Ed wrote:
>If you bet your whole bankroll on any edge, then X percent of the time you
>will bust and then it's impossible to grow the bankroll. That severely
>limits your average bankroll growth.
>
>Kelly seeks to maximize the average rate of growth of a bankroll. In other
>words, if you bet according to Kelly at a +EV game then you will experience
>a greater average bankroll growth than if you bet any other way.
Maybe an example would clarify. Let's say there's a gambling
proposition, similar to blackjack, that pays even money and has a
50.5% chance of winning and a 49.5% chance of losing. That's a 1%
advantage and the Kelly Criterion says to bet 1% of one's bankroll on
it. Let's say, for ease of use, that one's bankroll is $10,000.
After 1 $100 bet, one's average bankroll has grown by 1% of 1%, or $1,
and is now $10,001. If one bets $10,000, after 1 trial, one's average
bankroll is (maximized at) $20,000 x .505 = $10,100. 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.
