2009/12/30 by Fabián Crocce, Fabian Crocce, Ernesto Mordecki +2 · 1 citation
Computer Science · Engineering · Mathematics · #60J10 #91A15 #Artificial Intelligence in Games #Computer Science and Game Theory (cs.GT) #Computer science #Dice #FOS: Computer and information sciences #FOS: Mathematics #Guidance and Control Systems #Mathematical economics #Mathematical optimization #Mathematics #Minimax #Numerical Methods and Algorithms #Optimization and Control (math.OC) #Probability (math.PR) #Statistics #cs.GT #math.OC #math.PR #msc:60J10 #msc:91A15
paper · pdf · doi:10.48550/arxiv.0912.5518
published in arXiv (Cornell University) (Cornell University) · 14 pages
arxiv created 2009/12/30 · openalex publication_date 2009/12/30 · arxiv updated 2010/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.