Abstract
Under the assumption that wagers remain integer-valued, as would happen in most casinos, we identify the following bizarre situation: there exists a sequence of coin flips \(X\) such that some effective gambler manages to accumulate arbitrary wealth by betting on \(X\), however any such gambler goes bankrupt whenever he tries to take his winnings outside the casino.
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Acknowledgments
The author thanks Leonid Levin for conjecturing the existence of an integer-valued savings paradox.
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Teutsch, J. A savings paradox for integer-valued gambling strategies. Int J Game Theory 43, 145–151 (2014). https://doi.org/10.1007/s00182-013-0377-7
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DOI: https://doi.org/10.1007/s00182-013-0377-7