RogueRivered
Visionary
Silver Level
I just finished reading Fortune's Formula. It discussed, among other things, the optimal betting strategy called the Kelly Criterion. Basically, the Kelly Criterion says to bet the amount of your bankroll that is your edge. Figuring out your edge seems a bit tricky, but if my research has been accurate, the equation is:
Winrate = Standard Dev.* (2p-1), where p is your expected probabilty of winning.
So according to my calculations, at .02/05nl, my winrate is 8.81bbs/100 and my standard deviation is 69.11 (found in HEM). Solving for p, I find that I have an edge 12.7% at these stakes.
To calculate the ideal bankroll, we use the formula:
B = SD^2/(Kelly fraction * winrate), so mine is 69.11^2/(1*8.81) = 542 bbs. That's only about $27.
Some people like to bet less than the Kelly amount to be safer due to the uncertainties of these estimates, so say a 1/2 Kelly bet would require a bankroll of 69.11^2/(1/2*8.81) = 1084 bbs. A 1/2 Kelly bet is supposed to grow at 75% the maximum growth rate, but offer 50% less risk.
The key with the Kelly formula is that your bets get bigger as you win, but smaller as you lose. Your risk of ruin is supposed to be zero as long as you can keep reducing your bets, but realistically you can lose practically everything. There is a 50% chance using Kelly that your bankroll will fall to 50% of it's current level, and a 10% chance that it will fall to 10% of current. But overall, your rate of growth will be optimized. If you bet more than the Kelly bet, say, like double, you will almost surely go broke (or close to it).
I'm not too good at math, and it took me forever to figure out this much, so if anyone sees any errors, please let me know.
Winrate = Standard Dev.* (2p-1), where p is your expected probabilty of winning.
So according to my calculations, at .02/05nl, my winrate is 8.81bbs/100 and my standard deviation is 69.11 (found in HEM). Solving for p, I find that I have an edge 12.7% at these stakes.
To calculate the ideal bankroll, we use the formula:
B = SD^2/(Kelly fraction * winrate), so mine is 69.11^2/(1*8.81) = 542 bbs. That's only about $27.
Some people like to bet less than the Kelly amount to be safer due to the uncertainties of these estimates, so say a 1/2 Kelly bet would require a bankroll of 69.11^2/(1/2*8.81) = 1084 bbs. A 1/2 Kelly bet is supposed to grow at 75% the maximum growth rate, but offer 50% less risk.
The key with the Kelly formula is that your bets get bigger as you win, but smaller as you lose. Your risk of ruin is supposed to be zero as long as you can keep reducing your bets, but realistically you can lose practically everything. There is a 50% chance using Kelly that your bankroll will fall to 50% of it's current level, and a 10% chance that it will fall to 10% of current. But overall, your rate of growth will be optimized. If you bet more than the Kelly bet, say, like double, you will almost surely go broke (or close to it).
I'm not too good at math, and it took me forever to figure out this much, so if anyone sees any errors, please let me know.