Nontransitive dice with equal means and variances

Abstract

This study aims to investigate the nontransitivity of the stochastic precedence relation. The dice were taken as an example of discrete random variables with a finite set of values. The means and variances of the dice were assumed those of the classical dice. The whole variety of nontransitive sets containing three or four dice were found in case of one or two tosses and various ways to determine the advantage. The sets that reveal the strongest property of nontransitivity were obtained according to the specific function. The hypothesis has been tested about the emergence of non-transitivity after two tosses of dice in originally transitive sets.