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Holgininho
Joined: 01 Jan 2007
Posts: 468
Location: Essen
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 Posted: Tue Jul 10, 2007 9:27 am Post subject: Game theory and bluffing |
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I'm rereading Theory of Poker at the moment, and again I'm struggling with the chapter about game theory and bluffing.
I think I understand the concept, but I find it hard to apply it at the tables. One example from LHE:
I have a flush draw on the turn, say with 5s4s, I assume my opponent has a pair of 7s, giving me exactly 9 outs (this example is very similar to the one actually used in ToP). Before the river there are 5 BBs in the pot. The chance that my draw will arrive is 9/46 = 19,5 %. My opponent ist getting 5:1 to call a bet, so I should bluff 20 % of 19,5 % = 3,9 % of the time. That means I will bet the river 23,4 % of the time, and I will be bluffing one time in six. Is this correct? In practice I will probably pick two cards to randomize and bluff with a slightly higher frequency (11/46 = 23,9 % of the time). Still, if I have nothing but a flush draw on the turn the odds against me taking a stab at the pot on the river are 35:11.
In practice I think that most players will bluff far more often than that, when they are heads-up on the river and had a flush draw on the turn. Does this mean that most players fold too often, or is my assumption simply wrong? Is it possible to discuss this at all without looking at specific situations? I would think, however, that many players will semi-bluff with strong draws in aggressive games - and keep on bluffing when they don't hit on the river.
This posting isn't long enough yet, so there's still another question. 
It relates to NLH, where the bluffing player can control the odds he is getting/offering his opponent. How does game theoretical bluffing work under this circumstances?
I suppose you have to decide how much you will bet, before the river card falls. Or doesn't that matter?
The size of your bet then determines the correct bluffing frequency - the smaller your bet, the lower the frequency. Examples:
You bet half the pot, your opponent gets 3:1 on his call, you have 9 outs, you pick 3 additional cards to bluff. You bluff 6,4 % of the time.
You bet the pot. Your opponent gets 2:1 on his call, with 9 outs you pick 4 or 5 cards to bluff, you bluff 9,75 percent of the time.
That means you should call smaller bets more often, if you can only beat a bluff. You fold to a half-pot bet 1 time in 3, and to a pot sized bet 1 time in 2, if you can only beat a bluff - which is quite often the case in no-limit, if you face a big river bet.
Correct?
In practice: You have TPTK, your unknown opponent has check-called the flop and turn, on the river a 3rd flush card hits. Villain makes a pot sized bet. Instead of trusting some obscure read on your "typical" opponent you have decided to use game theory. So you flip a coin to decide if you should call. Is this wise?
Sorry for the long and unstructured post. I hope it's somewhat clear what I want to express/ask. As always I am grateful if you correct my numbers, because there are usually mistakes in my calculations. |
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Able2call
Joined: 18 May 2006
Posts: 40
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| Posted: Wed Jul 18, 2007 9:51 pm Post subject: |
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| In my limited NL play my bluffs are totally situational and read dependent. Putting a "should raise %" seems irrational as some tables you would rarely bluff and others scream for the table to be dominated by someone. |
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ebo8b
1K Club
Joined: 19 Jun 2005
Posts: 1096
Location: Northern VA
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| Posted: Thu Jul 19, 2007 12:39 pm Post subject: |
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Holgininho, I'd recommend that you read Mathematics of Poker if you haven't already. It's a tough book with a lot of math, but it deals with game theory and optimal play.
When playing a hand, especially heads up, you want to take a balanced line. In the 54s hand, that means that you want to keep your opponent guessing by raising the turn with both real hands and draws. Your range of real hands (such as TPTK) and draws is optimal if your opponent is making a mistake by calling more often, and your opponent is making a mistake by folding more often.
I haven't finished Mathematics of Poker, and I loaned out my copy of Theory of Poker, but this is my understanding. Your opponent is getting 6:2 or 3:1 to call on the turn and the river combined with his weak pair. This actually means that you should bluff 1/4 = 25% of the time. Your range should be something like real hands 75% of the time and draws 25% of the time. The advantage of the semibluff is that about 20% of the time your flush draw gets there and turns into a real hand on the river. This also means that you do not need to flip a coin to decide when to bluff and when to check. |
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Holgininho
Joined: 01 Jan 2007
Posts: 468
Location: Essen
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| Posted: Sat Jul 28, 2007 6:19 am Post subject: |
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Sorry for the late reply, I had little time, and this whole topic is so complicated for my that I postponed it endlessly.
| ebo8b wrote: | | Holgininho, I'd recommend that you read Mathematics of Poker if you haven't already. It's a tough book with a lot of math, but it deals with game theory and optimal play. |
I plan to get it at some point, but I fear the book is way above my head right now. Is it possible to get anything out of it, when you suck at math? The problem is I actually like math, but I have hardly used it since I left school (which was ten years ago), and I don't even understand most of the more complicated terminology.
| Quote: | | When playing a hand, especially heads up, you want to take a balanced line. In the 54s hand, that means that you want to keep your opponent guessing by raising the turn with both real hands and draws. Your range of real hands (such as TPTK) and draws is optimal if your opponent is making a mistake by calling more often, and your opponent is making a mistake by folding more often. |
Before reading your post I actually never thought about optimal bluffing frequencies with more cards to come. So I'm not sure at all, if I understand you correctly.
| Quote: | | Your opponent is getting 6:2 or 3:1 to call on the turn and the river combined with his weak pair. This actually means that you should bluff 1/4 = 25% of the time. Your range should be something like real hands 75% of the time and draws 25% of the time. The advantage of the semibluff is that about 20% of the time your flush draw gets there and turns into a real hand on the river. This also means that you do not need to flip a coin to decide when to bluff and when to check. |
In my example the pot contained 5 BB after the turn, so the numbers would look different, but that doesn't matter now. Just for me to understand it: If there are 5 BB after I have bet the turn, my opponent has to think he will have to call one more bet on the river, so he has to pay 2 bets to win 6, and I have to make the odds against bluffing 3:1. Does that mean I should bluff 25 percent of the time I have a draw? How do I factor in the number of outs I have? Surely there is a difference between a draw to 12 outs and a draw to 4 outs.
My coinflip question referred to calling a bluff on the river, and I am still thinking about it. Whenever I am in a situation where my opponent comes out with a PSB on the river (say I have checked to him with TPTK), and I can only beat a bluff, I can either rely on a read (for example the fact that he is an aggressive player, and I tried to induce a bluff by checking to him) or on game theory (when I have no idea what to do).
If I rely on game theory I think my reasoning goes like this: He is getting 1:1 on his bluff, when he decides to make a PSB. I am getting 2:1 on my call, but that doesn't matter - I only have to look at his odds for bluffing. So I call 50 % of the time.
If he is betting half the pot, I am getting 3:1 to call, but he is getting 2:1 on his bluff. His bluff only needs to be successful more than 33 percent of the time to be profitable - therefore I should call 67 % of the time.
Is this correct?
I have the impression, that in reality I call pot sized bets less often and smaller bets more often - but this is probably a deviation from game theory. I rely on my general read that "big bets mean big hands".
One more thing: At 2+2 I read that you shouldn't determine your bluffing frequency in the way I described above (using the number of outs you had on the turn to determine how often you will bluff the river). To me that sounds reasonable. After all, if you were on a flush draw, and the third flush card doesn't hit on the river you can't have made a flush. On the other hand using the number of outs to determine the frequency works in stud, when your opponent can't see your river card - here it makes sense. But in Hold'em?
According to the 2+2er you should rather decide how often you would bet the river with the made hand you are representing. But before I go on rambling I'll simply quote from the neighbors:
| pzhon wrote: |
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You have an open end draw with 8 outs. You will bet if you catch any one of them. Now, think up a bluff card. This is one single card in the deck that does not make your hand but you will bet if it comes out on the river. Now, when you bet the river, the chances are 8 to 1 against it being a bluff, the same odds your opponent gets to call.
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This is wrong. It is often repeated, but wrong. The number of cards that would have helped you is irrelevant. The problem is clearer if you imagine that you have a flush draw, and there is a decent chance that your opponent thinks you have a flush draw. It is usually obvious whether the river completed a flush draw or not, unlike in stud, where the 7th card is hidden. What you want is that, given the information your opponent has, the odds against you bluffing should be the same 8:1 as the pot odds. It's important that your opponent sees the river card.
When you get to the river in position with a hand with no showdown value, such as a busted straight draw, you should estimate how frequently you would get there with the same betting action with a hand you can bet for value. You should bluff in proportion with this likelihood. This means bluffing more frequently on a scare card if you have been acting like a draw than when the river looks safe. You should not bluff more frequently (in the same size pot) with a big (say, 12 out) busted draw than a missed gutshot. |
Link:
That makes sense. But how the hell do you determine how often you should bluff, in other words how often you will be getting to the river with the same betting frequency with a set or two pair?  |
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Holgininho
Joined: 01 Jan 2007
Posts: 468
Location: Essen
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| Posted: Sun Jul 29, 2007 2:11 pm Post subject: |
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| Holgininho wrote: | | If there are 5 BB after I have bet the turn, my opponent has to think he will have to call one more bet on the river, so he has to pay 2 bets to win 6, and I have to make the odds against bluffing 3:1. Does that mean I should bluff 25 percent of the time I have a draw? How do I factor in the number of outs I have? Surely there is a difference between a draw to 12 outs and a draw to 4 outs. |
Okay, obviously bluffing 25 % of the time I have a draw doesn't make sense, because it doesn't lead to the right (semi-)bluffing frequency. Things seem to be far more complicated. Let's assume you will raise TPTK or better for value on the turn. How often do you get these hands? How often do you arrive on the turn with a drawing hand? How do you figure out the correct frequency for semibluffing?
And still one more note regarding the 2+2 thread: Can there really be a theoretical difference between stud and hold'em because of the fact, that you can't see the river card in stud? It seems to be correct to choose your bluffing frequency as Sklansky describes it in stud. But it also seems to me the 2+2er is right regarding hold'em... |
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