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On the Failure of Gambling Systems Under Unfavorable Odds |
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PP: 31-36 |
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Author(s) |
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Jason Parker,
Subhash Bagui,
K. L. Mehra,
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Abstract |
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| The analysis of systems of gambling, in which the gambler attempts to overcome a disadvantage of unfavorable odds in a sequence of plays by judicious choice of bet sizes, has been a recurring theme in the development of probability theory. The impossibility of these and related systems has at times been used to formalize the notion of a random sequence of trials. A more modern approach is to prove theorems to the effect that such systems fail with probability tending to unity as the number of trials increases. That failure of systems is here made more precise with a strong convergence result first stated by Thorp in his book, The Mathematics of Gambling [1] . Thorp’s proof outline [2] apparently relies on the invalid assumption that the amounts won or lost on different trials are independent. Building on previous analyses by Doob [3] and Feller [4], we obtain a corrected proof.
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