Independent-valued minimax: Pathological or beneficial?

Authors:
Mitja Lutrek;Ivan Bratko;Matja Gams
Affiliations:
Joef Stefan Institute, Department of Intelligent Systems, Jamova cesta 39, 1000 Ljubljana, Slovenia;University of Ljubljana, Faculty of Computer and Information Science, Traka cesta 25, 1000 Ljubljana, Slovenia;Joef Stefan Institute, Department of Intelligent Systems, Jamova cesta 39, 1000 Ljubljana, Slovenia
Venue:
Theoretical Computer Science
Year:
2012

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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.