Abstract
In 1956, J.L. Kelly provided the formula for the optimal portion f of one’s capital to bet on a coin toss with favorable odds. We show that when the bet can be repeated a fixed number of times, but the game has a maximum payout M, the optimal portion f becomes a function of both k, the number of games remaining, and B, the current bankroll. We describe this function f k ( B ) and quantify the advantages gained over the fixed Kelly criterion. We also discuss the impact of changing the underlying utility function from a logarithmic utility to a more linear utility, and thereby optimizing a risk-reward ratio.
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