Die Rolls And Randomness
For Pencils and Paper Role-Playing Games
Copyright ©2012, 2013 J.D. Neal * All Rights Reserved. Dice are random random number generators. generators. Rolling a six-sided die will generate a random number from 1 to 6. How the die is made and rolled can affect the result result,, but honest honestly ly rolled rolled dice dice genera generate te random random numbers. Some Some peop people le pay pay far far too too much much atte attent ntio ion n to probabilities when dealing with dice. Probabilities are not laws: they do not state that said numbers must occur in said order with said frequency. Nor that they will. will. They only only indica indicate te the tenden tendency cy over over a wide wide number of rolls. The results are "probable", but not guaranteed. One die roll does not effect another and die rolls are not predic predictab table; le; if they they were were predic predictab table, le, they they would would not be random. random. A test must have outliers outliers and odd results, or else it is not random (or is itself a random fluke). If a test perfectly follows a predicted patt patter ern n each each time time it is perfo perform rmed ed,, eith either er it was was perf perfor orme med d wron wrong; g; or was was a oneone-of offf that that will will be corrected by further tests; or the subject being tested is not random. Indeed, consider the futility of running any test on random random subject subject matter matter as an attemp attemptt to prove prove or disprove anything. If the subject is truly random, the results will always be different each time the test is run. Actually, two or three tests could be close if not exact; exact; but other tests will vary. vary. T he best feel for any subject is to run multiple tests to get some idea of how random the result can be by how much the result differs. Due to this variability variability,, the same numbers numbers could very well occur frequently. Gamers might experience "streaks" where they get the same numbers over and over. They might suffer "bad luck" when most of their die rolls are poor; or "good luck" when they are often good. And later on things may change as the "streak" ends. Two elements can affect the result of die rolls and help determine how random they are (or are not):
How How a perso person n roll rolls s dice dice can can inde indeed ed affe affect ct outcomes. People who take the pains to ensure random randomness ness will see this this less less often often than than those those who for one reason or another set up a system that favors "skill". A player might pick up a die and "shake it up" without actually changing the side it is on, meaning the side it was on when picked up might occur frequently when thrown. They might keep keep roll rollin ing g the the same same numb number er ofte often, n, mere merely ly because they are not randomizing it. Consider a related subject: math teachers often use coin flips to illustrate probabilities. They assume said coin flips are perfectly random. In the real world, coins (like anything that is man made) are imperfect and can be lop-si lop-sided ded.. And some some people people practi practice ce flipping coins to the point where they can flip a coin to wher where e it land lands s on whic whichev hever er side side they they choo choose se.. People involved in magic (or cheating at games of chance) learn to control coins (as well as cards and other other object objects) s) well well enough enough to affec affectt probab probabil iliti ities. es. Never trust anyone who eagerly wants to flip a coin for anything! Someone Someone testing testing mathemati mathematical cal theory theory with real world coin flips might be dismayed to find that their system system does does not give give the predi predicte cted d probab probabili ilitie ties. s. They may think they have disproven reality. Actually, they they were were never never taught taught (or never never unders understoo tood) d) the idea that the "coin flips" used in math tutorials are actually artificial, imaginary constructs intended to be perfectly random. In the real world, coin flipping is not always perfectly random. Sometimes it may be; but other times it may not. Dice are the same: sometime a person may not shake a die up and hence it may give the same result frequently. Ensuri Ensuring ng random randomnes ness s will will help help player players s avoid avoid frustration. It might be fun when they keep getting the same high die roll, but if they keep getting getting the same low die rolls they may begin to hate the game. A frus frustr trat ated ed playe playerr who who angr angril ily y pick picks s up dice dice and and clenches them so hard they really do not randomize and then throws them on a surface that does not boun bounce ce them them much much migh mightt be causi causing ng thei theirr own own frustrations.
Most are made well enough to be fairly random, if rolled "honestly". Some may be poorly made and as such may favor certain sides, especially under certain conditions. "Che "Cheat ater er"" dice dice are are weig weight hted ed to favo favorr cert certai ain n numbers. 1. How the dice are made.
Random Tables 2. How How the the Dice Dice are are Roll Rolled ed .
Rando Randomne mness ss is crea create ted d by shak shakin ing g the the dice dice up such such that that a random random face will result when thrown; thrown; the surface that that it lands lands on can promote promote random randomnes ness s if it encourages bouncing.
One use of dice is in making random picks from tabl tables es.. How How the the tabl table e is orga organi nize zed d can can affe affect ct randomness. The more bias there is placed in any table, the less random it is. If a table using percentile dice (or d100 rolls) is weighted to favor a few entries 1
and and give gives s othe others rs a few few perc percen enta tage ge poin points ts,, the the slighted entries will not occur very often. As a result, the outcomes aren't actually that random. Yes, someone using said table and roling the dice and getting an odd result will think, “These tables allow anything!” But the majority of users will find that the tables generate the same thing over and over because they keep getting the entries that are favored. In order to create truly random tables, a gamer has to eliminate bias.
number range: i.e. a range of 1 to 20 for 3d6 and d20. The 3d6 range is not in any way adjusted for the pribabilities a 3d6 roll creates; it is a flat 1 to 18. Indeed, Indeed, the number number set used in the game allows allows the use of either a d20 or 3d6 roll without and changes. Neithe Neitherr die roll roll is perfec perfect; t; rather rather they they tend tend to create create a differen differentt flavor of play. play. Flat Flat die rolls do not favor any numer (a 1 will occur as often as a 20 on the d20) and thus instil a bit of randomness, allowing for a wide range of numbers. Combined die rolls tend to favor the middle numbers and slight the lower and high higher er end end numb number ers. s. This This make makes s them them more more predictable; they tend to result in the average quiet a bit. Which makes game play more predictable. Playe Playerr charac character ters s are are far more likel likely y to fail fail or succeed solely due to the die roll when using a d20 than with 3d6. On the other hand, a die roll like 3d6 is far more demanding: the higher the number needed for success, the lower the chance of acheiving it. Statistics are more forgiving for a d20 than for a 3d6; and more important for a 3d6 than a d20 . Those who prefer randomness will of course pick a flat roll roll like d12, d12, d20, or d100; d100; those who who prefer less randomness will pick a die roll like 2d6 or 3d6.
Succeed or Fail Rolls
Another example of randomness is the die roll used for success or failure checks: hitting a foe in combat, avoiding a trap, etc. The The rati ratio o of succ succes ess s vers versus us fail failur ure e affe affect cts s outcom outcomes es with with mathem mathemati atical cal monoto monotony ny.. Barrin Barring g random flukes, if a character has a 75% chance of failur (or success) they will fail (or succeed) 75% of the time. Consider how flat die rolls (such as a d20, d100, or d12) compare to combined die rolls (such as 2d6 or 3d6). 3d6). The follow following ing assume assumes s the same same basic basic
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