The phenomenon of decision oscillation: A new consequence of pathology in game trees

Abstract

Random minimaxing studies the consequences of using a random number for scoring the leaf nodes of a full width game tree and then computing the best move using the standard minimax procedure. Experiments in Chess showed that the strength of play increases as the depth of the lookahead is increased. Previous research by the authors provided a partial explanation of why random minimaxing can strengthen play by showing that, when one move dominates another move, then the dominating move is more likely to be chosen by minimax. This paper examines a special case of determining the move probability when domination does not occur. Specifically, we show that, under a uniform branching game tree model, whether the probability that one move is chosen rather than another depends not only on the branching factors of the moves involved, but also on whether the number of ply searched is odd or even. This is a new type of game tree pathology, where the minimax procedure will change its mind as to which move is best, independently of the true value of the game, and oscillate between moves as the depth of lookahead alternates between odd and even.