Paranoia versus Overconfidence in Imperfect- Information Games

In minimax game-tree search, the min part of the minimax backup rule derives from what we will call the paranoid assumption: the assumption that the opponent will always choose a move that minimizes our payoff and maximizes his/her payoff (or our estimate of the payoff, if we cut off the search before reaching the end of the game). A potential criticism of this assumption is that the opponent may not have the ability to decide accurately what move this is. But in several decades of experience with game-tree search in chess, checkers, and other zero-sum perfect-information games, the paranoid assumption has worked so well that such criticisms are generally ignored. In game-tree search algorithms for imperfect-information games, the backup rules are more complicated. Many of them (see Section 6) involve computing a weighted average over the opponent’s possible moves (or a Monte Carlo sample of them), where each move’s weight is an estimate of the probability that this is the opponent’s best possible move. Although such backup rules do not take a min at the opponent’s move, they still tacitly encode the paranoid assumption, by assuming that the opponent will choose optimally from the set of moves he/she is actually capable of making. Intuitively, one might expect the paranoid assumption to be less reliable in imperfectinformation games than in perfect-information games; for without perfect information, it may be more difficult for the opponent to judge which move is best. The purpose of this paper is to examine whether it is better to err on the side of paranoia or on the side of overconfidence. Our contributions are as follows: