The past day or two I've spent a great deal of time learning about Kelly criterion.
Something I've struggled with the last few months is that I feel stupendously overrolled for 2/3NL, but I feel underrolled for 5/10NL. I figured with Kelly criterion, I could have a better understanding about when it's time to move up and take shots, and ultimately I'd be more confident with risk.
First I had to figure out my standard deviation from excel spreadsheets, which was kind of difficult because standard deviation tends to operate on a per hour or per hundred hands basis. If you had a bunch of sessions of varying lengths, you can't just depend on STDEV in Excel to solve everything.
Fortunately I stumbled on this article which showed me how to calculate the standard deviation. So now I have standard deviation and winrate. By the way, if anyone thinks this website is wrong, please let me know. It's sort of the backbone of this entire blog.
This lead to a formula which I got from this book (which I highly recommend, and you can get it via kindle iPad).
The formula is:
Kelly Criterion bankroll = (standard deviation)^2 divided by winrate, or
Kelly Criterion bankroll = Variance divided by winrate
Where Variance is the same thing as STDEV squared.
Plug in your variance and winrate, and Kelly Criterion will tell you the most ruthlessly precise way to take shots for a given game.
So I ran into the following for the games I play (since mid-August):
Standard deviation: 49.8 big blinds per hour
Winrate: 10.3 big blinds per hour
Based on these figures, Kelly criterion thinks it's fine for me to play in this game with 240 big blinds!
A similar thing happens for 5/10NL
Standard deviation: 43.3 big blinds per hour
Winrate: 13.7 big blinds per hour
In this game it's okay to take a shot with 136 big blinds!
The first thing to draw from this is that I'm running hot. I don't expect to make $135/hr (practically 30bb/100) at 5/10 forever, even if I continue to game selecting absurdly well. More reasonable is like $100/hr bumhunting and $50/hr while accepting the "good, but not great" lineups.
The second thing to draw from this is that the amount of hours is a little too small. Everyone cites 1k hours as a benchmark and I'm only two thirds the way there. The standard deviation is close'ish, though.
But let's say I keep the same standard deviation and lower my winrate at 5/10 to $50/hr. Kelly criterion still says I should take a shot at this game with 375 blinds!
So pure Kelly criterion thinks that I should be aggromonkey with my bankroll. In Newall's book, he says some gamblers adapt a "One third kelly" style where they just multiply the magical bankroll number by 3. Others go so far as to multiply the kelly bankroll by 6.
The applications are pretty necessary if you plan on jumping into bigger games with smaller edges (like, say, 40/80 limit holdem live), but I don't have reasonable samples in anything except 2/3NL and 5/10NL. Even the most cautious kelly bankroll models seem to think that A) I'm overrolled for 5/10 and B) I should begin immediately taking shots at bigger games. I would obviously have to estimate winrates and standard deviation for these bigger games before figuring out the proper bankroll, but I'm sure I could grab them from someone else with more experience.
I'm curious if anyone else has studied Kelly criterion to this effect and uses a "One third kelly" or "One sixth Kelly" that could explain their bankroll philosophy.