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Gambling and information theory
Statistical inference might be thought of as gambling theory applied to the world around. The myriad applications for logarithmic information measures tell us precisely how to take the best guess in the face of partial information.〔Jaynes, E.T. (1998/2003) (''Probability Theory: The Logic of Science'' ) (Cambridge U. Press, New York).〕 In that sense, information theory might be considered a formal expression of the theory of gambling. It is no surprise, therefore, that information theory has applications to games of chance.〔J. L. Kelly, Jr., "A New Interpretation of Information Rate", ''Bell System Technical Journal'', Vol. 35, July 1956, pp. 917-26〕
== Kelly Betting ==
(詳細はinformation theory to investing and gambling. Its discoverer was John Larry Kelly, Jr.
Part of Kelly's insight was to have the gambler maximize the expectation of the ''logarithm'' of his capital, rather than the expected profit from each bet. This is important, since in the latter case, one would be led to gamble all he had when presented with a favorable bet, and if he lost, would have no capital with which to place subsequent bets. Kelly realized that it was the logarithm of the gambler's capital which is additive in sequential bets, and "to which the law of large numbers applies."
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