Empirical Exploration of the Performance of the Alpha Beta Tree-Searching Heuristic

Abstract

The alpha beta heuristic has been used extensively as a means for reducing the tree-searching effort in computer game-playing programs. It is well known that if the number of terminal nodes in a tree is N, then under optimal circumstances the alpha beta heuristic reduces the actual number of nodes examined to about 2N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">½</sup> . This is a substantial reduction in the case that N is on the order of ten thousand to a million. Unfortunately these optimal conditions are equivalent, in the case of game playing, to having immediate knowledge for every position in the tree as to which alternative is the best one; and this amount of foreknowledge would make tree searching unnecessary in the first place! This paper explores quantitively the performance of the alpha beta heuristic under a wide variety of conditions other than the optimal one, including several situations occurring in actual game-playing programs.