Generalized Intransitive Dice: Mimicking an Arbitrary Tournament

Author

Ethan Akin, Missouri University of Science and TechnologyFollow

Abstract

A generalized TV-sided die is a random variable D on a sample space of TV equally likely outcomes taking values in the set of positive integers. We say of independent TV sided dice Di, Dj that Di beats Dj, written Di →Dj, if Prob(Di< Dj) < 1/2. Examples are known of intransitive 6-sided dice, i.e. D1→ D2→D3 but D3→ D1. A tournament of size n is a choice of direction i → j for each edge of the complete graph on n vertices. We show that if R is tournament on the set [n] = {1,…, n}, then for sufficiently large N there exist sets of independent TV-sided dice {Di,…, Dn} such that Di→ Dj if and only if i→ j in R.

Recommended Citation

E. Akin, "Generalized Intransitive Dice: Mimicking an Arbitrary Tournament," Journal of Dynamics and Games, vol. 8, no. 1, pp. 1 - 20, American Institute of Mathematical Sciences, Jan 2021.

The definitive version is available at https://doi.org/10.3934/jdg.2020030

Department(s)

Mathematics and Statistics

International Standard Serial Number (ISSN)

2164-6074

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2026 American Institute of Mathematical Sciences, All rights reserved.

Publication Date

01 Jan 2021