# Coin game - applying Kelly criterion

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. - 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 ## 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.

-