Vol. 11, No. 4, 2018

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Properties of sets of nontransitive dice with few sides

Levi Angel and Matt Davis

Vol. 11 (2018), No. 4, 643–659

We define and investigate several properties that sets of nontransitive dice might have. We prove several implications between these properties, which hold in general or for dice with few sides. We also investigate some algorithms for creating sets of 3-sided dice that realize certain tournaments.

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nontransitive dice, probability, tournaments
Mathematical Subject Classification 2010
Primary: 05B30
Secondary: 60C05
Received: 15 December 2016
Revised: 22 May 2017
Accepted: 14 August 2017
Published: 15 January 2018

Communicated by Kenneth S. Berenhaut
Levi Angel
Department of Mathematics and Computer Science
Muskingum University
New Concord, OH
United States
Matt Davis
Department of Mathematics and Computer Science
Muskingum University
New Concord, OH
United States