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 (...

• Type: Journal
• Year: 2006
• Where: DAM
• Authors: Bart De Schuymer, Hans De Meyer, Bernard De Baets
• Keywords: DAM 2006, DICE, Dice Game, Zero-sum Matrix Game