Independent-valued minimax: Pathological or beneficial?

Abstract

Minimax search, which is used by most game-playing programs, is considered pathological when deeper searches produce worse evaluations than shallower ones. This phenomenon was first observed in theoretical analyses under seemingly reasonable conditions. It was most commonly explained by the lack of dependence between nearby positions in the analyses: if nearby positions have similar values, as is typically the case in real games, the pathology no longer occurs. In this paper, we show that the pathology can be eliminated even without position-value dependence, by assigning enough different values to the positions and modeling the heuristic error as normally distributed noise that is independent of the depth in the game tree. This leads to the conclusion that minimax is less prone to the pathology than was previously thought and indicates the importance of the number of different position values.