A cure for pathological behavior in games that use Minimax

Abstract

Minimax has long been the standard method of evaluating game tree nodes in game-playing programs. The general assumption underlying these programs is that deepening search improves play. Recent work has shown that this assumption is not always valid; for a large class of games and evaluation functions, deepening search decreases the probability of making a correct move. This phenomena is called game tree pathology. Two structural properties of game trees have been suggested as causes of pathology: independence among the values of sibling nodes, and uniform depth of win nodes. This paper examines the relationship between uniform win depth and pathology. A game-playing program is run using two different evaluation functions. The first recognizes wins only at the bottom level, the second at various levels throughout the tree. The minimax procedure behaves pathologically when the first function is used: the second shows no such pathology. This result constitutes the first experimental evidence linking uniform win depth to pathology. The effect of not recognizing wins until the bottom of the tree on the probability of making a correct decision is also analyzed. This analysis may lead to a general characterization of pathology in terms of win distribution.