best - least exploitable valuebet / bluff frequency?

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best - least exploitable valuebet / bluff frequency?

It´s not easy to explain it well with words but..
I am curious about the math or theorie behind the least exploitable - most profitable valuebet - bluff frequency.
like 25%-30% bluffs in any betting range sounds good to me..but I have no idea why...
what´s your opinion about that ?
and could this frequency change with the board texture ?
I just had an idea: to fully analyse a situation where villain is polarized on the river and we want to bluff IP - we also have to analyse how much % of bluffcatching, give-up-hands his range consists of, right? I think I have never seen anybody doing this

btw...how do you manage to stay in any frequency you choose for yourself?
For me this is very difficult - some good bluffspots I always would love to use and probably bluff there too often at the moment.

well it´s a difficult topic so feel to ask curiously and answer curiously ;)

3 Comments

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GameTheory 11 years, 11 months ago
I think your question is ill-defined. For instance what does it mean that villain is polarized on the river, you mean he either has nuts or air? If that is his range distribution relative to yours that means he is clairvoyant, when he has air he knows he is beat and when he has the nuts he knows it also.

Then the answer would be very easy, he should always potbet his nuts and potbet his air with a 2 to 1 ratio to make you indifferent between calling and folding your bluffcatcher, note that your entire range is a bluffcatcher here. So in particular you should never bluff here yourself, since you cannot valuebet any hand either.

Also "having 25-30% bluffs in any betting range" is bad. PLO is a semi-bluffing game, it is much better to barrel hands with some outs than to barrel hands with no outs (bluffs) since that means you have a stronger range on the river at little to no downside since you could've just given up with your bluffs on earlier streets.

So if you want accurate answers you will need to come up board textures and (perceived) range distributions.

If you want to manage your own bluffing frequencies in certain spots. For instance a "good bluffspot" where your opponents range is weak/capped. You can analyze your own range, and figure out how often you have your opponent beat given his most likely holdings, and then bluff in the right ratio with the best hands after you figure out how light you want to valuebet there.
homer5554 11 years, 11 months ago
First thing: thanks for your good answer on my confusing post ;)

second: your answer with the 2:1 ratio in this case is already a quite good answer to my initial question ;)
does "perfectly balanced" always means to make the opponent indifferent between calling and folding?
so if I want my valuebetsize to be 1/2pot - I have to reduce my vbet - bluff frequency to 3:1 right ?

third: by saying villian is polarized on the river I initially meant something like he´s checking to fold his air or he´s checking to call - but probablly knows what he´s doing BEFORE checking. (to simplify let´s say he never c/r)
to give a example: I found this hand quite interesting and illustrates my question well:
http://www.runitonce.com/plo/1020-hu-plo-river/

it is a spot where we are somewhat polarized (not sure if it´s the right word here?) between draws without sd value, straights and 2pairs which are good enough to valuebet.
at the same time villian probably knows what he´s going to do if we bet.

in this thread they are talking about numbers how often you could/should bluff..
so: the first thing is to figure out how light I want to valuebet and in what size, then I could use odds oracle to find out how often I´ve got a hand to valuebet, and lastly I choose the right bluff ratio to make my opponent indifferent between calling and folding - is this the way to go?

GameTheory 11 years, 11 months ago
First. I appreciate that.

Second. I don't think I used 'perfectly balanced', nut if I had to define it I would say no. In order to be perfect, your betting range does not try to make your opponent indifferent, but it is often the effect that he will be. But with real example with real range distributions you also have card removal effects, so the result could be that a lot of bluffcatchers always call since they have a slight positive expecation and that another large part of blfufcatchers always folds. So you often make your opponent indifferent between calling and folding with some bluffcatcher and he makes you indifferent between bluffing and checking some bluffs, but it doesn't have to be this way. And in order to call your betting strategy 'perfect' I would require that the betsize is also optimal, so if betting 1/2 pot is not optimal I would not calling that 'perfectly balanced', even if you bluff in a certain ratio that makes him indifferent with some hands.

Third. This is something different than a least exploitable betting/calling strategy between two players on the river. If your opponent is polarized like that you should minbet all your bluffs and potbet all your value hands. So what you probably mean is that the range of your opponent is known and also how he would react to certain betsizes, but then there is no need to balance since you just want to maximally exploit him.

In the A854ss hand you provided it looks like Hero can have QJ/87 for value, kings up for 'thin' value and missed flushes/straights for bluffs. The way you suggest to figure out betting ranges and sizes seems very good. Say you want to stick to one betsize for your entire range, then this is roughly how you could do it.

Suppose you assume he never folds T2+, and his range consists of two pairs, sets and missed draws, and you want to bluff all your hands worse than a 9 here. And also say that given you hold As8s54 he has T2+ 60% of the time, then you cannot bet full pot since he calls more than 50% of the time. So if you want to do it perfectly you must think about that for all your bluff and value hands at the same time: how much do they make in expectation if they bet a certain size, and given the size you choose what ranges can you bet.

Ideally you can do this all at the same time, in practice you can just try a few different sizes and different hands to bet with and then figure out which are best. I would be interested to see your results if you did that for the A854 hand, give a range for both players, give a betting, check/folding and check/calling range for the opponent and a betting range and size for the hero.

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