Technical question on bluffing in limit Hold'em

[Shandrax]

Ok, let's assume its the river and I know that I am beat. There are 8 big bets in the pot. If I bet I am laying 9:1, so should I bet in 10% of the cases to have the correct frequency?

Similar situation in NL would mean that I can chose my bluffing frequency by simply chosing specific odds I am laying. Let's say when I want to bluff with 33% frequency, I make a potsize bet once (laying 2:1) and fold twice.

Is this the correct approach, or did I completely miss the ballpark?

[WhiteWolf]

It is actually lots more complicated than that. To bluff at the optimal frequency from a game-theory perspective, you need to look at it from your opponent's point of view. If he is facing a 1 BB bet from you, and the total pot is now 9BB, he has to think that you are bluffing 10% of the time here (and beating him the other 90%) to make him indifferent between calling or folding. This means that the probablity (from his point of view) that you actually had a made hand before you bet comes into play - this is the important point. Some examples which will hopefully make this clearer:

Say there was a 20% change you had a made hand, 80% that you don't. You need to bet 22.2% percent of the time to make his call EV neutral (20% with the made hand, 2.2% bluffing). Thus, you need to bluff 2.2/80 = 2.75% of the time when you miss.

Now assume that you actually have a 50% chance of having a made hand. You need to bet 55.5% of the time here (50% with a made hand + 5.5% on a bluff), meaning you bluff 5.5/50 = 11% of the time you do not have a made hand.

Finally, say there is an 80% chance you have a made hand. Now you bet 88.8% (80% made hand + 8.8% bluffing), and the times you bluff when you miss is 8.8 / 20 = 44%.

As you see, the probablity that you have a made hand (from your opponent's point of view) has a big influence on how often you should bluff when you don't.

[Shandrax]

I know the example from Theory of Poker, but it applies more to draw poker or stud than to Hold'em. The problem with the made hand is that in Hold'em the last card comes face up.

What I can always represent is a set and my opponent will never know if I have it or not. Depending on my position and the flop he can guess that I won't play a small pair from early position, but he cannot take it for granted.

[broadcrawford]

Game theory is only used when playing against an opponent who is better then you. Game theory allows you to randomize your reaction to his potentioal bluff, or randomize your bluffing frequency. This allows you to negate his edge.

[WhiteWolf]

My examples apply to all poker games when bluffing on the river. The central point is that your bluffing frequency is not solely dependent on the size of the pot, as your original question was asking. You also need to factor in how your opponent evaluates the probablity that you have a better hand than his.

You do illustrate another important point about bluffing in different poker variants. In hidden card games like 7 card stud + 5 card draw, it is often very easy to figure out what our opponent would think our chances of having the best hand. If it looks like I was drawing one card to the flush in 5-draw, then it's easy to figure out that my opponent thinks I had a 9/47 chance of making my hand, and thus can also easily figure out the optimal bluffing frequency. However, in shared-board games like Hold'em where the river card is face-up, your opponent can easily see if you hit that draw or not, so you have to pick other strong hands to represent for your bluffs. These are harder to evaluate (what are the chances that you were slowplaying a set the whole way? That you just spiked a 2nd pair?), so it's much harder to figure out what the optimal bluffing frequency is in these situations.

[WhiteWolf]

True, if you know the other player's tendencies, you will devaite from the optimal game-theoretic bluffing frequency. If a player calls too much, bluff less. If he folds too much, bluff more. If fears 3-suited boards but doesn't care about paired boards, consider board texture.

From the tone of the OP's original question, I surmised he was looking for the way to calculate the 'game-theoretic' optimal bluffing frequency.

[Shandrax]

[ QUOTE ]
My examples apply to all poker games when bluffing on the river. The central point is that your bluffing frequency is not solely dependent on the size of the pot, as your original question was asking. You also need to factor in how your opponent evaluates the probablity that you have a better hand than his.

[/ QUOTE ]

I understand your point, but I lived under the impression that game theory works regardless what your opponent does. It should be the minimum of what you can archieve. If you can improve on this minimum by applying judgement (like a read) you go with your judgement of course.

You are claiming that if my opponent never believes me and calls in 100% of the cases then I will get busted. That is true of course, but you never bluff against a calling-station anyways.

[ QUOTE ]
However, in shared-board games like Hold'em where the river card is face-up, your opponent can easily see if you hit that draw or not, so you have to pick other strong hands to represent for your bluffs. These are harder to evaluate (what are the chances that you were slowplaying a set the whole way? That you just spiked a 2nd pair?), so it's much harder to figure out what the optimal bluffing frequency is in these situations.

[/ QUOTE ]

So I need the image of an unpredicable player to be successful with my bluffs. If I am capable of playing any two cards and truly randomize my bluffs based on the potsize I thought I was exactly that, unpredictable.

I guess I simply need more time to think this through. In poker sometimes it takes a bit to realize the obvious.

[broadcrawford]

By no means was I attempting to reprimand the original poster. I just want to make sure we aren't confusing two different topics. Optimal bluffing frequency is a much different animal then "game theory". True, both surround when to call a bluff, and when to bluff an oponent. However, game theory discusses how to make your approach to bluffing/calling a bluff completely random. Optimal bluffing strategies have to do with reading your opponent and their tendancies to certains boards, position, and everything else.

My opinion on bluffing really comes down to the player(s) you are up against. In low limit games against fish bluffing is almost worthless. However, in higher to mid limits (or if you got a TAG, TPA at your table) bluffing, and semi-bluffing become more valuable.

In lower limit games .25/.50, .50/1.00, 1/2 I do very little bluffing. There are just to many fish and they call down with anything. It's more profitiable to capitilize on that mistake, then it is to make them fold when they actually have you beat. This makes bluffing and semi-bluffing less valuable, and value betting and check raising move valuable. You do get some people at this level who do fold to bluffs, but they are rare and usually drop after flop. So in that scenario you are spending 1sb into a 3sb pot. In my opinion, why do I care about such a small pot. If I got a damn good read, and I know he will fold once out of the three times I bluff 1sb into a 3sb pot, then I will do it.

Skalansky really makes it simple. If you feel/know it's profitable to bluff here (you are getting a +EV) then do it. It's no different then drawing when you get odds. You lose money by not bluffing when getting the right odds.

[Shandrax]

Well, I was specifically talking about Theory of Poker p. 166 + chapter 19 (p.188).

[DavidC]

[ QUOTE ]
Ok, let's assume its the river and I know that I am beat. There are 8 big bets in the pot. If I bet I am laying 9:1, so should I bet in 10% of the cases to have the correct frequency?


[/ QUOTE ]

Only if he'll fold.

Er... I'm probably wrong on the math of this, but yeah, I mean, if the pot's 250bb, only bet if he'll fold. [img]/images/graemlins/smile.gif[/img]