Here is an introduction to [nontransitive dice](http://en.wikipedia.org/wiki/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?

Here is some related posts:

[What is the most extreme set 4 or 5 nontransitive n-sided dice?][1]

[What is the most unfair set of three nontransitive dice?][2]

[How far can probability intransitivity be stretched?][3]


  [1]: https://mathoverflow.net/questions/119867/what-is-the-most-extreme-set-4-or-5-nontransitive-n-sided-dice
  [2]: https://math.stackexchange.com/questions/260072/what-is-the-most-unfair-set-of-three-nontransitive-dice
  [3]: https://math.stackexchange.com/questions/57338/how-far-can-probability-intransitivity-be-stretched?rq=1