jgunnip
05-17-2007, 04:09 PM
My innernets were clogged last night ([censored] Comcast) so I couldn't play any poker or read 2p2 or anything else that I normally do at night on my computer /images/graemlins/frown.gif So I picked up the latest installment to my poker library, The Mathematics of Poker (FPP store ftw), and started reading. I had to put it down after a few pages since it got me thinking and motivated to do some number crunching. Being the aggrotard I am I started doing some EV calcs for stealing any two cards on the button. Hope some of you find this interesting and/or helpful.
Everyone knows stealing the blinds with a wide range is profitable against most opponents because you’ll either win the blinds preflop or take the pot down on the flop with a continuation bet. Sometimes you’ll even flop a big hand, stack a donk and get berated for playing trash like 75o. /images/graemlins/tongue.gif
My standard open raise from the button is 4bb so I’m risking this to win 1.5bb. Assume a strategy where we steal with any two cards and always fold to a 3bet and fold every time we are called and see a flop. The blind steal would be profitable if our steal was successful x% of the time where, 1.5(x)-4(1-x)>0. Solve for x and you get x>(4/5.5) or approx 72.7%. Now suppose both the sb and bb fold their blind 90% of the time. Under this strategy we would average +.455 bb every time we raised from the button [1.5(.81)-4(.19)]. If both blinds instead folded only 70% of the time the EV of our strategy would now be -1.305 bb. Ok, obv this strategy is dumb but its good to be aware that raising ATC is instantly profitable from the button if the blinds fold more than 73% of the time (ie the product of their fold the blind stats is greater than 73%).
In reality we’re not always folding when we don’t win the blinds right away, so I came up with another strategy using some arbitrary assumptions,
- Effective stacks 20bb+
- We raise ATC
- Our opponents will three bet us with 99+, AQ+, the top 5% of their hands and we always fold.
- We will always fold when both blinds call (They call independently of each other)
- When one opponent calls they will donkbet the flop 15% of the time and we fold
- When one opponent calls it gets checked to us 85% of the time and we always make a continuation bet
- When we cbet we win the pot 60% of the time and fold when we are called or raised
- We always cbet 7bb
- On average we’ll win a pot of 4.75bb when our opponent folds to the cbet
Assume again that both blinds fold 90% to steals. I won’t show all the math for different outcome but we win the blinds preflop 81% of the time. Get called by one blind 9% and 10% of the time we’ll get either raised or both blinds call. Given these probabilities we can calculate the EV of this strategy against these opponents as,
1.5(.81)-4(.1)-4(.09)(.15)+4.75(.85)(.6)(.09)-(4+7)(.85)(.4)(.09)= +.642 bb
Here are the corresponding EVs of this strategy against blinds who fold X% and Y% of the time to steals
(90-90) = +.642 bb
(90-80) = +.295 bb
(90-70) = +.006 bb
(90-60) = -.341 bb
(80-80) = +.020 bb
(80-70) = -.314 bb
(80-75) = -.138 bb
(50-50) = -1.69bb lol
The breakeven point appears to be when XY = ~ .62
Under the given assumptions, raising any two cards from the button theoretically shows immediate profit when both blinds will fold 62% of the time.
We could extend this example to the cutoff position as well and I think the same breakeven point would hold, that is when we can steal the blinds out right more than 62% of the time it is profitable to raise ATC. However, there aren’t many games where this will be the case.
Lol playingcrapaments!! I’m not trying to convince anybody to start raising everything from the button when it’s folded to them. When I used to play sngs optimal strategy was almost entirely mathematical. Most decisions are made at the zeroth level. Cash games aren’t that simple. One play might be the best against a certain type of opponent but very costly against another. But in some instances if we make certain assumptions about different variables of a hand we will be able to figure out a clearly correct and a clearly incorrect play. For example calling a bet on the turn if we are on a draw to the absolute nuts. Blind stealing isn’t as clear and while this model isn’t perfect, there is still much we can figure out by working with some numbers.
Generally a player who folds their blind 90% of the time will fold less against a button open raise than a cutoff open raise. Most tight players after seeing their blinds getting raised orbit after orbit will adjust and begin playing back more. You won’t always take down the pot on the flop with a continuation bet three out of five times. Some opponents will fold if they don’t flop at least TPTK. Others will call a cbet with any piece of the flop, any pair, and draw, overs, if it’s raining outside, who knows. Also sometimes we’ll actually hit a hand but lose a big pot to a better hand. There are many things that can happen.
However the math doesn’t lie. If your opponents are super nits in the blinds you are probably leaving some money on the table if you’re not raising 72o from the button when its gets folded to you. If you know which players at your table are weak postflop and fold to continuation bets most of the time, you can try and isolate them with almost any hand knowing that most times you’ll win a pot uncontested on the flop. You can also exploit players who cbet nearly every time by playing pots against them in position, float them and profit! Same goes for blind stealing. If you know you’re going to take down the blinds 90% of the time, then why not raise any two cards? I don’t consider any of this be a big secret or anything, it’s mostly basic. But I have a feeling a lot of uNL players as they move up through 10nl, 25nl, and 50nl don’t adjust and open up their game in spots where it is clearly profitable to do so. Thoughts? Feel free to ask any questions about the math I used.
Also, just because I fold my bb to a steal 88% of the time doesn’t mean you can start raising a2c, I’ll be waiting to 3bet J9o /images/graemlins/tongue.gif
Everyone knows stealing the blinds with a wide range is profitable against most opponents because you’ll either win the blinds preflop or take the pot down on the flop with a continuation bet. Sometimes you’ll even flop a big hand, stack a donk and get berated for playing trash like 75o. /images/graemlins/tongue.gif
My standard open raise from the button is 4bb so I’m risking this to win 1.5bb. Assume a strategy where we steal with any two cards and always fold to a 3bet and fold every time we are called and see a flop. The blind steal would be profitable if our steal was successful x% of the time where, 1.5(x)-4(1-x)>0. Solve for x and you get x>(4/5.5) or approx 72.7%. Now suppose both the sb and bb fold their blind 90% of the time. Under this strategy we would average +.455 bb every time we raised from the button [1.5(.81)-4(.19)]. If both blinds instead folded only 70% of the time the EV of our strategy would now be -1.305 bb. Ok, obv this strategy is dumb but its good to be aware that raising ATC is instantly profitable from the button if the blinds fold more than 73% of the time (ie the product of their fold the blind stats is greater than 73%).
In reality we’re not always folding when we don’t win the blinds right away, so I came up with another strategy using some arbitrary assumptions,
- Effective stacks 20bb+
- We raise ATC
- Our opponents will three bet us with 99+, AQ+, the top 5% of their hands and we always fold.
- We will always fold when both blinds call (They call independently of each other)
- When one opponent calls they will donkbet the flop 15% of the time and we fold
- When one opponent calls it gets checked to us 85% of the time and we always make a continuation bet
- When we cbet we win the pot 60% of the time and fold when we are called or raised
- We always cbet 7bb
- On average we’ll win a pot of 4.75bb when our opponent folds to the cbet
Assume again that both blinds fold 90% to steals. I won’t show all the math for different outcome but we win the blinds preflop 81% of the time. Get called by one blind 9% and 10% of the time we’ll get either raised or both blinds call. Given these probabilities we can calculate the EV of this strategy against these opponents as,
1.5(.81)-4(.1)-4(.09)(.15)+4.75(.85)(.6)(.09)-(4+7)(.85)(.4)(.09)= +.642 bb
Here are the corresponding EVs of this strategy against blinds who fold X% and Y% of the time to steals
(90-90) = +.642 bb
(90-80) = +.295 bb
(90-70) = +.006 bb
(90-60) = -.341 bb
(80-80) = +.020 bb
(80-70) = -.314 bb
(80-75) = -.138 bb
(50-50) = -1.69bb lol
The breakeven point appears to be when XY = ~ .62
Under the given assumptions, raising any two cards from the button theoretically shows immediate profit when both blinds will fold 62% of the time.
We could extend this example to the cutoff position as well and I think the same breakeven point would hold, that is when we can steal the blinds out right more than 62% of the time it is profitable to raise ATC. However, there aren’t many games where this will be the case.
Lol playingcrapaments!! I’m not trying to convince anybody to start raising everything from the button when it’s folded to them. When I used to play sngs optimal strategy was almost entirely mathematical. Most decisions are made at the zeroth level. Cash games aren’t that simple. One play might be the best against a certain type of opponent but very costly against another. But in some instances if we make certain assumptions about different variables of a hand we will be able to figure out a clearly correct and a clearly incorrect play. For example calling a bet on the turn if we are on a draw to the absolute nuts. Blind stealing isn’t as clear and while this model isn’t perfect, there is still much we can figure out by working with some numbers.
Generally a player who folds their blind 90% of the time will fold less against a button open raise than a cutoff open raise. Most tight players after seeing their blinds getting raised orbit after orbit will adjust and begin playing back more. You won’t always take down the pot on the flop with a continuation bet three out of five times. Some opponents will fold if they don’t flop at least TPTK. Others will call a cbet with any piece of the flop, any pair, and draw, overs, if it’s raining outside, who knows. Also sometimes we’ll actually hit a hand but lose a big pot to a better hand. There are many things that can happen.
However the math doesn’t lie. If your opponents are super nits in the blinds you are probably leaving some money on the table if you’re not raising 72o from the button when its gets folded to you. If you know which players at your table are weak postflop and fold to continuation bets most of the time, you can try and isolate them with almost any hand knowing that most times you’ll win a pot uncontested on the flop. You can also exploit players who cbet nearly every time by playing pots against them in position, float them and profit! Same goes for blind stealing. If you know you’re going to take down the blinds 90% of the time, then why not raise any two cards? I don’t consider any of this be a big secret or anything, it’s mostly basic. But I have a feeling a lot of uNL players as they move up through 10nl, 25nl, and 50nl don’t adjust and open up their game in spots where it is clearly profitable to do so. Thoughts? Feel free to ask any questions about the math I used.
Also, just because I fold my bb to a steal 88% of the time doesn’t mean you can start raising a2c, I’ll be waiting to 3bet J9o /images/graemlins/tongue.gif