Analysis of the Alpha-Beta Pruning Algorithm,
Abstract
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1973
- Accession Number
- AD0766293
Entities
People
- J. G. Gaschnig
- J. J. Gillogly
- S. H. Fuller
Organizations
- Carnegie Mellon University