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Algorithms for Games and Probability Theory

In: Algorithms for Games

Author

Listed:
  • G. M. Adelson-Velsky

    (Institute for Systems Studies)

  • V. L. Arlazarov

    (Institute for Systems Studies)

  • M. V. Donskoy

    (Institute for Systems Studies)

Abstract

In Chapter 2 we considered a probabilistic model of a two-person game in which the probability of a correct decision as to the score of the base position is an increasing function of the depth of the search. The results we obtained had a qualitative flavor, inasmuch as their proofs depended on the hypothesis that the values of the evaluation function f(A) for different positions A are independent. It is not clear that this hypothesis is valid; one of the postulates does not hold: The value of the evaluation function f(B) at the position B, following the move Ψ = (A, B) from the position A, depends on the value of f(A). Nevertheless, the method we used (recursive determination of the probability that the model score is correct, as a function of the value of the evaluation function f(D) for positions D of rank r(D) = n) can be applied under a much more general set of postulates.

Suggested Citation

  • G. M. Adelson-Velsky & V. L. Arlazarov & M. V. Donskoy, 1988. "Algorithms for Games and Probability Theory," Springer Books, in: Algorithms for Games, chapter 0, pages 144-174, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-3796-9_4
    DOI: 10.1007/978-1-4612-3796-9_4
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