Generalized Intransitive Dice II: Partition Constructions
Abstract
A generalized N-sided die is a random variable D on a sample space of N equally likely outcomes taking values in the set of positive integers. We say of independent N-sided dice Di,Dj that Di beats Dj, written Di → Dj, if Prob(Di > Dj) > (Formula presented) A collection of dice {Di: i = 1,…,n} models a tournament on the set [n] = {1, 2,…,n}, i.e. a complete digraph with n vertices, when Di → Dj if and only if i → j in the tournament. By using regular n-fold partitions of the set [Nn] to label the N-sided dice we can model an arbitrary tournament on [n] and N can be chosen to be less than or equal to N = 3n-2.
Recommended Citation
E. Akin and J. Saccamano, "Generalized Intransitive Dice II: Partition Constructions," Journal of Dynamics and Games, vol. 8, no. 3, pp. 187 - 202, American Institute of Mathematical Sciences, Jul 2021.
The definitive version is available at https://doi.org/10.3934/jdg.2021005
Department(s)
Mathematics and Statistics
Keywords and Phrases
digraph; Intransitive dice; mimicking a tournament; modeling a tournament; nontransitive dice; partitions; regular partitions; tournament
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 Jul 2021
