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arXiv · 2610.15421

General Constructions of Permutation-Fair Dice

Tomáš Gavenčiak·Bernhard Haeupler·Václav Rozhoň
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Abstract

Suppose that each of $n$ players rolls a different die and the players are ordered by their rolls. Can the dice use disjoint labels such that ties are impossible, while all $n!$ orders remain equally likely? We give two general constructions of such dice and solve some related problems.

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Tomáš Gavenčiak, Bernhard Haeupler, Václav Rozhoň. 2026-10-11. General Constructions of Permutation-Fair Dice. https://arxiv.org/abs/2610.15421

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