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On game graph structure and its influence on pathology

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Abstract

Almost all game tree search procedures used in Artificial Intelligence are variants on minimaxing. Until recently, it was almost universally believed that searching deeper on game trees with such procedures would in general yield a better decision. However, recent investigations show that there are many “pathological” game trees for which searching deeper consistentlydegrades the decision.

This paper investigates one possible cause of pathology. In particular, a class of games that is normally pathological is shown to become nonpathological when the games are modified so that game positions can be reached by more than one path. This result suggests that in general, pathology is less likely when game positions can be reached by more than one path. This may be one reason why games such as chess and checkers are nonpathological. In addition, this result supports the hypothesis(9) that pathology is less likely when sibling nodes have similar minimax values.

This paper also investigates a possible cure for pathology-an alternative to minimaxing called probability estimation which has been shown to avoid pathology and thus produce more accurate decisions than minimaxing on at least one pathological game. (11) The current paper shows that depending on what evaluation function is used, probability estimation can also produce more accurate decisions than minimaxing on at least one nonpathological game. Probability estimation or other related procedures could conceivably become attractive alternatives to minimaxing if suitable tree pruning procedures could be developed for use with them.

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Authors and Affiliations

  1. Computer Science Department, University of Maryland, 20742, College Park, Maryland

    Dana S. Nau

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  1. Dana S. Nau
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Additional information

This work was supported by NSF Grant MCS-8117391 to the Laboratory for Machine Intelligence and Pattern Analysis at the University of Maryland.

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Nau, D.S. On game graph structure and its influence on pathology. International Journal of Computer and Information Sciences 12, 367–383 (1983). https://doi.org/10.1007/BF00977966

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  • DOI: https://doi.org/10.1007/BF00977966

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