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puredie

# puredie - Pure Dice Olvk is very concerned by bias on dice...

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Sheet1 Page 1 Pure Dice ---- ---- Olvk is very concerned by bias on dice, and wants to make an unbiased 6-sided dice. He does this by taking an N sided dice and throwing it 3 times. If the 3 values thrown are different, they can come out in one of 6 orderings, and each ordering has the same probability. By assigning a number from 1 through 6 to each of the 6 orderings, Olvk effectively has an unbiased 6-sided dice. For example, if S represents the smallest of three different values, M the middle value, and L the largest value, then the 6 orderings might be assigned values by SML1 SLM2 MSL3 MLS4 LSM5 LMS6 One problem is that the three values may not all be different: if N were 6, one might throw 115 or even 111. In this case Olvk choses to ignore the three values he just threw, and throw 3 more times. If we call a set of 3 throws a `round', Olvk keeps throwing rounds until he gets 3 different values. Olvk must throw M rounds to get an 1 unbiased throw if the first M-1 rounds each have 2 or 3 equal values and the M'th round does not.

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