Probabilistic analysis of search

Abstract

The performance of decision making in computer game playing programs is determined by the search algorithm in their inner loops. This thesis involves several aspects of the special AI area, computer game playing, which include game tree modeling, search pathology investigation, pruning efficiency analysis, and position evaluation representation. It focuses on the application of probability. A new probabilistic model for game trees is proposed. In this model, node value dependence is simulated with conditional probabilities. This model eliminates some curious properties of the existing models, and its flexibility reflects the great variety of real games. Some interesting properties of this model are derived. One of them makes it possible for both the root and terminal nodes to have the same probability to take the same score. The minimax pathology that searching deeper makes the backed-up values more random is investigated for the new model. It is shown that for a certain class of games, minimax search does reduce the error propagation. Formulas are also derived for computing the probabilities of making a correct decision when an obvious evaluation function is used. The calculation provides strong evidence to support the relation between minimax search benefit and node value dependence. The commonly used game tree search algorithm, the alpha-beta pruning algorithm, is analyzed for more practical game trees. Recursive equations for the average number of visited terminal nodes are derived. In this way, the effect of node value dependence on the pruning efficiency can be analyzed. The alpha-beta pruning algorithm can also be generalized for probability-based game tree search when the strength of a node is described by a probability distribution. The new algorithm inherits some good properties from its point-value version. Several variations of this algorithm are presented, one of which is the degeneration of this probability-based algorithm into a range-based one.