Optimal minimax strategy in a dice game

Details Optimal minimax strategy in a dice game Optimal minimax strategy in a dice game

2009-12-30

arxiv.org/abs/0912.5518v1

Mathematics

Probability

14 pages

Scientific paper

Each of two players, by turns, rolls a dice several times accumulating the successive scores until he decides to stop, or he rolls an ace. When stopping, the accumulated turn score is added to the player account and the dice is given to his opponent. If he rolls an ace, the dice is given to the opponent without adding any point. In this paper we formulate this game in the framework of competitive Markov decision processes (also known as stochastic games), show that the game has a value, provide an algorithm to compute the optimal minimax strategy, and present results of this algorithm in three different variants of the game.

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