Abstract
We consider the optimal wagers to be made by a gambler facing cointossing games who desires to maximize the expected value of the utility of his final fortune in a fixed number n of plays. In the case of fixed probability of a win, the optimal bet is shown to be increasing in the probability. In the case of unknown probability of a win, the wager is shown to be monotone in the prior distribution under the monotone likelihood ratio ordering of these distributions.
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