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Quarter-sized stake

Expected valueMedium

A bet pays even money (win your stake or lose it) and wins with probability $\frac{11}{20}$ . Your bankroll is $2000$ dollars, and you stake exactly one quarter of the full-Kelly amount. How many dollars do you stake?

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Hint

First find the full-Kelly fraction, then scale.

Solution

With even money the full fraction is $p - q = \frac{11}{20} - \frac{9}{20} = \frac{1}{10}$ .
A quarter of that is $\frac{1}{40}$ of the bankroll.
The stake is $2000 \times \frac{1}{40} = 50$ .

Answer: $50$

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