Accession Number:

AD0766293

Title:

Analysis of the Alpha-Beta Pruning Algorithm,

Descriptive Note:

Corporate Author:

CARNEGIE-MELLON UNIV PITTSBURGH PA DEPT OF COMPUTER SCIENCE

Report Date:

1973-07-01

Pagination or Media Count:

55.0

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

Subject Categories:

  • Operations Research
  • Computer Programming and Software

Distribution Statement:

APPROVED FOR PUBLIC RELEASE