5 Apr
2006
5 Apr
'06
10:40 a.m.
Does anyone know if there is a recent summary of all that's known about intransitive dice? Searching on MathSciNet doesn't seem to get me very far. Suppose you have a cyclically ordered sequence of n dice, each of which has s sides, and each of which beats the (cyclically) next one with the same probability p > 1/2. I believe I saw some reference that claims p <= 3/4 under all circumstances; maybe another that sharpened this to p <= sqrt(5 - 1)/2 = .618.... --Dan