Building Sets of Permutation-Fair Dice

Abstract

We define what it means for a set of dice to be m/n permutation fair. We show how some collections of sets of m/n permutation-fair dice can be combined to create new sets of dice that are ( m + 1 ) / n permutation fair. By applying this method recursively, we show that our method is generic. That is, it can be used to create sets of dice that are m/n permutation fair for all m and n. We show that our method is more efficient than what we call the concatenation construction, which is the only other known generic method for constructing sets of permutation-fair dice. We conclude by demonstrating how our method can be used to construct a set of five 120-sided dice that is permutation fair.