I was reading this old post on Understanding game theory and hold'em

It's a really good post, but there's one thing I can't seem to get my head around. By the way, the same goes for Sklansky's exposition in Theory of Poker and this one (which seems pretty involved):

How do I apply it ?!

I mean, okay, so I'm supposed to bluff a certain percentage of the time, related to the pot odds I lay my opponent.

My bluffs should be a certain percentage of my value bets. That all sounds reasonable, but in an actual hand, when I'm sitting there with a busted flush draw, how do I know what that percentage is?

Do you get what I mean? How can I figure out the proper betting frequency in an actual hand? How do I know how often I would have had a hand in the exact spot I'm in?

How do I translate that into a bluffing frequency here and now so I can use my wrist watch to decide whether to bet or check?

Anyone?

(Maybe the flush draw example was unlucky. I guess that's one of the few places where this question actually might have a simple answer?)

First, optimal bluffing is usually a bad idea, as funny as that sounds. "Optimal" does not mean "best" in this context, it actually means "unexploitable". You'd want to use optimal bluffing percentages when playing an opponent who you think is as good as or better than you - someone that you are afraid will exploit you.

Second, I personally feel that it doesn't apply to holdem that well. Flop games like holdem have a revealed river card - you can both see the card. Draw games and stud games do NOT, the final card is hidden. So if you have a draw and your opponent has some kind of made hand, he can not know if you completed your draw on the final card, he has to guess. So this applies really well to draw games (especially lowball) and stud games (of any type, although it's easiest to see and apply in razz)

So, finally, the deal is, you would like these 2 ratios to be equal:
value bets : bluffs
pot size : bet size
In fixed limit games, pot:bet is a fixed quantity, so you have to vary the # of times you bluff to match that. In no limit games, you can adjust either quantity.

This can really never apply if your opponent has the nuts, because you'd have no value bets. It's a little bit of a judgement call but typically this applies in a circumstance where you believe your opponent has a reasonably strong made hand and he believes you have a draw. Say, he has TPTK or an overpair and you have a oesd or flush draw.

It doesn't matter if he knows how often you'll have him beat. *You* need to know. The flush and straight draw examples are good because if he has TPTK or an overpair, a flush or straight will almost always beat him. So value bets=the number of times you get there, so that would be 9 for a flush draw. Say the pot has 10bb in it and this is a fixed limit game where you can bet 1bb. To figure out the number of times you should bluff you just have to make this equation work
9:bluffs = 10:1
so bluffs=0.9 and basically you should bluff 9 times for every 90 times you value bet

Hope this helps

Thanks, your point about games with hidden river cards is good. I also understand that optimal bluffing may not be "maximal", but it's probably a good starting point.

Nevertheless, I still have this suspicion that the result (the bluffing frequency) isn't applicable in practice. It sounds really good and Sklansky's got a load of references for it, but I still wonder if it's possible to use it in an actual game situation.

After all, the percentage of time when I have the best hand needs to include the river card. It needs to be the probability given the river card. How do I know how often I'm betting with the best hand when the river card fills a possible flush draw, and when it doesn't?

Hell I'm not even sure my questions make sense anymore...

If anyone can give a convincing real-world example I'd be really greatful.

You use this when your hand is crap without a river that hits, but where you almost certainly win with a river that improves you.

The example in the Theory of Poker is a pretty good one... I'm on my way to work but I could gin up a stud high version...

Imo, that's where Sklansky's variable p comes into play. during the hand it's uber hard to figure out using the equation.
The variable p most probably will have something to do with your range, and the chance that the river card either made your combo, or didn't reduce ur hand's strenght.
I feel like its much easier to sharpen your GTO in a way that your bets are always the same be it a bluff or a valuebet. That way you can simply compare it to the pot odds ure giving to you opponent.
From there figuring out ur overall bluff frequency with no hand would be a piece of cake(hope you know what i mean).

You can figure out the percentage, but still would need to use a mental shortcut. Such as for instance: your bluff ratio is 38%, but you decide to make it 1 times out of 3 when you don't have a hand for the sake of simplicity. or you could make it 2 times out of 5 (which is closer to the real percentage)

please if anyone finds what I said stupid - flame right away.

OK so it's 7 card stud. You hold:

5 2 Q 7 T 3

and your opponent is showing

xx xx A 9 6 8

Because of the preflop action (you bet, your opponent raised) and the fact that he's bet every street from then on, you believe he has a pair of aces. Because of this, if you make your flush, it's extremely likely that you'll have the best hand. If you do not, it is extremely unlikely you'll have the best hand, because all you could make at best is a pair of queens. The table was full at the start of the hand and heads up from 4th on, so the number of exposed cards is 10 from 3rd st, and 2 from 4th 5th and 6th, for a total of 16 exposed cards. There are 36 unseen cards, 9 of them are the clubs you need, so odds against you improving are exactly 3:1

So on 3rd the pot was about 1.5sb, then you bet and your opponent raised, so a total of 5.5sb went in on 3rd, plus 2sb on 4th, 2bb on 5th and 6th, for a total of 7.75bb if I added it up right. Let's call it 8bb in the pot. Your opponent has the high board so he's first to act. Since it's pretty likely you're drawing to beat him, he checks to you.

If you bet, you'll be giving him 9:1 pot odds, so the ratio between your bluffs and vbets needs to be 9:1 also. Luckily, you have exactly 9 vbet cards, so you just need to pick one non-vbet card, say, K. If a K comes to you on the river, then you bluff, if a club comes, you value bet, simple as that.

If you like, try to see whether your opponent can profit by:
always folding
always calling
sometimes folding and sometimes calling


A big reason this doesn't work in holdem is, if your opponent has a made but vulnerable hand, he probably isn't going to be pushed off it in the river doesn't complete a draw, because he can see just as well as you that the draw didn't come in. So choosing a river card to bluff on doesn't really make that much sense.

As the others have said, bluffing on specfic cards in holdem isnt going to work very well.

First of all I assume you know your own range.

Then I also assume you know what hands you vbet, now you just need the amount of bluffs which is easily calculated.

Last step is to choose those bluffing hands from your range which has 0 SD-value. Then you pick out the best bluffs, namely the ones that blocks villain´s optimal calling hands and not blocking hands that belong to villains folding range.

This is obv not possible to do in action but doing the work on the side will improve your intuition for different spots and constantly reviewing spots too see youre somewhat close.

I don´t agree with Rusty that optimal bluffing isn´t a good idea, actually most regs on mid to highstakes are somewhat balanced in river bluffing spots although not always intentionally, those occur so often that good players will catch on. Also the fact that good players are hard to exploit in these spots is another argument. Obv no one is going to be perfectly balanced cause you´d need to be a computer to always have the exact correct bluffing freq but somewhat correct is often enough to not be badly exploited.

EDIT: Furthermore even if you wanna deviate it´s good to know where the thresholds lie so you know what kind of deviation you´re actually doing.

I've used the cards to randomize c-betting the flop in hold'em and omaha. After that though your bets need to make a certain amount of sense and I think bluffing becomes more of an art than science.

be it sience or art, it will still need a good balance in order to work out. Tilt makes certain ppl break that balance all the time which is why I love poker.

You're right, Sklansky's examples are really clear. Your's too. I guess things just get complicated when the river card is open, like you said. Bluffing optimally when you missed your flush draw doesn't really make sense. Comparing two hypothetical ranges to figure out your bluffing frequency definitely belongs in the preparation phase, but I'm sure it's worthwhile to study some recurring spots.

I think it's pretty straight forward - if you think you should be bluffing 25% of the time say, and you haven't bluffed in a while, then think about bluffing. Think about the story that a 3/4 pot bet would tell and if it seems credible. Think about your opponents range and likely holdings and what you would expect him to fold that beats you. Think about any tells he may have given you in this hand as to how confident he feels and whether he's the kind of player that can make laydowns. If he calls too much, reduce your bluffing frequency, obviously. If he's weak tight, increase it but lower the bluff size. If he's a LAG, decrease it but make sure the bluff makes sense over multiple streets. Probably increase the bluff size, especially if it looks probably a tight range can easily hit two pair or better and the board is dry. Think about your own image and whether or not your bet will be met with fear or skepticism. If the conditions are right, do it.