Alpha-beta pruning
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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 games (Tic-tac-toe, Chess, Go, etc.). It stops completely 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 and Richards, Hart, Levine and/or Edwards invented alpha–beta independently in the United States. McCarthy proposed similar ideas during the Dartmouth Conference 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 and Judea Pearl proved its optimality in 1982.
The benefit of alpha–beta pruning lies in the fact that branches of the search tree can be eliminated. This way, the search time can be limited to the 'more promising' subtree, and a deeper search can be performed in the same time. Like its predecessor, it belongs to the branch and bound class of algorithms. The optimization reduces the effective depth to slightly more than half that of simple minimax if the nodes are evaluated in an optimal or near optimal order (best choice for side on move ordered first at each node).
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