Nontransitivity and Probability

Nontransitivity is the condition where a property X is not transitive, in other words, aXb and bXc do not imply aXc. The simplest example of nontransitivity is rock-paper-scissors, where rock beats scissors, scissors beat paper, and paper beat rock. Most would assume that in probability, transitivity holds. However, this is not the case, as it is possible to create dice sets and probability situations with nontransitivity. A very peculiar and non-intuitive result, this merits research. My senior honors project aims to perform further research into the dice-game example of nontransitivity in probability, wherein dice are selected by two or more players, and the last player to select can always pick a dice with a probability edge over the others. To research this, I investigated and experimented using theoretical dice sets. The results reveal interesting facts on the number of dice and sides per dice needed for games with different numbers of players, as well as some sample sets of dice with certain nontransitivity properties. This research delves into an interesting non-intuitive result of probability, and discovers odd properties of nontransitive dice.