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Go First Dice for Five Players and Beyond. Cover
Open Access
|Jan 2023

Abstract

Before a game begins, the players need to decide the order of play. This order of play is determined by each player rolling a die. Does there exist a set of dice such that draws are excluded and each order of play is equally likely? For four players the solution involves four 12-sided dice, sold commercially as Go First Dice. However, the solution for five players remained an open question. We present two solutions. The first solution has a particular mathematical structure known as binary dice, and results in a set of five 60-sided dice, where every place is equally likely. The second solution is an inductive construction that results in one one 36-sided die; two 48-sided dice; one 54-sided die; and one 20-sided die, where each permutation is equally likely.

Language: English
Page range: 75 - 87
Published on: Jan 27, 2023
Published by: Ludus Association
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2023 Robert Ford, James Grime, Eric Harshbarger, Brian Pollock, published by Ludus Association
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.