An Incremental Negamax Algorithm

Abstract In certain models of game trees with erroneous evaluation functions the minimax algorithm does not reduce errors, even under favourable assumptions about the size of the errors and the frequency of their occurrence. We present an incremental negamax algorithm, which uses estimates of all nodes in the tree (rather than only those of the leaves) to determine the root value. Under the assumption of independently occurring and sufficiently small errors, the algorithm is shown to have exponentially reduced error probabilities with respect to the height of the tree.