# A Game of Nontransitive Dice

arXiv: https://arxiv.org/abs/1706.00849 · HTML: https://mlsanity.com/paper/1706.00849/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jun 2017.

## Built on by (most cited first, 1 of 1)

- [Intransitively winning chess players positions](https://mlsanity.com/paper/2212.11069/) (2022)

## Abstract (arXiv)

We consider a two player simultaneous-move game where the two players each select any permissible n-sided die for a fixed integer n. A player wins if the outcome of his roll is greater than that of his opponent. Remarkably, for n>3, there is a unique Nash Equilibrium in pure strategies. The unique Nash Equilibrium is for each player to throw the Standard n-sided die, where each side has a different number. Our proof of uniqueness is constructive. We introduce an algorithm with which, for any nonstandard die, we may generate another die that beats it.