Optimal strategies for equal-sum dice games

Authors:
B. De Schuymer;H. De Meyer;B. De Baets
Affiliations:
Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan, Gent, Belgium;Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan, Gent, Belgium;Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Gent, Belgium
Venue:
Discrete Applied Mathematics
Year:
2006

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Abstract

In this paper, we consider a non-cooperative two-person zero-sum matrix game, called dice game. In an (n, σ) dice game, two players can independently choose a dice from a collection of hypothetical dice having n faces and with a total of σ eyes distributed over these faces. They independently roll their dice and the player showing the highest number of eyes wins (in case of a tie, none of the players wins). The problem at hand in this paper is the characterization of all optimal strategies for these games. More precisely, we determine the (n, σ) dice games for which optimal strategies exist and derive for these games the number of optimal strategies as well as their explicit form.