I had just been trying to figure out how much I have to rebuild by bankroll to before I can safely play $1/2 NL. My model is a drift-diffusion model, where the "drift" is created by good play, which gives you a certain winrate, parameterized by v, and the "diffusion" is created by suckouts (going both ways), etc., and parameterized by s (for sigma). Over a certain time t (=number of hands / 100), you will make the following amount of money x with 95% probability:
x = v*t +/- 2*s*sqrt(t)
You can then use this formula to estimate your maximum unlucky losses as a winning player, or maximum lucky wins as a losing player. The results are:
x_{min} = -s^2/v
x_{max} = s^2/|v|
The interesting part is when you plug in some real numbers. Over a sample of nearly 5k hands, I got s=86 bb/100 and v=20 bb/100 for 25NL online. If those numbers were my "true" numbers, then I'd expect to lose no more than 370 bb's (=$92.50) at least 97.5% of the time. However, if I'm on a hot streak, and s stays the same but v=5 bb/100, say, then I could lose up to $370. Conversely, if I'm actually a very mediocre 25NL player, breaking roughly even before rake, but have been lucky, with v=-2 bb/100, then I could win up to $3698 before coming back down to earth. Pretty sick, huh? The lesson is it takes a lot of hands to determine whether you're a winning player.
Applying these numbers to live play, it's clear that even if I had the same winrate at $1/2NL in bb/100 before rake, then you probably have to subtract another 5 bb/100 for the extra live rake (10% capped live instead of 5% online), and subtract another few bb/100 for worse table selection (it's not as easy to find the biggest fish of all at Foxwoods, or quickly switch tables). So I think v=10 would be a good goal for now. So how much could I lose by chance before I started to come back? Well, according to this analysis: $1480. Since that's where my bankroll is at right now, I might in principle be able to still play live $1/2 NL. However, I think I should still build up a cushion in case these assumptions are too optimistic. It seems like a starting bankroll of twice that, or roughly $3000, should allow for a healthy margin of error. In the meantime, I've estimated the standard deviation of limit play with the same big blinds is roughly 40% of that -- so my max possible losses (with 97.5% likelihood) at a roughly equal winrate of 5 bb/100 would be $237. Sounds pretty safe -- limit ftw! :-)
Friday, May 22, 2009
Monday, May 18, 2009
Foxwoods short-stack experiment
I went to Foxwoods yesterday, and decided to try playing a short-stack ($100) at 1/2NL. Sadly, I didn't run well. A few key hands:
1. First orbit at table: 2 limps, I raise to $15 with AA, folds all around.
2. One limper, I raise to $10 with AT of clubs on the button, laggy limper calls. Flop comes AQ9, all spades. Limper checks, I bet $15, limper flats. Turn comes a 4 of spades, limper checks, I probe-bet another $15, limper comes over the top for $40. He flashes a 2 of spades, so presumably he had A2.
3. One limp, I raise to $10 with QT of spades in late position, tight button calls, BB and limper call. Flop comes AK8, 1 spade. Two checks, I bet $25, button calls, 2 folds. Turn comes a blank, I check, button bets $60, I fold.
4. New table: straddle is on; I'm down to $64. Super-lag raises to $12, ultra-loose player calls on my right. I wake up with AQs in the SB and move in. Super-lag snap calls with AK -- no help from the board. I rebuy to $100.
5. A few hands later... a few limps around, I wake up with Ac Ks in the SB, raise to $15, get 3 callers. Flop comes J58, 2 clubs. I check, super-aggro lady on my left bets $20 into $60 pot, 2 folds, I call getting 4-to-1 odds, with the plan to shove all-in on any A, K, or club (28% of turns). Sadly, turn comes a brick, and I check/fold. She claimed to have had AJ later, which I doubt, though truthfully 22 had me crushed!
Overall, I think these hands were fairly standard and I was just unfortunate to not win any big pots (biggest win was $20, I think). I also bled blinds like crazy (~$70 over 8 hours) because almost every hand was raised pre-flop, so I saw few flops (and couldn't call the raises with a short stack).
It also seems like the strategy of 2/3 of the players there is to see a flop with speculative hands for $15 or less and hope to bomb someone post-flop. This suggests two lessons:
1. I should wait to go back until I can afford to buy in deeper ($200 or more) and have 2 full rebuys in my back pocket, which would allow me to see more flops.
2. I should 3-bet people a little wider than QQ+ and AK, because it seems that people raise and call very wide pre-flop, but are also VERY uncomfortable with calling or 4-betting big 3-bets pre-flop themselves without a premium hand (i.e., AK or JJ+). Taking down a couple more raised pots with a 3-bet would add to my winrate enormously.
1. First orbit at table: 2 limps, I raise to $15 with AA, folds all around.
2. One limper, I raise to $10 with AT of clubs on the button, laggy limper calls. Flop comes AQ9, all spades. Limper checks, I bet $15, limper flats. Turn comes a 4 of spades, limper checks, I probe-bet another $15, limper comes over the top for $40. He flashes a 2 of spades, so presumably he had A2.
3. One limp, I raise to $10 with QT of spades in late position, tight button calls, BB and limper call. Flop comes AK8, 1 spade. Two checks, I bet $25, button calls, 2 folds. Turn comes a blank, I check, button bets $60, I fold.
4. New table: straddle is on; I'm down to $64. Super-lag raises to $12, ultra-loose player calls on my right. I wake up with AQs in the SB and move in. Super-lag snap calls with AK -- no help from the board. I rebuy to $100.
5. A few hands later... a few limps around, I wake up with Ac Ks in the SB, raise to $15, get 3 callers. Flop comes J58, 2 clubs. I check, super-aggro lady on my left bets $20 into $60 pot, 2 folds, I call getting 4-to-1 odds, with the plan to shove all-in on any A, K, or club (28% of turns). Sadly, turn comes a brick, and I check/fold. She claimed to have had AJ later, which I doubt, though truthfully 22 had me crushed!
Overall, I think these hands were fairly standard and I was just unfortunate to not win any big pots (biggest win was $20, I think). I also bled blinds like crazy (~$70 over 8 hours) because almost every hand was raised pre-flop, so I saw few flops (and couldn't call the raises with a short stack).
It also seems like the strategy of 2/3 of the players there is to see a flop with speculative hands for $15 or less and hope to bomb someone post-flop. This suggests two lessons:
1. I should wait to go back until I can afford to buy in deeper ($200 or more) and have 2 full rebuys in my back pocket, which would allow me to see more flops.
2. I should 3-bet people a little wider than QQ+ and AK, because it seems that people raise and call very wide pre-flop, but are also VERY uncomfortable with calling or 4-betting big 3-bets pre-flop themselves without a premium hand (i.e., AK or JJ+). Taking down a couple more raised pots with a 3-bet would add to my winrate enormously.
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