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Pure Dice
 
Olvk is very concerned by bias on dice, and wants to
make an unbiased 6sided 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 6sided
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 M1 rounds each
have 2 or 3 equal values and the M'th round does not.
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 Spring '11
 k.v.arya

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