Quote:
Originally Posted by Garick
Kelly Criterion has to do with bet sizing vs percentage of roll. Each stack at a cash table is not a bet, whereas each buy in for a tournament or SNGs is, in that you'll either get a return on it or lose it. Trying to use it for cash game BRM makes no sense unless you are basically playing a shove or fold strategy.
If you are thinking of win rate and variance, your buy-in to a game is very like a bet. You put money on the table, play a while, and then take money off the table. The amount you take off the table after a specific time is going to be related to the amount you put on the table by some probabilty distribution, and that distribution is going to have a mean and a variance (and higher-order statistical moments, but let's leave those alone). We have a mean and a variance, and so we can compute our Kelly criterion.
Bear in mind that the way we change our bet size in our attempt to maximize log(rate of bankroll growth) with poker cash games is by changing the stakes we play, e.g. from 1-3 to 2-5 to 5-10 to 10-25 et cetera. (Do bear in mind that our win rates are going to be different at these different levels, and that impacts the size of bankroll Kelly prescribes.)
I haven't actually done this calculation for plausible NLHE win rates, but back in the day, when I was a limit hold'em pro, the conventional wisdom was that for limit hold'em, a winning player needed a bankroll of 300 big bets (not big blinds) to comfortably play at a particular stake. When you plug the typical winning player's win rate and variance into a Kelly calculation, it turns out that playing a 300-big-bet bankroll was the equivalent of about 1/3 of Kelly, and that the way to maximize log(bankroll growth) would be to play with a 100-bet bankroll . . .
if you were disciplined about moving down in downswings as well as moving up in upswings.
The same people who recommended 300 bets for LHE recommended twenty buy-ins for NLHE. It is too much of a stretch to really say so, but if the relationship to Kelly was in fact the same for LHE and NLHE players, then a roll of only
7 buy-ins is all one needs to maximize log(bankroll growth), if, that is, you are as disciplined about moving down as you are aggressive in moving up.