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Even-money edge

Expected valueEasy

A bet wins an amount equal to your stake with probability $\frac{3}{5}$ and loses the stake otherwise. What fraction of your bankroll should you stake to maximise the expected logarithm of wealth?

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Hint

For even money, the optimal fraction is the win probability minus the loss probability.

Solution

For net odds $b = 1$ , the optimal fraction is $\frac{b p - q}{b}$ with $p = \frac{3}{5}$ and $q = \frac{2}{5}$ .
That is $\frac{\frac{3}{5} - \frac{2}{5}}{1}$ .
So the fraction is $\frac{1}{5}$ .

Answer: $\frac{1}{5}$

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