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DAM
2006

Optimal strategies for equal-sum dice games

13 years 10 months ago
Optimal strategies for equal-sum dice games
In this paper we consider a non-cooperative two-person zero-sum matrix game, called dice game. In an (n, ) dice game, two players can independently choose a dice from a collection of hypothetical dice having n faces and with a total of 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, ) dice games for which optimal strategies exist and derive for these games the number of optimal strategies as well as their explicit form. Key words: Dice game, Zero-sum matrix game, Non-cooperative game, Optimal strategy, Partitions. 1 Description of the dice game The (n, ) dice game is a game played between two players who want to obtain the highest individual profit. Both players choose independently a dice from the collection of (n, ) dice. An (...
Bart De Schuymer, Hans De Meyer, Bernard De Baets
Added 11 Dec 2010
Updated 11 Dec 2010
Type Journal
Year 2006
Where DAM
Authors Bart De Schuymer, Hans De Meyer, Bernard De Baets
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