Abstract

This short paper proposes a simple extension of the celebrated MINIMAX algorithm used in zero-sum two-player games, called Rminimax. The Rminimax algorithm allows controlling the strength of an artificial rival by randomizing its strategy in an optimal way. In particular, the randomized shortest-path framework (Saerens et al., 2009) is applied for biasing the AI adversary towards worse or better solutions, therefore controlling its strength. This framework takes into account all possible strategies by computing an optimal trade-off between exploration (quantified by the spread entropy in the tree) and exploitation (quantified by the expected cost to an end game) of the game tree. As opposed to other tree-exploration techniques, this new algorithm considers complete paths of a tree (strategies) where a given entropy is spread. The optimal randomized strategy is efficiently computed by means of a simple recurrence relation while keeping the same complexity as the original MINIMAX. As a result, the Rminimax implements a non-deterministic, strength-adapted, AI opponent for board games in a principled way, thus avoiding the assumption of complete rationality. Simulations on two common games show that Rminimax behaves as expected.

Citations