Calculating Fold [Steal] Equity On The Fly
I am a very +EV oriented player, who plays live $1/$2 no-limit holdem games at my local B&M Casino. I'm profitable, with a combination of fairly tight play and lethal trapping plays. I find this to be the easiest way to extract the most equity from the other players.
My next foray in developing my game is to develop my bluffing technique. Up to now, I considered bluffing in the way most players seem to approach it a fools errand. I don't see the point in a big uncalculated bet on the turn or river, which is usually a blatantly obvious attempt to buy the pot - it fails more often than it succeeds, especially to trap players like myself who are waiting for this type of bet to call.
To go back to first principles for a moment, in poker one can win either by having the cards, or getting the other fellow to lay down his.
My current quest is to find the most mathematically rigorous and elegant formula that one can use "on-the-fly" to determine optimum bet size on the turn, or river when bluffing at a pot such that a positive EV is arrived at.
When I bluff, I presume certain criteria will be present:
- I will be in the BB, SB or Button
- The players involved in the hand will be either Very Tight or Tight players
- The board will show either a 1) flush draw 2) straight draw 4) AA, KK, JJ, TT, 99
- All the other players will either have checked to me, or a small 1BB bet will be in play.
My initial nature would be to raise exactly as I would if I held the cards I needed in the pocket:
If a flush draw, bet a total of 36% of the pot
If a straight draw, bet a total of 32% of the pot
if any pair showing, bet a total of 28% of the pot.
These are all standard draw equities giving +EV for the respective hands. I feel this is incorrect due to the fact that I must base my bet size on the probability of the other players to fold, not the draw equity - but I suppose this is a place to start.
I wonder of any of you learned folks, or perhaps Mr. Scharf himself, would be gracious enough to shed some light on the best way to proceed in calculating the appropriate percentages based on if the player I'm bluffing is very tight/tight/loose and what is showing on the board so that we end up with +EV, even if the bluff is called the appropriate percentage of times.
My next foray in developing my game is to develop my bluffing technique. Up to now, I considered bluffing in the way most players seem to approach it a fools errand. I don't see the point in a big uncalculated bet on the turn or river, which is usually a blatantly obvious attempt to buy the pot - it fails more often than it succeeds, especially to trap players like myself who are waiting for this type of bet to call.
To go back to first principles for a moment, in poker one can win either by having the cards, or getting the other fellow to lay down his.
My current quest is to find the most mathematically rigorous and elegant formula that one can use "on-the-fly" to determine optimum bet size on the turn, or river when bluffing at a pot such that a positive EV is arrived at.
When I bluff, I presume certain criteria will be present:
- I will be in the BB, SB or Button
- The players involved in the hand will be either Very Tight or Tight players
- The board will show either a 1) flush draw 2) straight draw 4) AA, KK, JJ, TT, 99
- All the other players will either have checked to me, or a small 1BB bet will be in play.
My initial nature would be to raise exactly as I would if I held the cards I needed in the pocket:
If a flush draw, bet a total of 36% of the pot
If a straight draw, bet a total of 32% of the pot
if any pair showing, bet a total of 28% of the pot.
These are all standard draw equities giving +EV for the respective hands. I feel this is incorrect due to the fact that I must base my bet size on the probability of the other players to fold, not the draw equity - but I suppose this is a place to start.
I wonder of any of you learned folks, or perhaps Mr. Scharf himself, would be gracious enough to shed some light on the best way to proceed in calculating the appropriate percentages based on if the player I'm bluffing is very tight/tight/loose and what is showing on the board so that we end up with +EV, even if the bluff is called the appropriate percentage of times.
Comments
Although after typing this, I thought of a hand last night where I used math to bluff (Well not really, read on). Â pre-flop raise to $10 EP, 3 callers, i'm in position. Â $43 in the pot. Â Flop comes 2 suited. Â EP bets out $15 and it's folded to me. Â I have a gut-shot, not worth the call, but I believed EP has top pair and is protecting against the flush draw, but if I had the flush draw I would just barely have odds. Â I calculated it in my head for a minute (just for the hell of it) and call. Â Now unfortunately the turn was a dud, he went all in and I folded. Â After that, I had him and another by-stander say, "Flush draw didn't hit eh". Â I had everyone at the table convinced I had the flush draw when I had nothing. Â If that club would have come out, I have no doubt in my mind I would have taken that pot.
But I think it's all about acting. Â The way others percieve you and how they think you're going to act if you have a certain hand. Â Just bet, call, raise like you have the hand that beats them. Â At least that's the way I look at it.
My short answer is that I do not think that what you are asking for is, at least in a practical sense, possible. There are, I suspect, too many variables that are too difficult to determine.
I will grok on this, though.
Anyone else?
the only problem i have with this is that you said you would barely have odds even if you had the flush draw, and you didnt even have it, so you were calling hoping the flush card would hit AND that your opponent would fold...
David Sklansky (p.166 Poker Theory, 1999) describes the optimum bluffing percentage; when it makes it impossible for your opponents to know whether to call or fold. Mathematically, optimal bluffing strategy is to bluff in such a way that the chances against your bluffing are identical to the pot odds your opponent is getting. Thus, if your opponent is getting 35% from the pot, the chances against your bluff being successful should be 35%.
That being said, the three situations where I intend to bluff, with the preconditions mentioned earlier, are as follows:
1) Flush Draw on the board post flop
2) Straight Draw on the board post flop
3) AA, KK, JJ, TT on the board post flop
A tight or semi-tight player will play the following range of hands:
AA, AK, AQ, KK, QQ, JJ, TT, AJ, AT, A9, A8, A7, 99, 88, 77, 66, 55, 44, 33, 22, KJ, QJ, KT, QT, JT, A6, A5, A4, A3, A2
Well, I sat down with Poker Stove and calculated the average "Draw Equity" an opponent would have with the above range of hands against the board. They turned out to be as follows:
1) Flush Draw: about 35% Draw Equity on average
2) Straight Draw: about 30% Draw Equity on average
3) AA-TT: about 35% Draw Equity on average
So, if my math and my reasoning are correct, and assuming that villain will only call my raise a percentage roughly equal to his Draw Equity, bluffing with position against tight players who have checked is a very high probability play even by the numbers! our Steal Equity turns out to be as follows:
1) Flush Draw: (100% - 35% [villain's Draw Equity]) = 65% Steal Equity for Hero
This means that Hero can bet up to 65% of the pot to bluff on the flop, and still break even in the long run, even if he gets called and has to fold.Â
2) Straight Draw: (100% - 30% [villain's Draw Equity]) = 70% Steal Equity for Hero
This means that Hero can bet up to 70% of the pot to bluff on the flop, and still break even in the long run, even if he gets called and has to fold.
3) AA-TT about 35% - This means that Hero can bet up to 65% of the pot to bluff on the flop, and still break even in the long run, even if he gets called and has to fold.
Does this make sense, guys? am I missing anything? am I right? all comments and views appreciated....
You have asked a complex question which, I think, at times confuses game theory with the exigencies of reality. Game theory, at least as I understand it, assumes that your opponent plays optimally. This is, of course, never the case. In the sweaty confines of a poker room, after three Coronas, people do not play optimal strategy.
Also, you have made some assumptions that I quibble with.
So, your original observation:
You are correct. There is no point in an uncalculated bet on turn or river. You should only bluff when you expect it to show a profit. This will include the impossible-to-quantify “future effect†that getting caught bluffing will have.
This quote from Sklansky pertain to a game theory application to a bet on the river with no cards to some (I have an older version of TOP so I could be wrong about this). It can’t easily be applied to a situation on the turn when there is one card to come.
Under what circumstances will the player you have modeled play these cards? We may be differing about definitions, but I would not apply this range of hands to any player that I described as “tight.â€
I do not understand what you have calculated here. You ran the range of hands listed above against a flush draw? What were the board cards and what cards were held by the opponent? This will make A LOT of difference to what the pot equity of each hand is.
I do not understand what you have calculated. You are assuming that your opponent will only call based upon the actual pot equity that he has?
Has there been a bet to you? Are you first to act? What has the action been to that point in the hand? I am not following your point at all, I’m afraid. You are bluffing with any two cards? What is your hand? If you are launching a bluff on the turn you will need to define your hand, your opponents range of hands, and model various behaviors to determine where and how your play is profitable.
Back to your original question:
What I do is address one particular case of player classification at a time and then I model the behaviour that I expect to see. Then, in combat, I guess.
So, for example…
I estimate that rocks will raise with A-K to A-Q, and A-A to 9-9. If a rock has raised and it is folded to me in the big blind, what range of hands should I re-raise with, and how much. I would then run every single hand against the rocks range. I will assume that he will fold A-Q and J-J to 9-9 against a reasonable re-raise and then I will be able to arrive, precisely, with a list of hands that will show a profit in this VERY SPECIFIC situation.
The problem with your method, I think, is that you have attempted to do too much. Game theory has applications, but you need some very careful assumptions about what your opponents will do. I am not clear on your assumptions.
Am I missing something?