he starts with - in this diagram. +fter 4 "lack#s territory is one point smaller than in $ia. ' and !hite#s is, if we average !hite a and "lack a, two (* points larger.
2:
Problem 1. "lack to play.
2
Answer to problem 1. "lack - (four points in gote*, is better than - at (one point in sente*. Answer to problem 2. /f "lack plays ' at 2, !hite 2 at a makes a big, onesided ko. Answer to problem 3. "lack cannot fight this onesided ko, so he may as well connect at 4. "lack ' at 2, !hite ' would lose him the corner. Answer to problem 4. "lack - threatens "lack ', so !hite has to connect there and let "lack earn the ma)imum.
Answer to problem 5. !hite - takes advantage of the stone marked '. /f "lack answers at a, !hite can give atari at b, then turn elsewhere. Answer to problem 6. "#ack -, the eyestealing tesuji, cannot be captured 1 !hite ' at 0a0, "lack 2, for e)ample, or !hite 4 at , "lack 0b0, !hite a, "lack 4 1 so !hite#s best course is to connect at ' and 4 and make "lack link up in gote with 2 and .
2;
ut4 l%mp4 or H%ne5
Dia. 1. $uring the endgame, when a stone like "lack " is unprotected by any direct form of connection, there are generally three moves for !hite to consider. Dia. 2. /f nothing else works, !hite can always hane at - and "lack will have to give way at '. /f he blocks at 0a0, !hite can cut at ' and start a dangerous (for "lack* ko. Dia. 3. Much more effective is the clamping tesuji. /f "lack descends to a, !hite must be ready with a counter move at, for e)ample, b, c, or 0d0. Dia. 4. Most effective of all, when it cannot be captured, is the direct cut. Problems. /n each the question is whether to cut, clamp, or hane, e)cept that in problem 2 0push out# replaces 0cut#. !hite to play in - D 4, "lack to play in ' D 2
4?
Answer to problem 1. "lack connects solidly at ' so as to give himself the option of taking sente after 2. !hite - at ' would not work, because "lack would give atari at 0a0. Answer to problem 2. /f !hite plays ' at , "lack 4 leaves the whole side dead. Answer to problem 3.
H%ne or Des&ent5 Dia. 1. (ne)t page* /n this type of position, whether to hane or descend on the right side can be a difficult problem.
4-
Dia. 2. The hane gives more profit, but tends to be gote, unless !hite can follow it with a cut or clamp. Dia. 3. The descent gives a smaller profit than the hane if answered, but a larger profit if "lack ignores it and lets !hite jump in to 0a0.
Dia. 4. +nother possibility is to play the hane as a forcing move, as !hite is doing here, and not connect immediately at a. /f "lack cuts at 0a0, !hite has a good defense at 0b0. Dia. 5. /f "lack hanes at - first, !hite has to defend at ', not a, and after 2 "lack can hane again at 0a0, forcing !hite to give way to 0b0. Problem 1. "lack to play7 hane or descent% One of the two is automatically correct in this position. Problem 2. !hite to play7 ditto. Problem .3. "lack to play7 ditto. Problem 4. !hite to play7 ditto.
4'
Answer to problem 1. "lack descends in sente to i. !hite#s best answer is to connect solidly at '. 6ater, he will have to connect again at 0a0. Dia. 1a. /f "lack hanes, he gets only about one point more of profit than before, and in gote instead of sente.
Answer to problem 2. 5irst of all, !hite should hane at -.
42
Answer to problem 3. /n this position the correct move for either side is to descend. "lack 2 and are sente. Dia. 3a. Auppose "lack hanes. /f !hite omits 4, "lack is stuck with gote, while if !hite plays 4, "lack gets only the same profit as before, (assume !hite a, "lack b. That means that the hane may be worse than descending and cannot be better.
Answer to problem 4. /f "lack answers !hite -, then ' is the proper point, (although a jump down to the first line would probably come to the same thing*. /f "lack does not answer, then !hite will jump forward to ' himself. Dia. 4a. =ow !hite has gote, and !hite 0a0, "lack b etc. will yield him less than !hite -, "lack elsewhere, !hite ' would in the correct answer diagram. /f !hite wanted the result in $ia. 4a, he could get it by continuing from the correct answer. That in itself is enough to remove the hane at - from serious consideration.
44
CHAPTER 4 The Macroendgame
The preceding two chapters have been concerned with what might be called the microendgame, that is, with fairly small, localized situations. This chapter looks at the macroendgame, (in Japanese the oyose), where the moves are larger, precise counting is more difficult, and the board must be considered as a whole. The macroendgame has much in common with the middle game, and it is partly governed by middle-game strategy: attack weak enemy groups to make profit in sente defend weak friendly groups before your opponent attacks them don!t chase your opponent into your own potential territory etc. "erception is important, too. #ou have to see the crucial weaknesses in one side!s position that give the other side large moves. These weaknesses, which often amount to invasion points, may not be obvious, but they are what the endgame should really be all about. $ine macroendgame problems follow, with five possible answers marked %&% to %'% in each. ark down your choice, then turn the page. 'ach answer is evaluated and a scoring chart is provided at the end of the chapter.
)
Problem 1 *hite to play This problem comes from a game in a ladies! professional tournament. +f the five moves shown, one is very large, three are of moderate size, and one is a mistake.
Your choice :
Correct answer: C (10 points). This clamping tesui cuts lack!s biggest territory in half. *hite has other good moves at %a%, (which could lead to an e/change of most of lack!s center territory for most of *hite!s upper side territory0, and %b% to play ne/t, and she can hardly lose. 1f lack descends to in 2ia. ), *hite cuts at 3. D (8 points). <hough *hite ) in 2ia. on the ne/t page is not an urgent move, it is still big because it enables *hite to ump into the corner at %a%. lack will probably answer at and 4 in 2ia. 3, then go to the upper right, planning to meet *hite a with lack %b%. *hite ) has some additional value in that it enables *hite to link up with her group to the right, but that will not actually yield much territory if lack plays %c%, *hite %d%, lack e in sente first.
3
A (6 points). 5ompare 2ias. 4 and 6 below. 1f lack answers *hite ) in 2ia. 4 at %a%, *hite has gained nine points in sente. *hite or lack %a% is worth si/ points in gote (you should verify these figures0. *hite or lack ) is thus worth 78()9 / 0;) points in gote, but twelve points in gote are nothing when compared with the correct answer.
4
B (4 points). *hite ) in 2ia. is worth about nine points, *hite %a% being sente later. $ote that if lack hanes here, as in 2ia. <, her continuation is lack a, *hite b. =he cannot cut at the right of or clamp at %b%.
E (2 points). *hite ) in 2ia. > may not be completely worthless, but why play it? 1f lack descends to ) in 2ia. 7. *hite responds with , threatening a and b, thus capturing lack ) and two other stones.
6
The clamping play of the first problem is an e/ceedingly destructive tesui, but the ne/t problem contains some even larger moves. 1t is taken from a game between two nine-dans. The board is still rather open, for the endgame has ust begun.
Problem 2 *hite to play Your choice :
Correct answer: C (10 points). *hite ) is best not only because of its direct territorial value, but also because it attacks the eye space of the black group on the right side. 1f lack defends by running out with and 4, *hite has sente to take the ne/t biggest point at 6. 1f lack does not defend, *hite can attack at 3.and contain lack in sente, building toward a large center territory. E (8 points). *hite ) in 2ia. ) on the facing page is @uite large, and it gives eye space to a somewhat unsettled white group, but lack will ignore it and play . *hite can then ump from ) to a, but that does not make up for the loss he has suffered on the right side.
<
A (6 points). *hite ) in 2ia. works out to be worth about twelve points in gote. 1f lack connects at %a%, *hite has gained about si/ points in sente, as compared with 2ia. 3, and *hite a would be worth another twelve points in gote: 8()9/)0;). *hite ) does not attack or defend any weak groups, however, and its value is far below that of the previous two answers.
>
B (4 points0. *hite ) in 2ia. 4 is not really a good move. 1t comes too close to the solid lack wall above, and there is ample danger of lack!s being able to break through around it in the future. lack will reply at , of course.
D (2 points). *hite ) in 2ia. 6 is a bad overplay. 1t reduces lack to one eye, but at the same time it weakens the adacent white group to the left. etween defending that group and hanging on to ) and 3, *hite has no real chance of killing lack. The only result of this attack, then, will be to drive lack into the center and spoil the potential territory that *hite had there.
7
oves like the correct answer in the previous problem, that attack an enemy group!s eye shape and take a large profit at the same time, are never bad. They are almost always to be preferred to large moves that do not attack, or to attacking rnoves like the ones in 2ia. 6 on the facing page that do not make any direct profit. 1n the ne/t problem neither player has much chance of making territory in the center, so the choices are all at the edges.
Problem 3 lack to play Your choice :
_+++++++++++++++++| [{{{{{{{{{{{{{{{{{] [µ~{{{{{{{~~~~{`{{] [`{~~~{{~}{`{`}{`{] [{{{`{{{{{{{{{{`~{] [{`{{{{{{{{`{`{`~{] [{{{{{{{{{{{{{~~{{] [{{`{{{{{{{{{{{{{¶] [{{{{{{{{{{{{{{{~{] [{{}{{{{`}{{{{{}{{] [{`{{{{{{{{{{{{{`{] [{{{{~{{`{{{{{{`{{] [{{{{{{{{{{{{{{{{{] [{`{{~{{`{~{{{{`{{] [{Å{{{{`{{{{{~{{{{] [`{~{~{{{~{{{{{`{{] [~~{{{{`{~{{{~{`{{] [{{{{Æ{{{{{{{{{{{] -=================\ )A
Correct answer: B (10 points). lack ), 3, and 6 are a tesui combination that you should know. (1f *hite plays 4 at 6, lack plays 6 at 40. *hat makes them the best answer is not so much the profit at the edge as the fact that they leave *hite with uncertain eye shape. *hite will have to go on the defensive, and lack should be able to make additional profit out of attacking him. lack has the initiative. E (8 points). lack ) in 2ia. ) on the ne/t page will be met by a similar diagonal move at . *hite has defended his maor weakness and has some chance of taking over the initiative in the game. A (6 points). The "-' e/change has somewhat reduced the value of lack ) in 2ia. . *hite will respond with the same diagonal move as before.
))
)
D (4 points). lack ) in 2ia. 3 may be sente, but gives this white group plenty of eye shape. 1n the correct answer lack!s invasion left *hite much more unstable.
C (2 points). lack ) in 2ia. 4 is inferior to lack ) in 2ia. 3. *hite will defend by umping down to , and ne/t he can cross under at %a%.
)3
The correct answers in the two preceding problems were correct because they attacked profitably. The key word is %profitably!. &ttack and defense can be e/tremely important in the macroendgame, but it is well to remember that there can also be such a thing as an unprofitable attack, or an unnecessary defense.
Problem 4 lack to play Your choice :
)4
Correct answer: E (10 points). <hough the continuation is a bit difficult), there is no @uestion that lack ) is the right move. *hite!s strongest resistance is with , but after *hite 4 either lack 6 or lack a is possible. lack 6 gives the result shown in 2ia. ) below, and lack makes a large profit by swallowing up *hite!s e/tension marked '. =he has had to sacrifice three of her own stones, but three stones are only si/ points lack a holds the loss to e/actly that. 1f *hite plays > as in 2ia. , lack can push through at 7, and *hite cannot then play %a% because of lack %b% etc.
) 1 missed it, failing to answer *hite 4. This problem is from one of my own games. B +gawa
)6
D (8 points). lack ) in 2ia. 3 is big, but not really urgent. & white move at ) would be gote, since lack does not have any territory to speak of on the left side to defend. *hite will seize the chance to play , threatening a and b. (*hite a would lead to the capture of lack '0.
A (6 points). lack ) in 2ia. 4 is valuable in that it defends the cutting point at %a%. 1t also prepares for lack %b% B without ), *hite could answer lack b with %c%, but after ) he has to play d, lack %c%, *hite %e%. 1n spite of that, *hite will ignore lack ) and go to the lower right corner.
)
5 (4 points0. lack ) in 2ia. 6 is unnecessary the black group is safe without it. $ote that a is lack!s sente. 1f *hite attacks with b, then after lack %c% and *hite ), lack can even afford to play %d%.
B (2 points). lack ) in 2ia. is an overplay. lack would be accomplishing nothing if she played 3 at %a% and let *hite play 3, but lack 3 is a failure, as the continuation in 2ia. < below shows. *hite ) captures lack!s cutting stone. (lack a, *hite b).
)<
5ontact plays against a knight!s-move corner enclosure are fre@uently effective. 1n addition to the answer to the previous problem, recall the e/amples on pages )< and 4 in chapter ).
Problem 5 lack to play Your choice :
)>
Correct answer: C (10 points). lack ) may not look like much, but besides reducing *hite!s large center, it prepares for a cut at %a%, an attachment at %b% (or perhaps a deeper invasion0 etc., and gives lack e/cellent overall prospects. *hite almost has to defend at %c%, so lack ) is a sente move.
)7
B (8 points). lack ) in 2ia. ) at the bottom of the previous page is also an e/tension into the center, but it is actually somewhat off center. *hite will be glad for the chance to defend at .
E (6 points). This crawling move is always big-it aims at lack a, *hite %b%, lack %c% B but here *hite is much bigger. The center simply cannot be ignored.
A
D (4 points0. lack ) in 2ia. 3 is a bad move. The se@uence up to 4 may be sente for lack, but its main effect is to solidify *hite!s hold on the right side. lack 3 at 4 might be better, but the fighting that leads to is not particularly favourable either. 1f lack is going to play here, he should find some better starting point, such as a or b.
A (2 points). lack ) in 2ia. 4 gives lack gote at the worst possible time, actually helping *hite to make territory in the center. lack!s territorial gain on the upper side is negligible.
)
&s this last problem showed, a very big move can look rather small until it is tested against the enemy!s playing there. Try that test on the ne/t problem, too. ¬her lesson to be learned from the last problem is not to e/tend too deeply into a large center territory. =mall, solid e/tensions are better than large, loose ones that can be cut through.
Problem 6 lack to play Your choice :
_++++~++++++++++++| [{````~{{{~~``{``~] [{`{{`~{{~{`~~{`~{] [{~``~{{{}{`{}{`~{] [{{`{{{{{~{`{{{`{~] [{{{{{{{{{{{{{{`~{] [{`{{{{{{{{µ{{{{`~] [¶{{{{{{{{{{{{{{{{] [{~{{{{{{{{{{{{{{{] [{{}{`{{{}{{{{~}~{] [{{{{{{{`{Å{{{{{{{] [{~{~{`{{{{{{{{{{{] [~{{{~`{~{{{{{{~{{] [~`````~`~{{{{{{~Æ] [{{~{{{{{{{{{{{~`~] [{~}{{{{}{{{{~}``] [{~`~`{~{{`{{```{{] [{{~{{{{{{{{{{{{{{] -=================\
_++++~++++++++++++| [{````~{{{~~``{``~] [{`{{`~{{~{`~~{`~{] [{~``~{ê{}{`{}{`~{] [{{`{{{{{~{`{{{`{~] [{{{{{{{{{{{{{{`~{] [{`{{{{{{{{{{{{{`~] [{{{{{{{{{{{{{{{{{] [{~{{{{{{{{{{{{{{{] [{{}{`{{{}{{{{~}~{] [{{{{{{{`{1{{{{{{{] [{~{~{`{{{{{{{{{{{] [~{{{~`{~{{{{{{~{{] [~`````~`~{{{{{{~{] [{{~{{{{ì{{{{{{~`~] [{~}{{{{{}{{{{~}``] [{~`~`{~{{`{{```{{] [{{~{{{{{{{{{{{{{{] -=================\ Correct answer: C (10 points). lack ) is a multi-purpose move: it strengthens a weak black group it reduces *hite!s territorial prospects to the right it aims to attack the white group on the upper side at a; and it threatens lack b. *hite would like to play ) himself if he could. D (8 points). lack ) and 3 in 2ia. ) on the ne/t page are large, and there is some chance that lack may be able later to clamp at %a%, (if *hite descends to b, lack plays %c%, *hite d, lack e). *hite, however, will force lack at 4, then take the key point at , forestalling lack %a%, attacking the black center group, and surrounding a large territory. B (6 points). The diagonal move in 2ia. is not bad, but it affects only territory, lacking any offensive or defensive significance. *hite can ignore it because he is linked up at ", and similarly lack could ignore *hite ).
3
4
A (4 points). lack in 2ia. 3 is umping into a largely neutral area. *hite will probably welcome the opportunity to defend his upper-side group with .
E (2 points). lack ) in 2ia. 4 is a mistake. 1f *hite replies at , for instance, he has by far the best of the e/change. & better idea, although a risky one, would be for lack to play himself. 1f he is determined to rescue his stone on the lower side, then ) in 2ia. 6, not ) in 2ia. 4, is the proper way to do so.
6
The last two problems should have demonstrated that large macroendgame moves can occur in the center. ore often, however, they occur at the sides, as in the ne/t problem.
Problem lack to play Your choice :
Correct answer: B (10 points). &ll the other choices pale in comparison to the invasion at ). lack is not ust reducing or enlarging territory he is stealing territory from *hite and making it his own. Ce is also cutting into *hite!s eye space, and ne/t he can hane at %a% in sente. 1f *hite connects at in 2ia. ), lack should run head-on into his stone with 3. Ce can get out past *hite 4 with the hane at 6 and ump to <, a standard tesui combination. E (8 points). <hough not a large move, the hane at ) in 2ia. on the facing page can be played in sente right now. 1f *hite ignored it, his group could easily die.
<
D (6 points). lack ) in 2ia. 3 below gives eye shape to the black group on the lower side, but it does not pose any serious threat to the white group to the left, so *hite will ignore it to play to on the right side in sente. &fter this, lack!s chance to invade is gone, and his prospects in this handicap game are not good. lack ) at a would be a better move on the lower side, but still not up to the correct answer.
>
& (4 points0. lack ) in 2ia. 4 is worth about eleven points, but it does not threaten anything, nor is it necessary for the safety of the black group, which is connected to the center.
C (2 points). lack ) in 2ia. 6 is the kind of sente move that one should not make, because it destroys the better invasion se@uence starting with lack %a%
7
The intrinsic bigness of an invasion like the one in the previous problem cannot be overemphasized. ear also in mind the size of a defensive move that prevents such an invasion. The ne/t two problems are @uite hard.
Problem ! lack to play Your choice :
3A
Correct answer: E (10 points). lack ) resolves what has been a rather delicate situation involving the corner and the black group on the lower side. &fter defending both places with the se@uence to 7, lack has nearly si/ty points on the left and lower sides alone. That is e@ual to all of *hite!s territory put together, so lack leads by the margin of herD right side and center territory. 1f lack does not defend here, *hite will probe at the corner with ) and 3 in 2ia. ) on the ne/t page. 1f lack answers with and 4, *hite will shift and attack the group on the lower side with 6. lack can ust barely live by making the throw-in at ), but *hite gets to play 7 and )6 in sente, which means that he can live in the corner by connecting at )7. (1f lack a, *hite b, or if lack b, then *hite a, lack %c%, *hite %d%0. lack has already lost more than twenty points as compared with the correct answer, and she still has the clamp at %e% left to worry about. D
This is another of my games. B +gawa
3)
1f lack answers *hite ) by descending to in 2ia. , *hite will live on the left side with 3 and 6, and of course a will still be his sente, threatening the group to the right.
A (8 points). lack ) in 2ia. 3 is certainly a big movethe difference between it and *hite ) in 2ia. 4 is almost twenty points-and it secures ample eye space for the group on the right side, which is another plus factor, but it is not as big as the defence of the lower left corner.
3
D ( points0. lack ) and 3 in 2ia. 6 are also big, but less so than the upper right and lower left corners. 1n those areas either side could make territory here only lack can do so. lack ) is not a double sente point. 1t is worthless without 3, and *hite would not play l himself, but rather %a%, or some move around 3.
C (4 points). lack ) in 2ia. covers a thin spot in the black line, but leaves the corner open. *hite could not break through here even without lack l. B (2 points). lack ) in 2ia. < seems to be prompted by unnecessary fear for the safety of the center group. The e/change of ) for causes lack a loss. =he can no longer draw out her stones with 3 and 6 without having *hite invade the right side at .
33
The preceding problem showed the importance of foreseeing disaster before it occurs. & good player!s attention is aroused ust as much by defects in his own positions as by weaknesses in his opponent!s positions. This ne/t problem is the last of the chapter.
Problem " *hite to play Your choice :
34
Correct answer: B (10 points). *hite is perhaps a bit behind in this game, from one of the professional tournaments, but if he fails to defend at ), he drops out of competition altogether. The reason is that lack is threatening the attachment and cross-cut shown in 2ia. ) on the facing page, which would break up *hite!s only large territory. 1f *hite plays at 3, lack can play %a% in sente, then . Eollowing the cross-cut, if *hite gives atari at 4 in 2ia. , lack gives a countratari at 6 and connects at <. 1f *hite plays 4 in 2ia. 3, lack can break through with 6 and < and, if cut off by *hite )A, live with )) and )3. E (8 points). *hite ) in 2ia. 4 is a strong second-best. &fter *hite ) in the correct answer diagram, lack made two forcing moves, then played here himself with . 1f lack answers ) at a in 2ia. 4, *hite has made a big profit in sente. 1n this game lack will ignore *hite ) to play on the right side, however, as in 2ia. ).
36
Fet!s take this opportunity to go through some of the follow-up moves to *hite ) in 2ia. 4. *hite a and *hite b are two possibilities, but there is also the peep-and-hane combination shown in 2ia. 6. lack 4 is the simplest way to answer them ne/t a is the correct point for either side. lack 4 in 2ia. is also possible, and lack can defend his territory by playing as shown there, or he can shift to the right and play for the e/change shown in 2ia. <, cutting off the stones marked ". *hichever variation he chooses, however, he cannot avoid a sizeable loss.
3
D (6 points). *hite ) in 2ia. > is much smaller than *hite a would be. 1f lack answers at , *hite has gained rather little. Ce might actually prefer to play from the direction of G himself, instead of ).
A (4 points). *hite ) in 2ia. 7 is smaller than it looks even if lack plays here first, as in 2ia. )A, he cannot make much territory. *hite can press him with to > and then he has the hane at %a%.
3<
C (2 points). *hite ) in 2ia. )) does not work. &fter lack and 4, *hite has merely given lack two prisoners. The right way for *hite to play here is to make the hane at ) in 2ia. ).
"roblem
)
3
4
6
<
>
7
Total
#our score Total 6 or 64-6> A-4 --> >4->> score less Hank
>kyu <- I up kyu
6-4 kyu
3- kyu
3>
) kyu
-3 dan
4-6 dan
7A dan
CHAPTER 5 Games
In this last chapter we shall go through two more of my (Ogawa's) games, and in each of them I have set ten endgame problems for you to try to solve. The first game is one played in !"# when I was studying to become a pro$ fessional at the %itani Go &chool. (I believe I was also still attending unior high school.) I had blac with a four stone handicap, and inoru %itani, !$dan, was playing white.
*ooing bac on this game, I am surprised at how tight
and conservative many of my moves were. If I had it to play over again, I would play differently. I would shift +lac to - in igure , for e/ample, to eep 0hite from getting that ideal $1$- formation, and I would move +lac " to a on the right side. I would move +lac 2 to 3a3, too. The three$three point invasion at 0hite ! was obvious, and after +lac 42, it would be better to have 2 at 3a3, halfway between the blac positions above and below, than where it was, too close to the upper position and too far from the lower one. 0hite too advantage of my error by coming in at 4! in igure 4, and although I attaced and chased him with 15 and so on, he escaped. The impression one gets from the whole opening up through 0hite # is that +lac has let herself be triced. I closed the upper left corner with +lac 2, a move that also aimed toward an invasion of the left side, and 0hite responded with the attachment at !
4
6t +lac - the standard move is to press on the other side, with +lac in 7ia. . 0hite 4 to +lac # are a osei. I cannot recall why I avoided 7ia. 8 perhaps I thought it would mae the left side too hard to invade 8 but I leave you to udge the relative merits of it and the se9uence through " in igure 1.
1
0hite tried the same type of attachment on the lower side at "1 in igure 1, and this time I answered by e/tend$ ing to " and starting a running fight. 0hite settled himself with 21 to 2-, but I had gained the initiative for a promis$ ing$looing invasion at 2". +y the end of igure , however, my invasion had turned into a big failure. I had made only a few points of territory on the left side, and had gotten one of my own big groups into eye trouble. One reason for this was my hane at !5: I should ust have e/tended forward to !-. I must have been e/pecting 0hite to answer +lac !2 by connect$ ing the o at in 7ia. 4, after which I could tae a thirty$ point territory with +lac 4, , and ", but %itani upset my plans by playing 0hite !! and 5, forcing me to tae and connect the o. 0ith 51 his stones had gotten neatly out into the center, and mine were ammed against the left edge.
I could have still gotten a good result out of the fight$ ing on the left side if, after 0hite 51 on the last page, I had played +lac and 1 in 7ia. 1 instead of cutting at 3a3. If 0hite used 4 to forestall +lac 1, I could play 4 myself and either way I would capture a large area. ;aving missed this chance, I was now in a very cramped position. I tried to run my big group out to safety with +lac " and so on in igure -, but the road closed on me at 0hite 1. I had to abandon +lac 1, 5, and 4 in the center and go bac to the lower left corner to mae two eyes. I managed to live with +lac in igure ", but 0hite forced me with -, #, and !, then tied all his loose groups together by capturing four of my stones in the center with -. This last move mared the beginning of a grim endgame for me. +y now my original advantage from the handicap stones was more than all gone.
-
6ctually, I would not have survived even this far if 0hite ! had not let me tae the ey defensive point at -5. 0hite ! loos lie a good move$ne/t 0hite can invade the corner at 3a3 8 but if %itani had played , 1, and - in 7ia. instead, he could have ended the game directly. I would have had to connect at to eep my eyeless center stones from being detached, but then 0hite # would have illed my left side group. 6nyway, after -4, -, and -", I turned to the lower right, where both the blac and white positions were wea, and that gives us our first problem.
Problem 1. 0hat is the best way for +lac to play in the lower right< A, B, or 3=3> ar down your choice, then turn the page and read on. The answers are numbered , 4, and 181 for the best, for the worst$so you can score yourself by giving yourself , 4, or 1 points accordingly.
Your choice :
"
. 3+3. +lac in 7ia. lets 0hite get ample eye space and territory by e/tending to the ey point 4. 4. 363. +lac in 7ia. 4 is a bit better, provided that +lac follows with the hane at 1, but the $4 e/change gives 0hite a simple life with . +lac is the ind of forcing move that should be left unplayed ust on principle.
#
1. 3=3. The correct move is to start with the hane at -2 in igure #. ?ow it is not so obvious that 0hite can live, for +lac is holding in reserve not only the push down at A, but the attachment at d and all sorts of placement at$ tacs as well. 0hite did manage to live, with -! and " in igure 2, but there was some bad potential left for him. &ee if you can read the situation out. ?e/t I defended the upper left corner, to eep 0hite from invading with and 1 in 7ia. 1. 0hite 1 in 7ia. 1 is correct and damaging enough, but I may also have been worried about 0hite 1 and - in 7ia. : although they do not wor, anyone who can prove that to himself 9uicly is 9uite strong. Problem 2. 0hat is the best way for +lac to defend the corner< A, B, or 3=3>
Your choice :
2
. 3+3. +lac in 7ia. is the worst move because it lets 0hite play 4 and in sente. 4. 3=3. +lac in 7ia. 4 is better. It gives 0hite the wedging tesui at 4, but now 0hite 4 etc. are gote, and therefore less profitable to 0hite, even though they leave +lac in atari.
!
1. 363. +lac "4 in igure ! is correct. 0hite's move$the wedge at in 7ia. 18is again gote, and after 1 there is no blac stone left in atari as there was in 7ia. 4. In fact, since 0hite gave atari at "1 in igure 5, he lost even the possibility of 7ia. 1. ?ow I could answer the wedge with 4 and in 7ia. , trapping him in a shortage of liberties. This was a slight piece of carelessness by %itani: he should have e/changed for 4 in 7ia. - and then given atari at 1, with the connection at 3a3 left as a possible three$ point move for later on. 0hite "! was another mistae8it would have been better ust to capture at #8but 0hite's overall idea of ta$ ing away my eye on the lower edge was of course correct. +y threatening to ill my big group in the lower right he was maing profit in sente. Problem 3. ;ow should +lac defend her group$with A, B, or 3=3>
Your choice :
5
. 3=3. +lac in 7ia. is no defense at all. 0hite 4 leaves +lac with only one eye, and although she can mae a second one with 1 and -, she has to give up the larger half of her group when 0hite plays ".
4. 363. +lac in 7ia. 4 is much better, but 0hite an$ swers the double atari at 1 with and ", and if +lac tries to live by fighting the o at 3a3, 0hite has plenty of big o threats. ortunately +lac can live unconditionally with #, but the value of l, 1, and - is liely to be nullified by 0hite's playing 3b3 in sente, then taing the o below 1 and putting +lac - into atari. 1. 3+3. +lac # in igure is correct. +y starting with this move +lac can run all the way through 0hite's terri$ tory in the lower right center before having to mae two eyes on the right side. @ou should not have much trouble seeing that the se9uence through 2 in igure 4 is better for +lac than 7ia. 4. Problem 4. 6fter a forcing move at 2-, 0hite turned to the last large area, on the upper side. 0hat is the right e/$ tension for him to mae there< A, B, or 3=3>
Your choice :
4
. 3=3. 0hite in 7ia. goes too far. +lac can invade behind it at 4, and the whole e/change through 1 and is more profitable to him than to 0hite. If 0hite tries to play as in 7ia. 4, +lac pushes through at , cuts at ", and comes out with 2 and 5, leaving a and b as miai.
1
4. 3+3. 0hite in 7ia. 1 only invites the 4$1 e/change, which leaves 0hite with a glaringly bad empty triangle. 1. 363. The correct move here is the diagonal e/tension on the second line in igure 1. This is also the point that +lac would lie to tae if given the chance. ;aving sente again, I made two small forcing moves at 22 and !5 in igure . The first of these was all right, but the second would have been better left unplayed. Problem 5. ?ow it is +lac's turn for a large gote move. 0hich of A, B, and 3=3 in igure would be best> Your choice :
. 3=3. +lac in 7ia. is a belladonna move8attrac$ tive$looing, but deadly. If +lac captures at 1, 0hite ills her big group in the lower right. If +lac catches her$ self in time to play 1 at , 0hite will capture +lac l, and then +lac will have to watch out for a white placement at 3a3.
-
4. 3+3. 6t least +lac in 7ia. 4 causes +lac no loss, but it gains her very little. Imagine 0hite answering it at 3a3, for e/ample, and you will sce how small it is. 1. 363. +lac !4 and ! in igure - are worth a good five points. =ompare them with 0hite in 7ia. 1. If +lac connects at 3a3 there, 0hite has gained three points in sente: if +lac does not play 3a3 and 0hite does later, that is another four points. That maes 0hite worth 1A(B4 / )C- points in gote, and liewise +lac !4 and !. These moves tae on some added value, too, in the form of thic$ ness. Problem 6. 0hite's ne/t move was !- in igure ", which forced +lac to connect at !" to live. 0hich would be best for 0hite !#< A, B, or 3=3> Your choice :
"
#
. 3+3. 0hite in 7ia. is not very big, and +lac will give atari at 4. 4. 363. 0hite in 7ia. 4 is bigger, being worth a good five points, but +lac will still give atari at 4. 1. 3=3. 0hite !# and !! in igure # are sente, and they reduce +lac's territory while enlarging 0hite's. Once 0hite has committed himself by playing !- ( "), he cannot afford to delay !# and !!. Problem 7. +efore taing the large point on the upper side (I in 7ia. 4), 0hite decided to try something on the left side. ;e started by e/changing for 4 in igure 2. 0hat is his best continuation< 363, 3+3, or 3=3>
Your choice :
2
. 363. %itani actually played the worst move, 0hite 1 in igure !. This mistae cost him about four points. ;e must have thought that he could ill my group by continu$ ing with 0hite in 7ia. , but +lac 4, maing a and b miai, would tae care of that. 4. 3=3. 0hite and 1 in 7ia. 4 on the facing page re$ duce +lac's group to the minimum of three points, (count$ ing one prisoner at '), but 0hite cannot e/pect to mae any territory for himself this way. 1. 3+3. 0hite in 7ia. 1 rcduces +lac's group by the same amount, and now 0hite can get two or three points of territory by connecting at a, or two points by descending to 3c3 after +lac a, 0hite b. +lac cannot necessarily pre$ vent that by playing 3a3, 0hite 3b3, +lac 3c3 in sente be$ cause 0hite can resist in o with 3d3.
!
Problem 8. 6fter 0hite - and +lac " to 4 in igure 45 it is high time to see what can be done in the lower right corner. +lac to play< A, B, or 3=3> Your choice :
45
. 363. +lac in 7ia. would only wor if 0hite had no outside liberties. 0hite taes the ey point at 4, then s9ueeDes +lac with , " and 2 to live with seven points of territory. 4. 3+3. +lac and 1 in 7ia. 4 are a tesui combination that will often produce a o, but here they fail. (+lac 1 at would also fail, 0hite answering at 1 or ). 6gain 0hite s9ueeDes +lac with " and 2, and if +lac connects at ! in 7ia. 1, 0hite captures at 5. +lac cannot mae a illing re$ turn play at ! because his four stones to the left are in atari.
1. 3=3. +lac in 7ia. leads 9uite directly to a sei. It is worth noting, incidentally, that this possibility would not have e/isted if 0hite had not forced the "$' e/$ change earlier in the game, since without it 0hite would threaten to lin up to the group to the left. 6s you can see from igure 4, I somehow missed the sei in 7ia. and made the relatively worthless cut at instead. 0hite lost no time in descending to - and getting si/ points of territory where I could have reduced him to nothing. If I had played 7ia. , I would have had a com$ 4
fortable win. The score would have stood something lie< +lac Epper left
0hite 4-
*eft side
-
=enter and right side
*ower left
Epper right
Epper right
#
*ower side
2
*ower right
4
*ower right
5
#
1 Total 1! Total 0hen I missed 7ia. , the game became very close. Ferhaps I was e/pecting +lac 2 to be answered at 3d3, but %itani corrected that notion with 0hite 4. Problem 9. ;ow should +lac answer 0hite 4# in ig$ ure 4 < at 363, 3+3, or 3=3>
Your choice :
44
41
. 3=3. +lac in 7ia. is a tragic mistae. 0hite 4 ills the blac group. 4. 363. +lac in 7ia. 4 is unnecessarily cautious. It lets 0hite give atari with 4 and mae one point of territory, at 3/3 , in sente. 1. 3+3. +lac 42 in igure 44 is correct. 0hite no longer has that point of territory in sente that he had in 7ia. 4. To loo at it another way, if 0hite plays 3=3 later on, there will be no need for +lac to reply at 363. Problem 10. 0hite's ne/t move was 4! in igure 41. =hoose +lac's response from among A, B, and 3=3.
Your choice :
4
l. 3=3. +lac in 7ia. actually causes +lac a loss. The proper way for her to play here is to sacri$ fice a stone at 4, followed by 0hite , +lac a, etc., or, e9uivalently, to hane at b. 4. 3+3. +lac in 7ia. 4 gains one point. If 0hite cut at , +lac would later have to fill at 3a3. 3. `A`. +lac 15 and 14 in ig$ ure 4 gain two points. They, and +lac in 7ia. 4, are re$ verse sente plays, for if +lac ignores this part of the board completely, as in 7ia. 1, 0hite can gain two points with and 1, then two more points in sente with -, #, and !, and by this stage of the game two points in sente are bigger than anything else.
4-
6fter +lac 15 to 1 on the right side, 0hite used sente to play 1- in igure 4, forcing me into the undesirable e/$ change of 1" for 1#. 6t least +lac 1" raised the value of +lac 5, so that 0hite came bac to answer it at 1 in ig$ ure 4-, (one point in reverse sente). +lac was also worth one point in reverse sente, and thus e9ual in value to 0hite - (two points in gote).
4"
0hite played -1 in igure 4" in sente, then too the largest remaining point at --. +lac -" to "5 and 0hite " to "1 were miai: each being worth one point in gote, and +lac " finished the game. Frisoners had been captured at the points mared 33 and ', maing the final score< 0hite +lac Epper left
4"
*eft side
-
=enter and right side
*ower left
1
Epper right 1
Epper right
#
*ower side
#
*ower right
4
*ower right
"
1
Total
4
Total
"
I had won by one point. The reason that I set no problems on the last thirty$five moves is that in most cases where there were alternative moves to consider, the alternative move would have led to the same final score as the move actually 4#
played. I was badly outdone in the opening and middle game, and even though %itani missed the finishing blow at 0hite ! (igure "), I went into the endgame behind. I should have lost, but a number of un%itani$lie errors let me catch up and go ahead. I made one maor oversight toward the end, missing the sei in the lower right corner, but fortunately it was not 9uite enough to cost me the lead. ost of the problems in this game were tesui problems, and it is interesting to observe that none of them e/actly matched the standard tesui that appeared in chapter three. This illustrates the fact that every game generates its own uni9ue positions, and you have to try to read them out and hunt for the right plays on your own. ?ow score yourself.
Game 1 Froblem
4 1 - " # 2 ! 5
Total
@our score
Ferfect score< 15 In the ne/t game the stress will be less on tesui and more on udging the relative merits of various moves in different parts of the board. I thin you will find the problems more dif$ ficult. &ome of them call for considerable reading, so tae your time. The game is one I played recently against @utaa Ono, $ dan, in the preliminary rounds of the eiin tournament. 6gain I had blac, but this time, of course, there was no handi$ cap, and to mae the game e/actly even there was a -B4$point omi, that is, the final score would be adusted -B4 points in 0hite's favor to compensate for +lac's having the first move. To win, therefore, I would have to finish at least si/ points ahead on the board. 6s you will see, neither player was able to open up a big lead in the opening or middle game, so the issue was left to be decided in the endgame.
42
The fighting in this game started early, with a difficult variation of the small avalanche osei in the lower left corner. &ince 42 to 1 gave 0hite three liberties, I had to crawl out at 1- and let him capture my cutting stones with 1". The cause of this was +lac 4#, which I should have played at in 7ia. . The standard se9uence there is bad for 0hite because the stone mared ' is blocing his development. 7uring the game I was worried about his playing 4 in 7ia. 4 on the facing page before cutting$after 0hite 5 there I lose my stones on the lower side in a o$but I was overlooing the descending tesui at - in 7ia. 1. 0hite " was a double sente point. I would have lied to play there and have 0hite answer by living with a, +lac b, 0hite 3c3, but he could hold a-b-c in reserve and come out at d, and I did not want to encourage that. 6nyway, for future counting purposes, remember that 0hite has captured three stones in the lower left corner and +lac has captured one. The fighting continued in igure 4. &ince 0hite -2 cap$ tured +lac -1 without recourse to a ladder, (+lac a, 0hite b), I should have played +lac -# at -2. &till, by e/changing with +lac 21 to 2# to form a large area on the right side and attacing in the center with +lac !1 and !-, I was holding my own in the game. Problem 1. The blac group on the lower side has become isolated. If 0hite attacs it with in the diagram below, should +lac respond at A, B, or 3=3> This is a life$and$death 9uestion, but it is related to the endgame. Your choice :
4!
l. 3=3. =apturing at in 7ia. allows 0hite to force a o fight for the life of the whole group. 4. 3+3. In the first place, if 0hite answered +lac in 7ia. 4 directly at ", +lac would have accomplished noth$ ing. 0hite has an even better opportunity, however, in 4 and . +lac must answer at 1 and -, and then 0hite can play both " and 2 in sente. +lac lives, but three of his stones are left hanging,and the lower edge is sealed off. 1. 363. 7ia. 1 on the facing page shows the best de$ fense. Two blac stones are still left hanging, but now if 0hite plays in 7ia.
15
+lac can reply with 4, so 0hite cannot both seal off the lower edge and retain the option of capturing the cor$ ner, as he did in 7ia. 4. igure 1 brought the middle game to a close, and al$ though I made a mistae at 4, which I should have played at 3a3, and 0hite was able to gouge out my upper right cor$ ner, I was, if anything, very slightly ahead, considering that I had the ne/t move. Problem 2. +lac to play and start the endgame. 0hich is best< A, B, or 3=3> Your choice :
1
14
. 3+3. This is a blunder. 6s 7ia. shows, it ends in a shortage of liberties for +lac. 4. 363. 0hite will answer +lac in 7ia. 4 with 4, but then +lac has to continue with 1, which is clearly gote, and 0hite gets to tae the important double sente point at . +lac is not really the best move for +lac in the center anyway. 1. 3=3. +lac 1- in igure would have been sente for either side now, so I too it without delay. The center was, by comparison, a relatively neutral area. Problem 3. or the ne/t few problems you will be put$ ting yourself in 0hite's place. To start with, how would you answer +lac 1# in the figure below on the lower edge< at A, B, or 3=3> Your choice :
11
I. 3=3. +y blocing at in 7ia. 0hite can mae +lac defend at 4, but then he has to defend himself against +lac a by playing 1, and he has lost the opportunity he had to capture the two blac stones in the corner by cutting at b. If he cuts at b after +lac 4, +lac can answer with 3c3. 4. 363. It is better for 0hite to draw bac with I in 7ia. 4 on the facing page in order to preserve the possibility of capturing the two stones in the corner. This also, however, leaves +lac the possibility of descending to 3a3 at some time in the future and forcing 0hite to use e/tra moves capturing him.
1
1. 3+3. It is best to drop all the way bac to 0hite 12 in igure ", immobiliDing the two blac prisoners there. 0hite need not worry about losing territory on the lower edge, since he can always play 3=3 in sente and anything +lac did there would be gote. Problem 4. 6fter playir.g 1! and in igure # in sente, I pushed out at 1. 0hite to play< A, B, or 3=3> Your choice :
1-
. 3=3. The e/change in 7ia. only helps +lac by re$ moving the possibility of a white peeping move at 3b3 or clamp 1"
at 4. It would be better for Hhite to e/tend to 3a3 and aim towards those possibilities from the center. will still be his sente later if he wants it, while a blac descent to would be gote. 4. 3+3. +lac will push through and cut at 4 and in 7ia. 4 and force 0hite through the se9uence shown. This costs 0hite a great deal: he can no longer get into the lower left center area, and +lac can barge into his territory at 3a3. &aving the three white stones is not worth it. 1. 363. 0hite and " in igure 2 are sente, and com$ pared with a blac play at , they are 9uite large. If +lac omits - or #, 0hite can give atari to the right of or below and tae the lion's share of the center. 0hite 2 maes a good continuation. Problem 5. I retaliated in the center with ! in igure !, and 0hite used his ne/t move to attac my group on the lower side. 7id he play A, B, or 3=3> Your choice :
1#
l. 3=3. If 0hite plays in 7ia. +lac defends at 4, and 0hite has lost the possibility of capturing the two blac stones in the corner with a, as has already been e/plained twice. 4. 363. 0hite in 7ia. 4 on the facing page is answered by the same +lac 4, and although 0hite can capture the corner, +lac can return the favor by pushing out at a, or if 0hite plays a, +lac can capture 0hite .
12
1. 3+3. 0hite -5 in igure 5 is a tesui that enables 0hite both to bloc at -" in sente and to leave the two cor$ ner stones vulnerable to capture. In other words, 0hite now has the possibility of getting both plays, while in 7ias. and 4 he could get only one. +lac's territory is five or si/ points in the figure, si/ points in 7ia. , and about five points (an average value) in 7ia. 4, so the sacrifice of -5 and -4 does not mae +lac's territory any bigger. Problem 6. 0hat about 0hite's ne/t move< A, B, or 3=3> Your choice :
1!
. 3=3. =apturing these two stones is worth e/actly seven points in gote: compare 7ias. and 4 and you will see that 5
there is a difference of si/ points of white territory and one white prisoner. There are bigger gote moves elsewhere. 4. 363. 0hite in 7ia. 1, stopping a blac play there, is big, but too passive. It gives +lac a good e/cuse to play 4 and . If 0hite is going to defend here, 0hite 3a3, in sente, would be better. 1. 3+3. 0hite -2 in igure is a reverse sente move, since 0hite would have to respond to a blac atari at -2, and the difference between 0hite -2 and +lac -2 is not small. Problem 7. &ince 0hite had ignored +lac ', I ept on with -! and ", threatening to draw my stone out at 3a3 and capture the whole center. 0hite "4 restored the shortage of liberties that had been preventing +lac a earlier, (now if +lac plays a, 0hite gives atari above a, then from the right), and +lac "1 left an interesting position. &hould 0hite's ne/t move be A, B, or 3=3>
Your choice :
. 3+3. It is still too early for this hane. 0hite still has other potential here that he should eep open. 4. 363. 6lthough worth eight points at the very least, this connection would be gote. That sets it apart from the ne/t move.
4
1. 3=3. 0hite " in igure 1 is large in itself, and it conceals an even larger threat. If +lac ignores it, 0hite can play and 1 in 7ia. , then clamp at -. +lac has to answer this at " and let 0hite mae a tidy profit in sente with # and !. If he tries to cut 0hite off with " etc. in 7ia. 4, he loses a big group of stones, being behind, four liberties to three. 0hen you consider that after " 0hite can push into the space below it and capture two stones, and that 0hite " destroys three or four points of territory that +lac could mae by playing there, you can easily appreciate its value. Problem 8. &ince 7ia. would have been both large and sente for 0hite, I defended at "- in the figure below, and now that he finally had no other possibilities to save on the left edge, he played "". ;is connection at "2 left me a choice of three big points around the edges< A, B, and 3=3. 0hich was the biggest>
Your choice :
1
. 3=3. (#2 in igure -). 6s we saw before, this move is worth only seven points in gote. 4. 363. (# in igure -). If you compare the figure with 7ia. , where a is 0hite's sente, you will find a difference of points of white territory and -(8) points of blac territory, maing this a !(8)$point gote play. There is also the possibility of 0hite's descending to in 7ia. 4. If +lac answers, 0hite has gained about four points in sente, and if +lac does not answer, 0hite can play the money ump in 7ia. 1. 7ias. and 1 should be devalued slightly because they reduce the effectiveness of 0hite # in the figure.
1. 3+3. ("! in igure -). This play only gains four points as compared with 0hite in 7ia. , but it threatens the eight$ point capture shown in 7ia. -. That maes it sente: +lac can play it and, 0hite #5 and #1 being about e9ual, 0hite has nothing better to do than answer. ?ote that the se9uerce +lac "!, 0hite #, +lac #1, 0hite #5 would leave +lac with sente to tae #2. Problem 9. I too the last large point at #! in igure ". &hould 0hite's ne/t play be A, B, or 3=3>
Your choice :
-
. 3=3. This is a mere two points in gote. 4. 3+3. This move is worth four points. If +lac plays in 7ia. , she gets two points for taing the prisoner, one for not having to connect at 3/3, and another because she can push down at 3a3 in sente, whereas after 0hite 3+3 in the figure, 3a3 weuid be 0hite's sente.
"
1. 363. 0hite 25 in igure # is worth about three points, but unlie 0hite 3+3, it is sente. If +lac does not reply, 0hite to in 7ia. 4 end the game. Problem 10. 0hite made sente plays at 24 and 2 in igure 2, then cut at 2" and pushed all the way down the edge to !". ;e played 2" to !" to eep me from answering !2 at !", so that later on he could gain another point by playing 3a3. Of course he did not lose anything e/cept possible o threats by filling my territory with prisoners in this way. 0hite 5 was the last move worth more than two points, and now, taing into account that +lac's turn is ne/t, can you tell how the score stands> Try to wor out the rest of the endgame in your head, or on the board if you have been laying the moves out on one, and see if you thin< 363. +lac has a clear lead, ( B4 points or more). 3+3. The game will be decided by half a point. 3=3. 0hite has a clear lead. 7on't forget the -B4$point omi.
Your opinion
#
Answer o !roblem 10 . . 6. 4. +. 1. =.
+lac - to ! ept 0hite from maing any e/tra territory at " or 5, and +lac turned out to be sente, since it was worth a good two points for 0hite to defend at 4. 0hite's defending moves at and 2 were also worth two points, eeping ' from being a false eye, and I too the last two$ point play at !. 0hite 45 and 44 were worth one point each, (eventually I would have to connect at 3a3), and +lac 41 finished the game. This whole se9uence was more or less unavoidable. =ompare your counting with the follow$ ing< 0hite
+lac
=enter and lower right 4!
*eft side
41
Epper side
ight side
-2
*ower left
4
*ower side
#
2-
Total
22
Total
2
