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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!2012-11-13

2 Answers 2

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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.