Bias and pathology in minimax search

This article presents the results of experiments designed to gain insight into the effect of the minimax algorithm on the error of a heuristic evaluation function. Two types of effect of minimax are considered: (a) evaluation accuracy (are the minimax backed-up values more accurate than the heuristic values themselves?), and (b) decision accuracy (are moves played by deeper minimax search better than those by shallower search?). The experiments were performed in the KRK chess endgame and in randomly generated game trees. The results show that, counter-intuitively, evaluation accuracy may decline with search depth, whereas at the same time decision accuracy improves with depth. In the article, this is explained by the fact that minimax in combination with a noisy evaluation function introduces a bias into the backed-up evaluations, which masks the evaluation effectiveness of minimax, but this bias still permits decision accuracy to improve with depth. This observed behaviour of minimax in the KRK endgame is discussed in the light of previous studies of pathology in minimax. It is shown that explaining the behaviour of minimax in an actual chess endgame in terms of previously known results requires special care.