Towards Understanding Conceptual Differences Between Minimaxing and Product-Propagation

Advantages and disadvantages of minimaxing versus product propagation back-up rules for game tree searching have been intensively discussed in the literature. So far, examinations have almost exclusively been carried out through experiments, demonstrating slight superiorities for one or the other back-up rule. In contrast to these purely quantitative investigations, we aim at elaborating differences in strength of these back-up rules by characterizing properties of critical situations in which these differences prove relevant. Evidence from the examinations carried out shows that minimaxing is better for a uniform error distribution under pathologically high and very low error rates, while high frequencies of critical cases favoring product propagation lead to a dominance of this back-up rule for realistic error distributions in depth 2 searches. The results provide insights for assessing degrees of competence of the two back-up rules, suggesting combined uses when facing move decisions.1