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I'm looking at a simple coin game where I have \$100, variable betting allowed, and 100 flips of a fair coin where H=2x stake+original stake, T=lose stake.

  1. If I'm asked to maximise the expected final net worth $N$, am I meant to simply bet a fraction of $\frac{1}{4}$ (according to the Wikipedia article on the Kelly criterion)?
  2. What if I'm asked to maximise the expectation of $\ln(100+N)$? Does this change my answer?

Thanks for any help.

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Sorry, missed my morning coffee. I wrote dice but this is completely a coin game. I'll go back and edit this! –  Derek Nov 13 '12 at 12:56
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1 Answer

The Wikipedia essay says bet $p-(q/b)$, where $p$ is the probability of winning, $q=1-p$ of losing, and $b$ is the payment (not counting the dollar you bet) on a one dollar bet. For your game, $p=q=1/2$ and $b=2$ so, yes, bet one-fourth of your current bankroll.

Sorry, I'm not up to thinking about the logarithmic question.

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