Optimal Bluffing Strategy

[bknollenberg]

One thing that I've found people ignore when they're trying to work out how they should bluff and be believable is to analyze how you're betting and what the person that is calling may have when you are NOT bluffing.

For example, say you have a hand like pocket 5's. You raise and get called by someone in position. The flop is Ac5c8d. You like the ace, since it's a raised pot, and you bet out 75% of the pot. He calls. You bet the pot on the turn when the Ad hits. He calls. You push the river on a 9s. He folds. Now, clearly unless he was really slowplaying you, you are going to win this hand. But notice he called, called and then folded on a push on the river.

It seems like a simple concept but look at it this way:
If you had 23os in that situation and bet those exact same amounts in the same way, you would have gotten 2 calls and a fold on the river when you pushed. Paying attention to this fact has helped me a lot and really reaffirms the fact that your two cards mean absolutely nothing unless you showdown. Only your opponents cards matter.

[mvdgaag]

The mathematical approach with randomised moments to bluff works a lot better in games where there are no shared/visible cards, because a bluff needs to be believable. In holdem the optimal frequencies still apply in a game theoretical sense, but correct timing of is far too important to allow for randomised bluffs to be effective. So if a hand will look like a bluff you probably should not bluff at all, even if you get your key-card or whatever method you use to randomise your bluffs. While if someone can almost certainly not call with a lot of hands that have you beat you are better off making that bluff.

EDIT: also the optimal frequencies work against opponents that play optimally as well! Most people on low stakes call too often so should be bluffed less. And of course opponents that fold too often should be bluffed more.

[Cloodie]

Funnily enough I've just finished reading the chapter on optimal bluffing in TOP and was wondering about it's application to hold 'em (In TOP the example given uses Draw Lowball).

I've only read the chapter once so I've not really given it too much thought (like to read a book once through and then go back and pick out the interesting chapters) but from what I can see optimal bluffing strategy involves bluffing with a number of cards based on the odds you are getting to hit your hand and how this compares to the pot odds. Is this correct?

[qpw]

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I've only read the chapter once so I've not really given it too much thought (like to read a book once through and then go back and pick out the interesting chapters) but from what I can see optimal bluffing strategy involves bluffing with a number of cards based on the odds you are getting to hit your hand and how this compares to the pot odds. Is this correct?

[/ QUOTE ]There are two separate things here.

One is devising a method to make random bluffs (where this is appropriate). Here the author suggests working out how often a certain card or one of a set of cards comes up in order to randomise your bluffing (but see above for reasons why you need to be very careful of completely random bluffing in HE).

The second factor is actually determining how often to bluff and this (where you are reliant on game theory) is down to selecting a percentage so that it makes no difference whether your opponent calls or folds on your bluffs.

[Mike]

In holdem when bluffing it does not matter if you hit your hand as much as you have a high confidence your opponent(s) are willing to fold their hands to you.

Because of the shared nature of the cards anyone in the pot with you (should have if they are reasonable players) has a hand close in power to yours. You need to know that they have the ability to have doubt about their hand being best and lay it down.

What you are describing would be closer to a semi bluff, where there is a possibility you will hit your hand and it will become the best hand.

[Shandrax]

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Stud is similar to hold 'em in the sense that you can see the up-cards your opponent is playing, his actions and what do you make of his hand given his actions. In Hold 'em, the 'up-cards' are actually the community cards, so there’s no big difference here. Actually - bluffing in Stud is fundamentally more difficult because there are more exposed cards and hence more information available about what likely holdings player might have. If you try to represent a heart flush and an expert opponent counted another 5 exposed hearts, he will probably look you up.

To sum this up - I'm not sure that bluffing is easier on Stud. [img]/images/graemlins/smile.gif[/img]

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In Stud you pick your bluffcards in relation to your nut-outs. In your example if there are only 4 live hearts left and you want a 2:1 bluffing ratio for instance (potlimit), you just pick 2 bluffcards. If he looks you up or not doesn't help him, you will always get your value.

Of course in this situation you can improve on the unexploitable game theory solution and don't bluff in a spot where you are sure to get called, at least until your opponent adjusts and starts folding.

Bluffing in Hold'em works backwards. The end of your story has to be in line with the beginning and this makes keeping the correct ratios much more difficult. Bill Chen has an entire chapter on this in Mathematics of Poker, but don't expect any hard answers from it.

[drzen]

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Without wishing to be rude, if you don't see that it clearly applies to holdem, and obviously so, you probably aren't going to be able to use it as a way of working out when to bluff.

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I don't think that's entirely fair - I had good reason to question the use of it in holdem.

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No, I don't think you did. Bluffing is about what information your opponent has about your hand: the "story" your action has told, and what ending, if you like, you can sell for that story. Of course draw and stud are different from holdem in the information your opponent has, but why would that mean that you cannot use an optimal bluffing strategy in holdem?

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In 5 card draw if you take one card on the turn your opponent might conclude you have 2-pair, a flush draw or a straight draw. He knows nothing about whether the card dealt to you helped your hand and thus is in the dark if you bet the river.

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This has nothing to do with the question though! Anyway, a thinking player will be aware that a single card will not help your hand all that often. And in a community game, your opponent is equally as unaware whether the river actually did help you.

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However, in holdem lets assume at the turn Player A bets and Player B calls. The board is Js,6h,Qs,2d and Player A has AQo. The river is 2h and Player B bets (what we know to be a bluff but player A doesn't). Even if Player A knows that B uses OBS can he not deduce that all the draws have missed here (i.e. spade flush, K10, AK, 89, etc) and act accordingly.

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This is a particularly bad board for a bluff. What story can you be selling here? But he doesn't know that you were drawing, does he? If player A bet and player B raised, is player A snapping it off every time? Are you in his spot?

What if the river is the Th? You were chasing the spade flush. If you raise the river, can player A call with confidence?

And does player B *never* slowplay a set? Is there no chance at all that he has filled on the river? Maybe he called the preflop raise with 62s.

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If player B would usually have been aggressive with 2p/set then surely a bet on this broken board is a bluff or blocker more often than not and OBS or not Player A will call far more often and snap that bluff off far more often?

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The point is that if you are bluffing optimally, you are indifferent to his calling or folding. You need to reread the chapter, because this is not a question of what kind of information your opponent has. It's simply that when you see the turn, you are saying "I will bet with every hand in which I make my draw on the river and enough others to bluff optimally". Or you might say to yourself, I don't think this is developing into a board I can bluff on, so I won't be bluffing at all.

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Is that not a reasonable basis on which to question OBS in community card games or am I missing something?

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What have you actually just discussed? You have shown that the information your opponent has in draw is different from what he has in holdem. Well yes. So that means you bluff differently in the two games. Yes, true. So in draw you can sell more stories more easily. Yes, also true. And you've picked a board on which a bluff would be difficult to sell. Yes, true again.

But does that mean that you cannot use OBS in holdem? No, it doesn't.

It's going to be much more useful to think of spots in which you don't want to be predictable but are not sure how often to bluff. Say you have AK in a game of limit holdem. You raise PF, only the BB calls. You whiff the flop and bet. You don't help on the turn and bet again. There are no draws on the board, so you're pretty sure your opponent has a pair of some sort, and he knows that no river card will complete a draw for you.

What do you do on the river? If you hit your A or K, you'll be betting again. But you'd like to bet some other amount of the time in the hope that your opponent will lay down his bottom pair.

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if you don't see that it clearly applies to holdem, and obviously so, you probably aren't going to be able to use it as a way of working out when to bluff.

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As a little aside that is pretty defeatist - there is nothing I can't/won't understand about this game. If it can be learned, I can (and hopefully will) learn it eventually [img]/images/graemlins/tongue.gif[/img]

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Well, I don't use it but I do try to bluff at roughly the right frequency. It's a lot easier at limit, where if the pot's heads up, you're not talking about a lot of bluff cards. In the situation I gave, you might say "I'll bet any A or K, and any red T too".