Maximising the expected return of a single throw is different to maximising the growth rate over many throws. This is perhaps a bit unintuitive, for the reason

Maximising the expected return of a single throw is different to maximising the growth rate over many throws. This is perhaps a bit unintuitive, for the reason that the expectation doesn't tell you a great amount about a distribution. You could imagine a similar game in which one choice of bet results in an enormous return with a tiny probability, or else ruin. Whilst your expected return method would tell you to repeatedly make this choice, doing so is clearly insane.