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.
Thursday, December 4, 2008
game theory in poker
I'd definitely recommend reading The Theory of Poker (TP), by David Sklansky. It has some really great concepts that can serve you well up to the higher levels (at least, I've been using it with apparent success in 100NL). Note that a lot of the same basic concepts can apply to limit and no-limit, but you must modify their use in each one -- for example, the free card play. One of the most important chapters in my opinion in TP is chapter 19, on bluffing and game theory. It shows how you can construct a non-exploitable strategy for betting. Basically, it boils down to picking a bluffing frequency f, where bluffing occurs at random, then laying your opponent odds when you bet so that they get 1/f-1 to 1 odds on a call. For example, let's say you're tight-aggressive and raise only about 10% of your hands, and generally create heads-up situations on the flop against a loose opponent who's generally dominated by your range. Then let's say you always continuation bet, and that when you do so, 75% of the time your hand is good, e.g., overpair, set or top pair good kicker, and 25% of the time you brick the flop or are up against a set, etc. Then the non-exploitable strategy is to c-bet 1/2 of the pot, which lays your opponent 3-to-1 odds on a call. However, since he's a 3-to-1 dog to have the best hand, there's no simple way he can adjust his folding frequency to exploit you. Even looking at the board may not help, since by assumption, he's often dominated (so if the flop is K-high, you might have AK or TT, and your opponent holding K4 can't tell since you bet no matter what the flop is). Clearly, if he always folds, you always win money, whereas if he always calls, you two break even (ignoring rake).
Of course, just because it's non-exploitable doesn't mean it yields the highest winrate. However, this provides a baseline or starting point where you can start making adjustments to exploit the weaknesses of your opponents.
Of course, just because it's non-exploitable doesn't mean it yields the highest winrate. However, this provides a baseline or starting point where you can start making adjustments to exploit the weaknesses of your opponents.
Tuesday, November 25, 2008
broken sunglasses
A few days ago, I was playing 50 NL online, and bought in for $30. I had AQ of spades pre-flop, and decided to call a mid-position raise to $2 from the cutoff, as did the BB. Then the flop came down:
Ad Ks 8s
Bingo! Top pair plus the nut flush draw. After BB checked, MP bet $4, and I decided to go for the overcall by just flat calling the bet -- and the BB obliged. A blank 4c came on the turn, and the BB bet out, MP moved in, I moved in, BB called. River came a Qc. I have two pair, which should be good -- right?
Nope: MP had QQ. He hit his one-outer. At this point, I realized, we have quite a fish on our hands. So I re-bought. However, it did NOT go well. I then had another hand with this guy where we both limped, when I had 46 suited. The flop came:
3d 5s Tc
Villain checked, I bet $1.50 with my open-ended straight draw. Turn came a 2h. That's my gin card! However, oddly, he led into me, so I raised, he reraised, I raised again, and he called. Then the river came a 6h. At this point, he led again, I just ship the rest in, and he insta-calls, and flips over the inevitable 24 off-suit. At this point, he'd caught his 3-outer to chop a $90 pot. I was so mad that I snapped a pair of old sunglasses that I'd been playing with clean in half. LOL!
Thus my downswing started. I believe after that I started assuming most of my opponents in 25NL and 50 NL were like that idiot. However, that's probably not a good thing. I got stacked twice in 5 minutes on Sunday. First, I ran AK with a wheel draw plus a pair of kings (and top kicker) into AA on the turn. Then, I had JJ with a flush draw running into a set, shipped it all in on the turn -- he quadded up on the river of course haha. :-)
I guess the lesson is that there are ALL KINDS of opponents on PokerStars. In all likelihood, the safest strategy, which I've been employing lately, is to give people credit by default, until I see a couple of examples of egregious play and/or egregious stats which should be exploitable. Although you decrease the chances of having those guys stack off to you, you also protect yourself against good tight-aggressive players. In short, think twice before calling any big bets.
Here's how I'm trying to define a "bad player":
1. VPIP (voluntarily puts money into pot pre-flop) > 50% with 95% confidence. If you see someone play 10 out of 10 pots observed, you could be pretty sure they're way too loose. Best way to exploit: raise more with your strong hands, and hope they call. Sometimes these people are tight post-flop, so a different strategy may be necessary then.
2. Pre-flop raise > 30% with 95% confidence. If someone raises 6 out of 9 pots observed, they're raising too much. Best way to exploit: 3-bet pre-flop with a wider range of hands.
3. Aggression factor < 0.5 with 95% confidence. Aggression factor is the number of post-flop bets + raises over the number of post-flop calls. This can take longer to figure out if someone is tight pre-flop. However, if in the post-flop action, they call 10 times and raise only 2, that's an AF of 0.2, and WAY too passive against any but the most insanely aggressive opponents. That basically means they're calling stations, most of the time. Occasionally, it also means they won't bet without the nuts, but call with good hands / draws almost exclusively. You can tell the difference by observing how often they stick around for the turn and river. Obviously, someone who's loose-passive post-flop is generally a terrible player. Best adjustments: decrease c-betting frequency, especially when in position, but increase range of hands you bet for value. Consider betting as little as mid-pair on every street, sometimes such people will call down with pocket deuces unimproved and without any draws -- believe me, it happened the other day in 25NL.
Any comments?
Ad Ks 8s
Bingo! Top pair plus the nut flush draw. After BB checked, MP bet $4, and I decided to go for the overcall by just flat calling the bet -- and the BB obliged. A blank 4c came on the turn, and the BB bet out, MP moved in, I moved in, BB called. River came a Qc. I have two pair, which should be good -- right?
Nope: MP had QQ. He hit his one-outer. At this point, I realized, we have quite a fish on our hands. So I re-bought. However, it did NOT go well. I then had another hand with this guy where we both limped, when I had 46 suited. The flop came:
3d 5s Tc
Villain checked, I bet $1.50 with my open-ended straight draw. Turn came a 2h. That's my gin card! However, oddly, he led into me, so I raised, he reraised, I raised again, and he called. Then the river came a 6h. At this point, he led again, I just ship the rest in, and he insta-calls, and flips over the inevitable 24 off-suit. At this point, he'd caught his 3-outer to chop a $90 pot. I was so mad that I snapped a pair of old sunglasses that I'd been playing with clean in half. LOL!
Thus my downswing started. I believe after that I started assuming most of my opponents in 25NL and 50 NL were like that idiot. However, that's probably not a good thing. I got stacked twice in 5 minutes on Sunday. First, I ran AK with a wheel draw plus a pair of kings (and top kicker) into AA on the turn. Then, I had JJ with a flush draw running into a set, shipped it all in on the turn -- he quadded up on the river of course haha. :-)
I guess the lesson is that there are ALL KINDS of opponents on PokerStars. In all likelihood, the safest strategy, which I've been employing lately, is to give people credit by default, until I see a couple of examples of egregious play and/or egregious stats which should be exploitable. Although you decrease the chances of having those guys stack off to you, you also protect yourself against good tight-aggressive players. In short, think twice before calling any big bets.
Here's how I'm trying to define a "bad player":
1. VPIP (voluntarily puts money into pot pre-flop) > 50% with 95% confidence. If you see someone play 10 out of 10 pots observed, you could be pretty sure they're way too loose. Best way to exploit: raise more with your strong hands, and hope they call. Sometimes these people are tight post-flop, so a different strategy may be necessary then.
2. Pre-flop raise > 30% with 95% confidence. If someone raises 6 out of 9 pots observed, they're raising too much. Best way to exploit: 3-bet pre-flop with a wider range of hands.
3. Aggression factor < 0.5 with 95% confidence. Aggression factor is the number of post-flop bets + raises over the number of post-flop calls. This can take longer to figure out if someone is tight pre-flop. However, if in the post-flop action, they call 10 times and raise only 2, that's an AF of 0.2, and WAY too passive against any but the most insanely aggressive opponents. That basically means they're calling stations, most of the time. Occasionally, it also means they won't bet without the nuts, but call with good hands / draws almost exclusively. You can tell the difference by observing how often they stick around for the turn and river. Obviously, someone who's loose-passive post-flop is generally a terrible player. Best adjustments: decrease c-betting frequency, especially when in position, but increase range of hands you bet for value. Consider betting as little as mid-pair on every street, sometimes such people will call down with pocket deuces unimproved and without any draws -- believe me, it happened the other day in 25NL.
Any comments?
Tuesday, November 18, 2008
semibluffing: try this at home?
I was playing someone's home game for the first time ever last Thursday. It was a NL hold 'em cash game with blind of $0.25 and $0.50. Most players bought in for only $20, but the host usually bought in for double that, so I followed suit. Our mutual friend characterized him as a hyper-aggressive player who nonetheless would fold to strong raises post-flop. With that as a background, let me tell you about the hand!
Pre-flop, it was folded around to the cutoff, who raised to $1.50. I called with 79 suited on the button, and the host called from the BB.
Then the flop came down:
6d 8h Ks
The action went: BB checks, CO bets $2, I raise to $6, BB re-raises to $12, CO folds, and then I pause to think. Based on what our mutual friend told me, if I put in another raise, I should have a ton of fold equity in this spot. That, plus the equity of my draw, should have made this a very +EV spot to reraise. Thus, I put in a reraise to $32 total. After thinking for a while, BB just calls. The turns comes a Tc, BB puts me all-in for another $17 -- I beat him into the pot. He flips over KK for top set! River came a 4c.
My feeling is that given the information that I had, as well as the way the hand played out, I played it reasonably well. I certainly also lucked out on that turn. But that also illustrates why semibluffs are so much better than a pure bluff.
Pre-flop, it was folded around to the cutoff, who raised to $1.50. I called with 79 suited on the button, and the host called from the BB.
Then the flop came down:
6d 8h Ks
The action went: BB checks, CO bets $2, I raise to $6, BB re-raises to $12, CO folds, and then I pause to think. Based on what our mutual friend told me, if I put in another raise, I should have a ton of fold equity in this spot. That, plus the equity of my draw, should have made this a very +EV spot to reraise. Thus, I put in a reraise to $32 total. After thinking for a while, BB just calls. The turns comes a Tc, BB puts me all-in for another $17 -- I beat him into the pot. He flips over KK for top set! River came a 4c.
My feeling is that given the information that I had, as well as the way the hand played out, I played it reasonably well. I certainly also lucked out on that turn. But that also illustrates why semibluffs are so much better than a pure bluff.
why bad beat expert?
Hey Guys,
Welcome to my new blog -- The Bad Beat Expert! Just to be clear, I don't think I'm the world's greatest expert on poker by any means. I'm just using the title to convey the sense a lot of tight-aggressive players like me have that we've experienced every bad beat known to man. :-)
I intend to write about my experiences playing poker, both live and online (I play on PokerStars), talk about hands and hopefully get some good feedback from you guys. I mainly play no-limit hold 'em cash games, for buy-ins ranging from $5 to $50, though I prefer to play at the higher end when I can find a good game. I'm also hoping to move up to $100 NL soon, but will put that off until my bankroll at least hits the "magic" 20 buy-in threshold. Overall, I believe I play winning poker, but have certainly had days where I questioned that assumption, mainly due to either bad luck or tilt.
Anyway, if you have specific topics you'd like me to talk about, or comments on my strategies, please feel free to let me know!
--BBE
Welcome to my new blog -- The Bad Beat Expert! Just to be clear, I don't think I'm the world's greatest expert on poker by any means. I'm just using the title to convey the sense a lot of tight-aggressive players like me have that we've experienced every bad beat known to man. :-)
I intend to write about my experiences playing poker, both live and online (I play on PokerStars), talk about hands and hopefully get some good feedback from you guys. I mainly play no-limit hold 'em cash games, for buy-ins ranging from $5 to $50, though I prefer to play at the higher end when I can find a good game. I'm also hoping to move up to $100 NL soon, but will put that off until my bankroll at least hits the "magic" 20 buy-in threshold. Overall, I believe I play winning poker, but have certainly had days where I questioned that assumption, mainly due to either bad luck or tilt.
Anyway, if you have specific topics you'd like me to talk about, or comments on my strategies, please feel free to let me know!
--BBE
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