Balanced Non-Transitive Dice

2016/02/02 by Schaefer, Alex, Schweig, Jay · 2 citations
#05A99 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1602.00969

Abstract

We study triples of labeled dice in which the relation "is a better die than" is non-transitive. Focusing on such triples with an additional symmetry we call "balance," we prove that such triples of n-sided dice exist for all n ≥ 3. We then examine the sums of the labels of such dice, and use these results to construct an O(n²) algorithm for verifying whether or not a triple of n-sided dice is balanced and non-transitive. Finally, we consider generalizations to larger sets of dice.

Cited by

• Winning Probabilities of Balanced and Nontransitive n-tuples of Dice
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