4 ms·
Don't look at the expectation of a single throw. Look at the distribution of the outcome after many throws. Relate that to the product of each throw's relative
by imh 8y ago
Don't look at the expectation of a single throw. Look at the distribution of the outcome after many throws. Relate that to the product of each throw's relative return. Look at how the log expectation of the product of n random variables converges as n gets big, and you see what to optimize.
- imh 8y ago(too late for me to edit my post, so I'll reply to it) The logic I posted above will show you that the log of your money X converges in probability to some value x that you can optimize. Optimizing x will optimize a monotonic utility f(x), which seems useful, but isn't. The problem is that just because X converges in probability to x, doesn't mean that f(X) converges in probability to f(x). Probability and convergence are weird.