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Algorithms for Games and Probability Theory

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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.

Keywords

  • Evaluation Function
  • True Score
  • Model Game
  • Model Score
  • Probability Characteristic

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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  • DOI: 10.1007/978-1-4612-3796-9_4
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© 1988 Springer-Verlag New York Inc.

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Adelson-Velsky, G.M., Arlazarov, V.L., Donskoy, M.V. (1988). Algorithms for Games and Probability Theory. In: Algorithms for Games. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3796-9_4

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  • DOI: https://doi.org/10.1007/978-1-4612-3796-9_4

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-8355-3

  • Online ISBN: 978-1-4612-3796-9

  • eBook Packages: Springer Book Archive