Resolución del Juego del Backgammon Utilizando la Estrategia MiniMax

El presente trabajo fue realizado como proyecto final para una materia que introduce al análisis y diseño de algoritmos, dictada en el segundo año de una carrera de Informática. Consiste en la implementación del juego Backgammon utilizando la técnica de Backtracking, específicamente la estrategia Minimax. Incluye tanto la interfaz gráfica como el diseño de los algoritmos que solucionan el problema.Sociedad Argentina de Informática e Investigación Operativ

Machine Learning Techniques for the Development of a Stratego Bot

Stratego is a two-player, non-stochastic, imperfect-information strategy game in which players try to locate and capture the opponent\u27s flag. At the outset o f each game, players deploy their pieces in any arrangement they choose. Throughout play, each player knows the positions of the opponent’s pieces, but not the specific identities o f the opponent’s pieces. The game therefore involves deduction, bluffing, and a degree o f invention in addition to the sort o f planning familiar to perfect-information games like chess or backgammon. Developing a strong A.l. player presents three major challenges. Firstly, a Stratego program must maintain states o f belief about the opponent’s pieces as well as beliefs about the opponent’s beliefs. Beliefs must be updated according to in-game events. We propose to solve this using Bayesian probability theory and Bayesian networks. Secondly, any turn-based game-playing program must perform tree search as part o f its planning and move-making routine. Search in perfect-information games such as chess has been studied extensively and produced a wealth o f algorithms and heuristics to expedite the process. Stochastic and imperfect-information games, however, have received less general attention, though Schaeffer et al have made a significant effort to revisit this domain. Interestingly, the same family o f algorithms (Ballard’s Star-1 and Star-2) used in the stochastic perfect-information game of backgammon can be used in the deterministic, imperfect-information domain o f Stratego. The technical challenge here, just as in the stochastic domain, is to optimize node cutoffs. Thirdly, a strong Stratego program should have some degree o f inventiveness so that it can avoid predictable play. The game’s intricacy comes from information being concealed from the players. A program which plays too predictably (that is, according to known or obvious tactics) has a significant disadvantage against a more creative opponent. There is a balance, however, between tactics’ being novel and being foolish. Current, strong Stratego programs have been developed by human experts (such as Vincent deBoer), whose tactical preferences are hard-coded into those programs. Since we claim no especial talent for Stratego ourselves, part o f the development challenge will be to allow the program to discover tactical preferences and advantages on its own. Withholding explicitly programmed heuristics and allowing machines to discover tactics on their own has led to original and powerful computer play in the past (note Tesauro’s success with TD-Gammon). We hope our program will likewise learn to play competitively without depending on instruction from a mediocre or predictable player. Various techniques from machine learning, including both supervised and unsupervised learning, are applied to this objective. At our disposal are more than 50,000 match records from an online Stratego site. Part of developing a strong player will involve separating the truly advantageous features in these data from features which are merely frequent. The learning process must be objective enough to avoid bias and predictability, yet robust enough to exploit utility. We introduce a modeling method which allows partial instruction as guidelines for feature detection

minimax performance in backgammon

Abstract. This paper presents the first performance results for Ballard’s *-Minimax algorithms applied to a real–world domain: backgammon. It is shown that with effective move ordering and probing the Star2 algorithm considerably outperforms Expectimax. Star2 allows strong backgammon programs to conduct depth 5 full-width searches (up from 3) under tournament conditions on regular hardware without using risky forward pruning techniques. We also present empirical evidence that with today’s sophisticated evaluation functions good checker play in backgammon does not require deep searches.