A Theory of Evaluative Comments in Chess with a Note on Minimaxing
Classical game theory partitions the set of legal chess positions into three evaluative categories: won, drawn and lost. Yet chess commentators employ a much larger repertoire of evaluative terms than this, distinguishing (for example) a ‘drawn’ from a ‘balanced’ position, a ‘decisive’ from a’ slight’ advantage, an ‘inaccuracy’ from a ‘mistake’ and a ‘mistake’ from a ‘blunder’. As an extension of the classical theory, a model of fallible play is developed. Using this, an additional quantity can in principle be associated with each position, so that we have not only its ‘game-theoretic value’ but also its ‘expected utility’. A function of these two variables can be found which yields explications for many evaluative terms used by chess commentators. The same model can be used as the basis of computer play. It is shown to be easier to justify, and to adjust to realistic situations, than the minimax model on which state of the art chess programs are based.
KeywordsExpected Utility Relative Probability Terminal Position Game Tree Opponent Model
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