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Expected-Outcome: A General Model of Static Evaluation
February 1990 (vol. 12 no. 2)
pp. 182-193

The expected-outcome model, in which the proper evaluation of a game-tree node is the expected value of the game's outcome given random play from that node on, is proposed. Expected outcome is considered in its ideal form, where it is shown to be a powerful heuristic. The ability of a simple random sampler that estimates expected outcome to outduel a standard Othello evaluator is demonstrated. The sampler is combined with a linear regression procedure to produce efficient expected-outcome estimators. Overall, the expected-outcome model of two-player games is shown to be precise, accurate, easily estimable, efficiently calculable, and domain-independent.

[1] B. Abramson, "Control strategies for two-player games,"ACM Comput. Surveys, June 1989.
[2] B. Abramson, "On learning and testing evaluation functions," inProc. Sixth Israeli Conf. Artificial Intelligence, 1989, to be published.
[3] B. Abramson and R. Korf, "A model of two-player evaluation functions," inProc. 6th Nat. Conf. Artificial Intelligence, 1987, pp. 90- 94.
[4] H. Berliner and C. Ebeling, "The SUPREM architecture: A new intelligent paradigm,"Artif. Intell., vol. 28, pp. 3-8, 1986.
[5] M. M. Botvinnik,Computers in Chess: Solving Inexact Search Problems. Berlin: Springer-Verlag, 1984 (translated by A. Brown).
[6] M. A. Bramer, "Correct and optimal strategies in game playing programs,"Comput. J., vol. 23, pp. 347-352, 1980.
[7] J. Christensen and R. Korf, "A unified theory of heuristic evaluation functions and its application to learning," inProc. Fifth Nat. Conf. Artificial Intelligence, 1986.
[8] J. H. Condon and K. Thompson, "Belle chess hardware," inAdvances in Computer Chess, vol. 3, M. R. B. Clarke, Ed. New York: Pergamon, 1982.
[9] P. W. Frey, "Machine Othello,"Personal Comput., pp. 89-90, 1980.
[10] A. K. Griffith, A comparison and Evaluation of three machine learning procedures as applied to the game of checkers,"Artificial Intell., vol. 5, pp. 137-148, 1974.
[11] D. Hartmann, "How to extract relevant knowledge from grandmaster games, Part 1,"Int. Comput. Chess Assoc. J., vol. 10, no. 1, pp. 14-36, 1987.
[12] D. Levy,Chess and Computers. Rockville, MD: Computer Science Press, 1976.
[13] P. B. Maggs, "Programming strategies in the game of reversi,"BYTE, vol. 4, pp. 66-79, 1979.
[14] N. Nilsson,Principles of Artificial Intelligence. Palo Alto, CA: Tioga, 1980.
[15] R. Richards, "The revised USOA rating system,"Othello Quart., vol. 3, no. 1, pp. 18-23, 1981.
[16] P. S. Rosenbloom, "A world-championship-level Othello program,"Artificial Intell., vol. 19, pp. 279-320, 1982.
[17] A. L. Samuel, "Some studies in machine learning using the games of checkers,"IBM J., vol. 3, no. 211-229, 1959.
[18] A. L. Samuel, "Some studies in machine learning using the game of checkers II--Recent progress,"IBM J., vol. 11, pp. 601-617, 1967.
[19] J. Schaeffer, "Speculative computing,"Int. Comput. Chess Assoc. J., vol. 10, no. 3, pp. 118-124, 1987.
[20] C. E. Shannon, "Programming a computer for playing chess,"Phil. Mag., vol. 41, pp. 256-275, 1950.
[21] S. L. Stepoway, "Reversi: An experiment in game-playing programs," inComputer Game Playing: Theory and Practice, Chichester, England: Ellis Horwood, 1983.
[22] J. von Neumann and O. Morgenstern,Theory of Games and Economic Behavior. Princeton, NJ: Princeton University Press, 1944.

Index Terms:
artificial intelligence; decision making; game theory; expected-outcome model; game-tree node; heuristic; Othello evaluator; linear regression; artificial intelligence; game theory
B. Abramson, "Expected-Outcome: A General Model of Static Evaluation," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 12, no. 2, pp. 182-193, Feb. 1990, doi:10.1109/34.44404
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