Boštjan Kaluža (2008) ANALYSIS OF PATHOLOGICAL MODELS OF MINIMAX AND PEARL'S GAME. EngD thesis.
Computer games based on the minimax principle usually produce better results when searching deeper. When researchers attempted to explain this formally using mathematical models, they found that under certain conditions the minimax behaves unexpectedly: deeper search produced worse results. This phenomenon was termed minimax pathology. We examine pathological models of minimax search and factors influencing on the pathology. The most important factors are the branching of the game tree, the number of position values, the probability of loss for player on the move and the dependence between nearby positions. Our goal is to elucidate their impact on the pathology. We design an independent minimax model and combine it with several dependent models. One of them is originally constructed in this work, others were already presented by other authors. The pathology is also analyzed on partly dependent trees. We conclude that the analyzed models behave qualitatively similarly. The pathology is decreasing with increasing dependence and increasing number of position values. Increasing branching strengthens pathology in pathological regions and weakens it in non-pathological regions. Models are experimentally verified on Pearl game, which was already used in the pathology research in the past. The original game is expanded with several factors and tested with several heuristic functions. The pathology is analyzed with the selected heuristic function average confirming influence of the branching factor and dependence between nearby positions. The number of position values using the selected heuristic function does not impact on the pathology as predicted by the model.
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