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Concept
Alpha–beta pruning
Summary
Alpha–beta pruning is a search algorithm that seeks to decrease the number of nodes that are evaluated by the minimax algorithm in its search tree. It is an adversarial search algorithm used commonly for machine playing of two-player combinatorial games (Tic-tac-toe, Chess, Connect 4, etc.). It stops evaluating a move when at least one possibility has been found that proves the move to be worse than a previously examined move. Such moves need not be evaluated further. When applied to a standard minimax tree, it returns the same move as minimax would, but prunes away branches that cannot possibly influence the final decision.
Allen Newell and Herbert A. Simon who used what John McCarthy calls an "approximation" in 1958 wrote that alpha–beta "appears to have been reinvented a number of times". Arthur Samuel had an early version for a checkers simulation. Richards, Timothy Hart, Michael Levin and/or Daniel Edwards also invented alpha–beta independently in the United States. McCarthy proposed similar ideas during the Dartmouth workshop in 1956 and suggested it to a group of his students including Alan Kotok at MIT in 1961. Alexander Brudno independently conceived the alpha–beta algorithm, publishing his results in 1963. Donald Knuth and Ronald W. Moore refined the algorithm in 1975. Judea Pearl proved its optimality in terms of the expected running time for trees with randomly assigned leaf values in two papers. The optimality of the randomized version of alpha–beta was shown by Michael Saks and Avi Wigderson in 1986.
A game tree can represent many two-player zero-sum games, such as chess, checkers, and reversi. Each node in the tree represents a possible situation in the game. Each terminal node (outcome) of a branch is assigned a numeric score that determines the value of the outcome to the player with the next move.
The algorithm maintains two values, alpha and beta, which respectively represent the minimum score that the maximizing player is assured of and the maximum score that the minimizing player is assured of.
Official source
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