--- In vpFREE@yahoogroups.com, 007 <007@...> wrote:
> How does the
> Kelly Criterion maximize average bankroll growth? The same comparison
> can be made after the next trial, and so on, forever, the fact that
> betting one's entire bankroll on any advantage runs the risk of losing
> all of it notwithstanding.
One trick is that it's the geometric mean that counts, not the arithmetic mean. Taking the arithmetic mean assumes you can just go on forever averaging a series of outcomes, but in the real world you can not. Once you bust out, that's it, you're busted, game over, no more chances and it doesn't matter how well you were running before you busted out. Having a zero in a list that is arithmetic meaned just lowers the mean. Having a zero in a list that is geometric meaned sets the mean to zero, irregardless of how great the other results were. Kelly optimizes the geometric mean of bankroll growth, which is why a Kelly better would never bet it all, unless there was no risk of losing. Under the Kelly system, if you bust out once, that's it. You have not only not optimized bankroll growth, you have in fact committed bankroll suicide.
http://en.wikipedia.org/wiki/Mean
http://en.wikipedia.org/wiki/Kelly_criterion
