Assumption:
-We are defending 100% of hands preflop to an open.
-We never are allowed to xr on the flop
-We are striving to play gto/balanced with respect to value/bluffs

Hand:
Heads up NL, 100bb effective.

button opens 3xbb, we call XX.

Flop: 7c2c5h (6bb)
hero check, button bets 4bb, hero calls.

Turn: 3s (14bb)
hero check, button bets 10bb, hero 32bb, button calls.
opponents pot odds: Needs to be good at least 28.2% not accounting for potential implied odds.

River: Jd (76bb)
hero all in 61bb,
opponents pot odds: Needs to be good at least 30.5%

On the turn this is our value range:
1.) Total value combos: 52 combos
sets: 77, 22, 55, 33 (12 combos, 3 of each)
straights: 64s/64o, A4s/A4o ( 32 combos, 16 of each )
top 2pr: (10 combos, 8 offsuit and 2 suited)
*I assume he isn't going to value xr much lighter then top 2pr!

I am offering my opponent pot odds on the river of 30.5% so under gto analysis that should be my bluff frequency. Which means if I arrive at this river with my total 52 value combos, I need ~75 total combos or ~23 bluff combos on this river. As 23/75 = ~30.5% bluff %.

Now how do I go about find the optimal bluff frequency on the turn? In my analysis I put a blankish river with the Jd, but assuming this is not known, how can I still go about with this analysis? Obviously assuming some rivers the value combos for shoving will be smaller and this needs to properly be accounted for. Any other potential noteworthy things of mention?

Thanks for any future help. Cheers.

Figure out what makes villains bluffcatchers be ~breakeven calls OTT.



Ps. It isn't the 28%.

mind giving a hint ( ) or point of reference? I believe this is reffered to as 1-A? But I can see why on dynamic boards this method could be troublesome when examining bluff/value ratios .

....Anyone else know?

Been pretty busy with work so do not get to study this poker math like I'd like too.

You need more bluffs on the turn than on the river because you have outs when called. Similar to flop play, where you would not even bluff catch such a range because the opponent is betting or raising too strong (has the outs twice).

What the opponent calls the turn with is his problem and another question, but mostly he should be thinking if he up to ever wins with a bluff catcher, as there are regular situations where he would up to never win because the opponent isn't bluffing the turn often enough.

Makes sense. But I am looking for the actual math, i.e.:

So on the river we have 52 value combos and thus bluffing 23 bluff combos makes opponents call 0EV given pot odds we are offering him. If we were to work backwards going to the turn - how does that exactly affect the value/bluff ratio?

In some analyses I've seen from Janda he treats river bluffs as turn value bets and proceeds to calculate turn bluffs from your river valuebets + river bluffs.

No idea if it's correct to do so and I'm a little fuzzy on the logic so I don't know if that method has been taken out of context.

Turn potodds need to be same as aggressors river giveup frequency.

I've been deep down this rabbit hole in the past, but now I just think it's best to create flop or turn bluffing ranges with an eye towards maximizing equity when called while maintaining some form of randomization with the key draws.

I think this is a poor assumption that will only confuse the solution.
I think this is a poor assumption that will only confuse the solution.
Your opponent's hands have equity in almost all situations, thus checking will almost always be a +ev option. I don't know how to do the math to figure out how to make my opponent's hands indifferent under this condition. However, unless the flop or turn bet is all in, I think striving to make my opponent indifferent on the flop or turn is a mistake. Doing so would either miss profitable bluffing opportunities or miss profitable value bets.

Work from the river backwards, pretty simple tbh.

52 valuecombos and we give 30% pot odds. 52/0.7 = 74.28, so we want 22 bluffs OTR

Then OTT we give villain 28% pot odds, and here we treat our river betting freq as "valuecombos", because everytime we bet river, villains turn call is -EV.

So now 74/0.72 = 102.77 total turn raises, so we have around 50 bluff combos OTT.


This is toygame where bluffs are 0 equity OTT. If we want to add equity, just treat these equity bluffs as x% valuecombos, x being the frequency we actually have a valuebet OTR. Like oesd is 0.16 valuecombo OTT, gutshot is 0.08 valuecombo. Also to point out, in 2 street model these equitybluffs don't actually even increase the bluff-value ratio much, in 3 street games it gets noticeable.



Then you could also prob take into account bluffs that have equity to win at SDV, but the hand isn't actually valuebet OTR. But to provide math for this I'd need to think a bit, and can't be arsed atm.



Obviously this is just a model, but the value-bluff frequencies are actually pretty sound, even in real game situation/simulations.

This is just plain gibberish. We still want to make villains indifferent OTT and OTF. The option of villain to check isn't really that hard to take into account.

So you know how to figure out exactly how much of the pot your opponent is realizing by checking back on the flop taking into account showdown value, implied odds and reverse implied odds? Show us please.

Nowdays there are tools available to solve that. But even before you could do estimates of using realizing factors that gave you pretty damn good estimates.

Just estimate the R factor of river action. 1-A gives a good indication of this, assuming we have an idea of betsize.


Villains betting frequency on next street is good indication for the R factor of bluffcatchers.



Estimating stuff on flops are a bit more complicated but still very doable. Turn spots are actually pretty simple to make a reasonable model of with just pen and paper. Mostly because it's easier to point out, what hands we should try to make indifferent. OTF it's not that easy.

Like if you know you want to make a gutshot indifferent OTT, it's not hard to come up with a defending frequency with pen and paper that is like very very close to correct frequencies.





Point is, models are never 100% accurate, even solver simulations. But when you get a model to be like correct with a 10-20% marginal, you can pretty much get the answers to the questions you are asking.

Like the first quote i took from you was suggesting that we shouldn't try to make villain indifferent in a turn raising spot. When I clearly showed in my post that it's super easy to get pretty damn accurate bluff:value ratios to the exact scenario.

Even if we totally ignore the equities, the solution shouldn't even change by a huge marginal and if we use the R factors for equities etc, even if we use wrong R with like 25%, the solution is still like pretty damn close.

Ok. My point is that your method will result in a pure strategy that's non exploitive, which is a bad combination.

Well if you are looking for perfect models, you are **** out of luck, although solver stuff is pretty good if you can use it correctly.

But the point isn't to create perfect models, the point is to create models that are close and give you better idea of what is going on.

I agree, which is why I think using indifference as a goal is a mistake.

Sure, but the next step in understanding what should be going on in a hand of poker is employing mixed strategies.

Using super balanced mixed stragies is not even that important in practice as no one has clairvoyance and thus blocking effects or lack in runout coverage isn't punished as hard as it would be if the other player knows 100% what range you have in every spot, as is the case in the dream machines.

If you're going to use a pure strategy, I think it should be exploitive. In the case of the op, that would mean either value check raising thinner and bluffing less, or value check raising tighter and bluffing more, neither of which involves intentionally making hand xx indifferent.

The problem I have with using indifference as a goal, and using a pure strategy at the same time, is that you're going to end up making one of these mistakes:

a) you value bet too thin and bluff too much as a result of trying to make your opponent indifferent.

b) you miss value and don't bluff enough as a result of trying to make your opponent indifferent.

This is why I think that if you're going to play a pure strategy, that it should be exploitive. In the first case (a) you obviously think that your opponent calls too much or else you would have a tighter value betting range. Since he calls too much, you should eliminate the weaker bluffs from your betting range. You can maintain a pure strategy here that includes thin value betting and semi bluffing with strong draws at 100% frequency. This strategy will likely win lots of money vs a bad player that calls too much.

I the latter case (b) you must think that your opponent folds too much or else you would value bet thinner. Since he folds too much, bluffing at the rate that will cause indifference will be inferior to bluffing lots and lots of hands. The more he folds, the less equity we need to make a bluff more profitable than a fold, check, or call. You can maintain a pure strategy here that includes tight value betting and lots of bluffing. This strategy will likely win lots of money vs a bad player that folds too much.

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I don't think you're giving your opponents enough credit. Discounting players is a mental game error imo. With evidence that they suck, sure go ahead and play a pure exploitive strategy. Without it, I'm sticking to the mixed strategy.

Can you explain what you mean by pure strategy? And how is using approx. value-bluff ratios even considered using pure strategy?


I just don't see any logic behind your ramble. Can you give a bit more concrete example?


I think you might be mistaking the idea behind the indifference principle. The point isn't trying to make his whole range indifferent, but certain hands.

A strategy that takes a specific action with individual hands at 100% frequency; the opposite of a mixed strategy.

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The math laid out in the op will yield ranges that will be a part of a pure strategy, which I think is a mistake for the reasons I listed above. This is how I used to construct my ranges, but now I think mixed strategies are better without an exploitive plan.

[QUOTE=doctor877;49758368] Because you'll end up value betting with your predetermined value range at 100% frequency and bluffing with your predetermined bluffing range at 100% frequency.

Don't know how to be more concrete than this:

Think about the implications of using a pure strategy that intentionally causes the opponent to be indifferent. Then consider that gto is a mixed strategy. The value hands and bluffs included in such a strategy are included at frequencies. Let's say you wanted to be really aggressive against a loose player with value hands. So you start value betting thinner and you stop mixing in checks with could be value hands. Your value range expands. Should your bluffing range expand as well in an attempt to maintain a good value:bluff ratio? I think not because your opponent's mistake is that he's loose and calls too much. Indifference goes out the window once you decide to play a pure strategy.

Just because our bluffing range has set amount of combos, doesn't mean we need to always use the exact same combos. Value range is pretty set in stone tho.

Even when using mixed strategy with value and bluffs, the value-bluff ratio still exists.

So when you are not sure if V is calling too much or folding too much, you just click buttons without any idea what is considered balanced approach there?

Your checking ranges are gonna get demolished by anyone half decent if your value range is set in stone and you don't mix with the key draws imo.

What the ****? Obviously when we know how to exploit villain, we aren't trying to make anything anywhere indifferent, because with every hand we have one option that is higher EV. The point of trying to make villain indifferent, is that we don't really know how he plays and the EV options in our gametree are very similiar between different options, and then we also try to make us unexploitable.


Lets take a situation OTT BUvBB and we have cbet flop.


So now we have 3 type of villains.

1) We know V is playing too tight.

-> We bluff all potential bluffcombos, good draws and total crap.
-> We still valuebet all clear 3 street valuehands, but might just go B-B-X with some of the more marginal. We also might just play B-X-X with normal 2 street value hands.



2) We know V is playing a bit too call happy.

-> We don't bluff any of total crap bluffs. We still probably bluff good draws, because it's more +EV than checking them back.
-> We valuebet all normal valuehands, and might but a bit more money in with valuehands than they are supposed to put in. Like go B-B-B with TPWK when it's supposed to only put 2 streets of money in.



3) We know V is good, but have no other reads.

-> We bluff the best draws like we are supposed. Then we add worse draws to extent that V's bluffcatchers turn bluffcatchers are pretty much indifferent. Depends on the texture and the amount of our value hands. So we want to bluff enough that V's bluffcatchers don't have easy fold, but not enough that he can XC all of them easily.

-> We valuebet hands that are supposed to valuebet. 3 street hands goes B-B-B, with a little bit of slowplaying on the more static textures, on dynamic textures this isn't needed. Mainly to prevent V from making too big river bets with hands that shouldn't be able to do that.



And here the amount we bluff OTT is depending on the amount of our valuehands, and the equity of our bluffs. Just because we are using mixed frequencies with some of valuehands and some of bluffs, we still should keep the value-bluff amount prettymuch in line, or V can exploit us. Just using the word "mixed strategies" doesn't magiaclly throw away the need for balance and correct ratios.

And this can be figured out to close extent with simple models.