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Mathletics by Wayne L. Winston

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OPTIMAL MONEY MANAGEMENT

The Kelly Growth Criteria

Suppose we believe we have an almost sure bet on Colts—12. We believe the Colts have a 90% chance of covering the spread. This would probably never happen, but let's assume that such a bet really exists. What fraction of our capital should we allocate to this bet? If we bet all our money many times on bets with a 90% chance of winning, eventually we will be wiped out when we first lose a bet. Therefore, no matter how good the odds, we must be fairly conservative in determining the optimal fraction of our capital to bet.

Edward Kelly determined the optimal fraction of capital to bet on any one gamble.1 Kelly assumes our goal is to maximize the expected long-run percentage growth of our portfolio ...

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