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Analysis of the Alpha-beta Pruning Algorithm

S. H. FullerJ. G. GaschnigJ. J. Gillogly

出版	Carnegie-Mellon University. Department of Computer Science, 1973
URL	http://books.google.com.hk/books?id=fPqjNwAACAAJ&hl=&source=gbs_api

註釋

Many game-playing programs must search very large game trees. Use of the alpha-beta pruning algorithm instead of the simple minimax search reduces by a large factor the number of bottom positions which must be examined in the search. An analytical expression for the expected number of bottom positions examined in a game tree using alpha-beta pruning is derived, subject to the assumptions that the branching factor N and the depth D of the tree are arbitrary but fixed, and the bottom positions are a random permutation of (N sub D) unique values. A simple approximation to the growth rate of the expected number of bottom positions examined is suggested, based on a Monte Carlo simulation for large values of N and D. The behavior of the model is compared with the behavior of the alpha-beta algorithm in a chess playing program and the effects of correlation and non-unique bottom position values in real game trees are examined. (Author).