Minimax Pathology and Real-Number Minimax Model

Game-playing programs usually evaluate moves by searching the game tree using the minimax principle. Practice shows that deeper searches produce better results. However, theoretical analyses indicate that under apparently reasonable conditions, the behavior of minimax is pathological, i.e. deeper searches produce worse results. In this paper, a minimax model that – unlike most work in this area – uses real numbers for positions’ values is introduced. It usually does not exhibit pathology. Mechanism that improves evaluation with depth is explained. Comparison to chess is made, showing the model not to be unrealistic.