Multi-player alpha-beta pruning
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This work presents a generalized theoretical framework that allows incorporation of opponent models into adversary search. We present the M* algorithm, a generalization of minimax that uses an arbitrary opponent model to simulate the opponent's search. The opponent model is a recursive structure consisting of the opponent's evaluation function and its model of the player. We demonstrate experimentally the potential benefit of using an opponent model. Pruning in M* is impossible in the general case. We prove a sufficient condition for pruning and present the αβ* algorithm which returns the M* value of a tree while searching only necessary branches.