Santaur

On phone so can't really elaborate. But a significantly large % of BBs range will be AX due to him calling so many off suit aces. The result being that I think it will be hard for the button to bet any medium pair type hands more than one street which will limit his overall cbet frequency.

And fwiw I don't think 55/45 is a huge hot cold equity when BU vs BB flat. But I haven't looked into it in a while. I do agree that it would be a lot in other situations just not BU vs BB. Maybe you can confirm or reject.

i've been aware that i'm at big a range advantage the entire way

Why do u think that you're at a "big range advantage" more than any other situation? If I were BB, I'd have nearly all the A9, J9... and I'm not sure that everyone 3-bets all the AJo. It just seems that it's not a particularly bad board for BB than in general from a standpoint of how well it hits our range.

From looking at how dynamic and static the board is... it's probably about equal maybe leaning a little more toward dynamic. However, when we have very wide ranges as in the case of BU vs BB, then both players often end up with lots of mediocre weak hands on 9 high type boards where for the BB most of his pairs will be vulnerable to overcards and thus at a range disadvantage since position will be more valuable. However, that is NOT the case here. In this situation, most of our hands are only vulnerable to gut shots, oesds, flush draws which granted there are a fair number of, but it's not nearly as often as in the case when we're facing overcards on a 9x board. This is a long way of saying that I don't think the board texture is particularly bad for the BB either.

if i were btn i would be goin apeshit c-betting on this flop

Not sure it makes a lot of sense to go ape shit on this board because I think the Villain can defend relatively easily. For example, if the Villain is defending with his actual hand in this post Q9 and better... plus all gutshots and better, then he'd be defending close to 60% of his range on the flop. And therefore unless he's folding a ton on the turn and river, and there's not a lot of reason to assume he folds a ton on the turn and river, since it's pretty easy to call with top pair + and any oesd or flushdraw. I wouldn't want to bluff a ton on the flop assuming the Villain is folding too much.

@ shibulon

your approach is not wrong... in fact, it's the most common and usually the easiest way for people to understand. But it's not the ONLY way to do it. You can instead start with your bluffing range and then add the requisite value hands.

why can't we decide how many value hands we can bet based on amount of bluff combos we get to a spot with? i believe both value and bluffs work together synonymously in a balanced strategy

Epriest is right here. From a GTO standpoint, you DONT decide how many bluffs you use based on the number of value hands. And AT THE SAME TIME, you DONT decide how many value hands to bet based on the number of bluff combos. They both exist symbiotically relative to each other in balance... neither has an a priori position ... they're EQUALLY dependent upon each other.

I laid out the assumptions (except for one) pretty clearly, before proceeding w/ a calculation, which (incidentally) I did not claim was relevant for any advice.

So are you in the habit of making "observations" which are "irrelevant"... cause you might want to get that looked at.

I'm not sure what assumptions except one that you claim to lay out clearly, but I just took your words at face value.

If you could not tell that the nut-flushdraw was included in the betting range...

I'll explain where my confusion stemmed from. You wrote this as your betting range:
[AA,KK,QQ, AhKx,AsKx,AxKs,AxKh]

Now a literal interpretation of your AK hands would read as follows:
AhKs
AhKc
AhKh
Ah,Kd
TOTAL = 4

As,Ks
As,Kc
As,Kh
As,Kd
TOTAL = 4

AcKs
AdKs
AcKs
TOTAL = 3

AcKh
AdKh
AcKh
TOTAL = 3

GRAND TOTAL of 14 combos:

According to your calculation above, you're supposed to have 12 combos of AK (12/25 = 48%), but it wasn't clear which 12 you were referring to, since you had included 14 combos in your range.

But then I read this sentence of yours:
"and (even) if you want to include the nut flush-draw in the value range, which is a fair point,"

Which I then took to mean that your initial range which never explicitly stated to include any suited connectors that what you meant was to not include the AhKh or AsKs which would give you the correct combos of AK.

But who knows maybe I should just engage in a reading comprehension course.

if you have Aces, and Kings, and Queens (and you're planning on calling all-in with those), and all of the Ace-King, and you know that Villain has Queens, then you can bet the size that you did at (about) a value:bluff of 52:48

This assumes that ranges are perfectly polarized which they're obviously not in this case, since all of the Hero's bluffs have quite a bit more equity than 0%. And your number would be WAY OFF if our bluffing range wasn't transparent when it hit... in other words, if the Villain didn't always know when our bluffs improved.

In terms of betting, if you have Aces, and Kings, and Queens (and you're planning on calling all-in with those), and all of the Ace-King, and you know that Villain has Queens, then you can bet the size that you did at (about) a value:bluff of 52:48, and Villain isn't able to jam QQ profitably.

If you knew that the Villain had Queens, why would you ever have a bluffing range in the first place, assuming that the Villain is never folding his Queens. And why do u mention that the Villain wouldn't be able to jam profitably as if that's the criteria by which you judge whether you constructed your range correctly?

Also, even when you bet 97.50, you're calling w/ one of the Ace-Kings that you bet

This also doesn't seem to make sense unless you're suggesting that we're calling with the nut flushdraw which it appears that you didn't include in the betting range in your next post. In other words, why are we calling with any hands that would be a -EV call? If the villain has QQ, then all AKs except the nut flush are -EV as calls right?

#2 is a ballsey comment and not accurate in my opinion. While some of his assumptions can be called into question, I don't think you could challenge that he has a rudimentary understanding of game theory or that his math is inaccurate given his assumptions.

Given a recent post of yours asking for verification of a basic math equation, if I were you, I'd just apologize for making such a claim without proving any evidence and just ask for someone with a basic understanding of game theory. I don't want to derail your thread, and good luck finding a study partner.

personally, i think it's easier to solve and makes more sense, although both ways are correct, to just set folding equal to zero.

Looks good to me.

River sizing maybe should be a little smaller... Not sure though.

You're not exploited on the river as long as u don't fold too much. Kinda depends on what stronger hands that u have.

I think the initial raise on the turn is fine fwiw. Just add some bluffs to your range if you don't usually have any.

On the river, theoretically it's almost certainly a mixed strategy, since we don't have any other calling hands from the turn. From an exploitative standpoint, you just need to decide how you think the Villain is going to construct his ranges. For example, if the Villain thought it was suspect for you to check-back the flop to raise a blankish turn, so he decides to 3-bet the turn as a bluff. However, you call his turn 3-bet. What is the chance that you're floating his turn 3-bet with a hand that you're planning on folding or turning into a bluff on the river? I'm not sure that most "good regs" as you described him, are going to think that you're folding a ton on the river to make bluffing profitable.

When you check the As, it's kinda a double edged sword...
you can check-call lots of turn even if the flush gets there. On the other side, you also block lots of hand which he would bluff with.

I'm not sure that it's going to make that big of a deal in terms of balancing, since stack to pot ratio is so small. And I assume the Villain 4-bets AK preflop, therefore his range is capped at KQ.

You also might want to take a look at whether you should be c-betting KQ here, given that our opponent never has a higher one pair hand. There might be some issues with him having a ton of KJ though, but my guess is that you can still c-bet it here.

I think this hand is fine to bet for value/protection on the turn.

When we do check back de turn we never have a better hands than 5x. So we can't bluf much rivers since our value range is so narrow. Is this a problem?

I don't necessarily agree with your assumption that we can't bluff much rivers since our value range is so narrow. Even if we can only bet 5x and better on the river, it's still going to be a significant chunk of our hands because we bet so many other hands on earlier streets. Therefore, our frequency for betting river (value + bluffs) will not be particularly low.

I liked how you played the hand so far. I think turn can be played as flat or raise, depending if I think the Villain can overbet rivers.

As played, on the river, I think it's pretty close between leading and check-calling. But I think I'd tend to lead the river.

I think the topic of proper adjustment to exploit your opponent is very important and not approached with the same rigor as other situations. So I think this could turn into an interesting thread.

Our goal is to maximize our EV by exploiting our opponents imbalances. Let's assume that our opponent has a static strategy and won't make any adjustments regardless of how we play.

I like SPrince idea of limp calling some hands OR you'll need to probably open raise less unless Villain is making really big errors in the rest of his game.

I disagree with SPrince that you should 4-bet less. In fact, I think the proper adjustment would be to 4-bet for value wider since the Villain is 3-betting too much and rarely folding. Along the same lines, I would never 4-bet bluff.

Our 3-bet flatting range might need to be a little tighter since the Villain has a very high flop and turn c-bet frequency, so we won't be able to call wide preflop... unless the Villain gives up a TON on the river in which case we could probably flat against 3-bets about normal. Along the same lines, when we flat a 3-bet and the Villain c-bets then we'll probably have to fold the bottom of what is our usual calling range unless he gives up a TON on the river. A more subtle adjustment might be that we call with all made hands and top unmade hands that can call down, but we fold hands which require the Villain to give up on future streets like overcards with bdfd.

In single raise pots where our opponent DIDN'T 3-bet, I would likely be very aggressive. Since our opponent is 3-betting us soo much and hardly folding to 4-bets, I assume that he's 3-betting a very depolarized range which means that his preflop calling range when he doesn't 3-bet is going to be very weak. Either we're going to be able to get ALOT of folds postflop OR we're going to be able to value bet very thinly.

This spot is solved to considerable accuracy for the turn, I'm extrapolating to the flop in a way I think is reasonable but can't prove to you.

Outside of GTO range, I don't think anyone has anything close to solving for a turn situation, and GTO ranger requires quite a handful of simplifications and most importantly that the ranges provided on the turn be GTO. That's not to say that I don't think it would be a fairly good representation.

While it's true that you could end up at that strategy by misapplying a mixed strategy approach I think it's important to realize that if you don't try to apply a mixed strategy approach you will always end up with zero percent of your top pair hands in every line except one and that this is a much easier thing for an opponent to exploit.

I don't understand what you mean when you write, "you will always end up with zero percent of your top pair hands in every line except one". What if you bet your strong top pair and checked your weak top pair? Mixed strategies are usually the result of blockers / hiding information.

However, with that being said, unless our opponent plays in a way deviant from GTO we will still have the same EV by doing this as long as we never mix into a non-equilibrium line.

Without getting into the weeds, there's not a bunch of equilibrium points. My argument was that when you take a huge chunk of hands (ie all top pair) and then suggest that you can play them with any percentage mix without it making much of a difference than your over simplifying the process. Instead, it will be very important to have pretty close to the right % mix of hands even if there supposed to be a mixed strategy. For example, simplifying things, if overall you're supposed to be betting ~75% of your top pair hands and you're only betting 30%, then your overall betting range is going to be much smaller and likely very noticeable. In other words, if you want to make the argument that all of the top pair type hands should be a mixed strategy, then I think it's also important to give a sense of the overall mixes.

I think you can probably answer this question better than anyone. You know the equity that you need on the river to make a call and you have a better sense (than at least me) on what the Villains range will look like. So I'm not sure why you posted the hand... is it that you don't know what his river range would look like or you don't know how to calculate whether it's a call?

I think your confusing the idea of "ranges". Either the Ac is in our range or it isn't... even if we didn't have this particular hand in this case shouldn't effect our range. Unless you thought for some reason that we weren't 3-betting AA with a club until you saw the hand (which wouldn't make much sense.)

Why? Typically speaking top pairs should be mixing between betting and checking on flops and turns and bluffcatchers should be mixing between x/f and x/c.

What makes you think this is the case? I don't think this is an assumed truth by any means. And I can't really think of a way in which you could prove this without solving the flop and turn, since as you stated it requires knowing exactly that the two hands have equal EV.

If we don't (know how our opponent plays) then it's impossible for us to gain EV in and there's little reason for us not to just take whatever option we're most comfortable with.

Following your logic to its end would mean that typically you could play all your top pair hands on the flop and turn by only betting them 1% of the time which would mean that on the river you'd have .01% of your top pair hands. And that it wouldn't effect our EV. I think that this would be a clear mistake and easy for our opponent to exploit.

While there's degrees of how much you need to dig into a situation and make the best choice, I think you're underestimating how much poker is a game of thin choices.

^ while there are plenty of mixed strategies in poker, I think you're taking it a bit far here.

What position are u in?

Should I address SRP or 3BP first?

My general advice is that you should spend the most time on the spots which offer the most opportunities:
1) BU vs BB -- Cause it comes up way more than any other spot
2) BU vs 3-bet pots -- Comes up fairly often and most people make mistakes
3) SB vs BB -- Comes up about as often as CO vs BU -- but I think has more potential cause people play it so differently and it's somewhat easier to model with only 2 players. Also look into SB vs BB 3-bet pots.
4) CO vs BU -- Comes up fairly often. Also look at CO vs BU 3-bet pots and CO vs Blinds 3-bet pots

All other spots I'd spend less time on as I feel they don't come up enough... so get a rudimentary sense. Or look into after first going through the above.

i think your line and logic are both fine, but I would probably fold river if i was playing GTO.

The difference between betting and checking flop are both going to be pretty close. But I'm definitely check-calling the turn given your description of the villain.

Everyone saying its a call, what's the worse hand u call here?

Do you 3-bet TT here preflop... just saying that I'm not sure that's in your range here. It's definitely getter to have a Q or T blocker if you think he's doing this with those hand types. But at the same time, you need to ask yourself which of these hands that you would be betting the river with anyways. Do you 3-bet AQ preflop? And if so, do you check it on the flop? Just some things to think about in terms of your range on the river.

From an exploitative standpoint, it's one of those spots where you just have to decide if the Villain bluffs enough. Most people don't, but if he has a weakish middle pair or even a weaker top pair, it's probably not too hard for him to realize that his hand is a bluff catcher and might turn some of them into a check-raise bluff. On the other hand, when you call the turn, how often does he try and check-raise the river, when your hand looks relatively weak (didn't bet flop) and most players in your shoes often check back the river too much. So this would suggest that he should c-bet the river with his nutted type hands. However, from a GTO standpoint IF he's betting the turn with a lot of marginal middle pair type hands (not saying this would be good but u implied that he might bet these hands), than on the river he's going to want to have a check-raising range to disuade you from betting the river for thin value.

it's hard to think of a spot where it won't be profitable for you to call the turn... unless the Villain can soul read that you're on KJ.

is it super obvious that we should start with the value requirements and then extrapolate the bluff size, rather than vice versa?

No. It's neither obvious nor correct. While traditionally people start by thinking about "value" hands first, they have no priority over bluffing hands. (You can apply a whole french literary deconstruction analysis to this question). But the point is that both value and bluffing hands just exist simultaneously in an equilibrium, there is no sequence to them. You must play ALL your hands in the highest ev manner which means that both your bluffs and value hands share equal priority.

In context of a river situation where you have nutted hands though and your bluffs are worth 0 EV... than you're going to want to bet as large as possible (all-in) because your bluffs will always be 0 EV and it maximized the EV of your value hands.

On the other hand, where your bluffs and value are not perfectly polarized, then you won't necessarily bet as big as possible.

The trouble with having two different sizes is the range we're up against. Namely, he's check folding complete air, or check calling close to the nuts. There is no in-between where our bet size is going to greatly influence his frequency for calling, and in any case I don't think betting a non-polar range VS a polar range would be in our interests- leaving us with a betting range of nuts, or bluffs.

So you're right that if our opponent hands are either always ahead or always behind (perfectly polarized), then there's no point in us ever betting... but then again he shouldn't be checking any of his nutted hands in that situation either.

The point is that you're trying to over simplify the problem by characterizing our opponents range as polarized... and in the next breath say that a hand like KT doesn't have showdown equity.

This isn't a particularly hard problem to solve if you just provide both players ranges to the river.

I don't think I end up with a lot of bluffs in this spot, so I'm going small (how small will depend on how many bluff combos compared to value combos I have) with all my betting range.

I don't think this is the correct way to analyze this situation. Just because a hand is not air (ie it has decent showdown value), doesn't mean that it shouldn't be turned into a bluff.

It's hard to really understand your question for a variety of reasons. It's not clear whether you're asking about what is the GTO optimal betting size for your hand / if it's GTO optimal to bet it at all OR if your asking what is the EXPLOITABLE betting size given Villain's tendencies.

From an exploitative stand point, you seem to suggest both that the Villain will either fold or call regardless of bet size AND the Villain might call down wider even if you bet small. So we really can't answer it from an exploitative standpoint without you being more clear about Villain's tendencies... the strategy he'll use against different bet sizes.

From a GTO standpoint, it's not particularly clear either. You ask at the end of your post, "what size fits all?" The first problem with this question is the assumption that you should be using a single bet size. Instead, you probably should use multiple bet sizes depending on your hand. From a value standpoint, you'll bet bigger with your nutted range and smaller with your strong but not nutted value range (although you'll likely need to protect your small betting range with some nutted hands). From a bluffing standpoint, it's mostly going to come down to a combination of your blockers and the showdown equity of your hands. So you'll likely use a hand which has decent showdown equity if it has good blockers. However, assuming everything to be equal with blockers, than you're going to bluff with the lowest showdown equity hands. In order to have a more definitive answer for this exact hand, then you'll need to provide ranges for both players 'on the river.