Here is an introduction to nontransitive dice. The question is: given $n$-player with a $m$-sided dice each one, the what is the minimum of $m$ for a fixed $n$ to produce nontransitivity?
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What is the most extreme set 4 or 5 nontransitive n-sided dice?What is the most extreme set 4 or 5 nontransitive n-sided dice?