The History Heuristic and Alpha-Beta Search Enhancements in Practice

Many enhancements to the alpha-beta algorithm have been proposed to help reduce the size of minimax trees. A recent enhancement, the history heuristic, is described that improves the order in which branches are considered at interior nodes. A comprehensive set of experiments is reported which tries all combinations of enhancements to determine which one yields the best performance. Previous work on assessing their performance has concentrated on the benefits of individual enhancements or a few combinations. However, each enhancement should not be taken in isolation; one would like to find the combination that provides the greatest reduction in tree size. Results indicate that the history heuristic and transposition tables significantly out-perform other alpha-beta enhancements in application generated game trees. For trees up to depth 8, when taken together, they account for over 99% of the possible reductions in tree size, with the other enhancements yielding insignificant gains. Index Terms Alpha-beta search, minimax search, game trees, history heuristic, transposition tables, minimal window search, killer heuristic.