Solid thread guys!

On a flop with trips like 222, as BB in srp, we have to continue with all Qhi+ (all 3rd+ hicard kicker or some other combination of hicards) to make an ATC 1/2 cbet indifferent - ie folding ~33%. What is your approach on this?

You think a 75% 2barrel is GTO? Couldn't the BB just exploit that by folding flop more with hands that can't stand heat?


The obvious reason, you get more money from bluffs when you call. When you c/r 8x, the vast majority of his stack off range is going to be 8x too by the river (even on blank/blank), and you block half that...

I'm not saying call ~only is better than 30% checkraise for sure, don't get me wrong. It's just that I feel call only makes a lot more intuitive sense than regularly blowing up the pot with hands that want a small pot, just for protection.




Yeah you're right, I didn't think about the way you could read what I wrote. I meant "there are no unprofitable river calls in GTO vs GTO" (because those would be folds), but that's not what I wrote. Clears this up, was surprised to see you disagreeing but now I see why


Yeah, for sure. That being said, assuming minraise pre, postflop betsizing (say 75% everywhere), BB can never raise. How would you go about determining BTN's bottom valuebet hand on a given runout? Seems like you can't do that without making a judgement call about what you think BBs flop defending range should be.

Are you sure you've read the thread?

Why do you think it's important to prevent the SB from c-betting ATC profitably? You're at least the second person I've seen espouse this idea, and it is obviously utter nonsense. Has someone famous been propagating it or something? I can't figure out what else could be going on.

No, I'm quite confident that it isn't. I'm just not sure in which direction it's wrong or by how much. 75% is my best guess. Recall from earlier itt that I check this flop more often than most; this is one of the reasons.

If my range is too strong and overly weighted towards value hands, yes. I try not to let it be though.

The obvious counter is that you get more money from thin value hands and stronger semi-bluffs when you raise.

So?

Think I addressed this already in post 79, but I don't mind repeating myself once or twice.

The only hands that DON'T want a small pot on any particular board are strong value hands. Yet it seems obvious that one cannot have a c/r range consist only of strong value hands. One should either never c/r or c/r other hands as well. On this particular board, I feel many combos of 4x make decent hands to balance a c/r range with, and I believe many combos that people would use as c/r semi-bluffs actually play better as calls.

If we fix the pf ranges, this actually sounds like a game that could be solved in a reasonable amount of time with a non-insane amount of computing power. You're basically just talking about an extremely truncated version of limit hold 'em, right? So it should be vastly simpler than the full game, and we're almost to GTO for that . . .

I've read through this entire thread and feel there are a couple of Splade's points that don't make sense.

PREFLOP:
Preflop you suggest that KJo is higher EV as a call, yet at the same time you're saying that it can also be correct for it to be a 3-bet. If it can both be a 3-bet and a call, then by definition, they should be EQUAL EV. I'm sure you get this, but I thought I would point it out.

Your reasoning that it's higher EV as a call are two points. You want a smaller spr with this hand and you don't want to be 4-bet. In terms of being 4-bet, I don't see how this is much of an issue because if the bottom of our 3-bet range is KJo, then the Button won't likely be 4-betting hands much worse than AQ for "value". I'd be surprised if we'd be getting 4-bet more than 12% of the time, so it's not a large factor. Also I'm not sure why you think the spr is going to be back for a hand like KJo in a 3-bet pot. Sure it doesn't make the nuts a ton, but it's going to get quite a few dominated hands to call preflop and also get hands with decent equity to fold.

But the most contradictory part of you suggesting that KJo is a flat preflop is that this suggests that you 3-bet a very polarized range preflop. Yet at the same time you argue that postflop that you DON'T want a very polarized check-raising range. Why does your logic apply postflop and not preflop?


POSTFLOP:
You argue that you don't c-bet this flop often because the board is static and relatively good for the BB. I don't think I really understand your logic. You also point out in a different post that how static/dynamic a board is dependent upon the opponents ranges. For the BB, while he'll have some 8x hands which are more or less nutted here, they only make up ~11% of his hands. Therefore, for the other 89% of his hands, the board is very dynamic and they're all very vulnerable to the BU outdrawing them. I think this is a significant reason for you wanting to check-raise hands like 4x. So it seems to me that this board is very dynamic especially compared to the majority of flops which will contain a face card which would be more static since equity of ranges wont change as much on future streets. And more importantly, it's a very dynamic flop compared to the majority of both players ranges. You know I was just thinking that you might have been talking about the staticness of the board relative to the BUs opening range. While hands like AA,KK,QQ aren't very vulnerable on this board, I still think the vast majority of the BUs hands will still be vulnerable in a similar way as the BBs.

And if this board is very dynamic, it makes it difficult for the BB to defend against a c-bet. For example, you're suggesting that you're check-raising with some of your 8x, and your 4x. So what hands are you check-calling on this flop? How often in total between check-raising and check-calling are you defending against a c-bet? I agree that the SB should be able to c-bet this board with any two cards (and frankly I can't think of a board in which it wouldn't be GTO for him not to be able to -- I have my reason and it's not by looking at GTO bots.) I think the BB will have a pair or better 22% of the time and everything but the 8x are going to be very vulnerable. So I think it's going to be very difficult for the BB to defend enough where the SB isn't going to want to c-bet his entire range. So I can't understand why you want to be checking back on this flop much?

My approach on this thresholds is that as you came close to the river its less and less of an issue since it will be very hard for the bettor to get to the river profitably with enough bluffs after encountering "perfect" calling ranges on previous streets. So, while preflop its imperative to defend at least at thresholds, for me it makes a lot of sense to be concerned at least about the flop thresholds too.
Obv I could be wrong so can you give an insight on why you dont want to cbet your whole bluff range (aka low equity hands) vs someone which is folding a lot vs cbets? Ie you cbet 1/2pot and he folds >50% of the time everytime.

How are you "balancing" a checkraise range by adding meh hands to it? I've mentioned a checkraise range with like 35% strong 8x, 65% semibluffs. Can follow up turn enough to always check/fold when it checks a blank and still not get exploited by floats, and can deal with 3bets. That people might choose the wrong hands to bluffraise with doesn't really mean a lot.

There's no reason to raise 4x to "balance" iyam. If we raise 4x (or some 4x), it's because they do better as a checkraise* than as a checkcall, and I see no reason to think that they do.

*Or checkraising them even though they'd rather check/call does good things for our range to the point that it makes up for checkraising.

The question wasn't can it be solved, but how you would go about solving it.

I do think KJo has higher EV as a call (against a min-raise 100bb deep), yet at the same time it can also be correct for it to be a 3-bet if I'm wrong, which is a possibility that one should always account for. I don't play a mixed strategy with KJo in that spot, but I know of people better than me who do. I would not be very surprised at all to learn that the GTO play was 100% call, 100% raise, or a mixed strategy. Thus, I think it's reasonable to say that 3-betting KJo there is fine even though I never do it, because numerous people have demonstrated that it's possible to be an enormous winner while having that be part of your strategy, and I couldn't even begin to "prove" what the right play is. The only thing I'm sure of is that you shouldn't fold.

I think you may have meant to write either "a smaller pot with this hand" or "a larger spr with this hand," because as worded this is a little confusing. Either way, I'm afraid you've misinterpreted my comments. The only hands that don't want a smaller pot are very strong ones. I've mentioned itt that I 3-bet 43s as a default. Do you think that's because I want to play a big pot with 43s? Most of the profit garnered by 3-betting any but your strongest hands will come from ending the hand immediately, yet 3-betting more than just your strongest hands is clearly right. The question, then, is which hands play best as calls, and which play best as "light" 3-bets.

In the same vein, the only hands that want to be 4-bet are very strong hands that are happy to 5-bet. Yet clearly we want to 3-bet many hands that dislike facing a 4-bet and cannot profitably 5-bet.

I hope this makes it clear that the reasons you think I have for not wanting to 3-bet KJo against a 2x open 100bb deep are not the actual reasons I have for not wanting to 3-bet KJo against a 2x open 100bb deep.

I'd be surprised if pocket pairs flop sets more than 12% of the time, so it's not a large factor.

I'd be surprised if suited hands flop a flush/flush draw more than 12% of the time, so it's not a large factor.

I can think of a few more hands for which this is true that I would never 3-bet. Can you?

Does it suggest that? I'm afraid I don't see how. Would you mind explaining?

I have elsewhere argued against 3-betting a polarized range OOP pre-flop, so I'm afraid you'll need to demonstrate one of the premises behind this question before I can reasonably be expected to answer. As is, it feels a bit like I'm being asked whether I've stopped beating my wife.

Is that what I argue?

In general, I think the SB should bet less frequently on boards that are more favorable to the BB's range than on boards that are less favorable to it, because range strength is a source of ex-showdown equity, and I think that on average one should bet more frequently with a larger ex-showdown equity advantage and less frequently with a smaller (or non-existent) one. Does that clarify things?

Whether this is true really depends on what you mean by "difficult." Because so many of the SB's semi-bluffs have such good equity against a large swath of the BB's potential "bluff-catchers," the BB cannot profitably continue with as many hands on 884r as he could on most other boards. However, because the top of the distributions are static - and because the BB's range is heavier in the hands that make up the top of the distributions - the BB can defend aggressively (i.e. by check-raising) much more often than he can on most boards. The ability to frequently raise and immediately bring an end to the hand is a powerful one, and its value should not be underestimated, even if exercising it necessarily lowers the overall frequency with which he can continue.

Some 8x, some 4x, some high-card hands. About the only hand type that I'm always check-raising and never check-calling here is gutshots.

Depends on the size of the c-bet/this has been addressed elsewhere in the thread.

Mind sharing that reason?

You seem to be mistakenly assuming that just because the SB can profitably bet a hand, it will necessarily be more profitable to bet than to check. Needless to say, this isn't so.

What?

Why do you think that it's "imperative to defend at least at thresholds" pre-flop? Why do you think it makes sense to be concerned about the flop thresholds too?

Because I expect checking to have a higher EV than betting.

Could you give some insight into why you want to c-bet your whole bluff-catching range (aka hands that never fold out better and so do not function effectively as bluffs but have less than 50% equity against the BB's continuing range and so do not function effectively as value bets) vs someone who is check-raising a lot vs c-bets? i.e. you hold 22 (or A2, or A5, or KQ, etc.) on 884r and he folds >50% of the time but also check-raises >25% of the time.

Because that's . . . that's what "balancing" a check-raise range means. A range that holds only very strong hands is not balanced, by definition, because it holds only one type of hand (very strong ones). Similarly, a range that holds only meh hands is not balanced because it holds only one type of hand (meh ones). "Balancing" a check-raise range means adding both very strong and meh hands to it in an appropriate ratio.

And that's nice, but I'm pretty sure the BB can get away with check-raising more frequently than this. What fraction of your overall range does "35% strong 8x, 65% semibluffs" translate to?

These two sentences seem to me to be flatly contradictory. If a particular hand does better as a raise than a call, it will almost always be because there are other hands that also play better as raises than callsonly so long as the hand in question is raised. The particular hand in question will serve to "balance" the raising range, thereby allowing more total hands to be raised profitably, and other hands will serve the same function for it.

Well, if we assume that the SB can only bet the turn 48% of the time after having a flop c-bet called, then I might agree with you.

There are no loss leaders in game-theoretically optimal play. Every hand is played in order to maximize its EV against the nemesis (which is also game-theoretically optimal/the Nash equilibrium).

Well, I probably wouldn't, because a game that could be solved so simply likely couldn't be the source of much profit, so it wouldn't behoove me to pay someone to solve it like I otherwise might.

If you're asking about the precise method that might be used if I did, I'd advise you to start here, then check the references, then check the references in the references, etc.

I'm not sure the term "balanced" is defined like that. To be specific, I'd say a range that checkraises only 8x and 4x is very unbalanced

But I'm sure you know I would not advocate raising strong 8x only.



I'm sure BB can too. I just don't see why that would be the most profitable play.

Idk, like 5%?


I don't quite understand how these three statements can be correct (which they would have to be for 75% 2barrel to be GTO *edit* or your best guess for GTO):

1) BTN can 2barrel 75% of the time
2) BB can't exploit this by folding more on flop
3) BB can't exploit this by calling more on turn

And that's even ignoring that a quick look at what a 75% 2barrel range would look like with the cbet range posted above gives me no clue what you do to defend vs leads when it goes c/c ch ch.

I'd say intuitively it's unlikely checkraising 4x is GTO, you haven't really offered any reason why it would be, other than a blanket statement you feel SB GTO is 2barreling 75% of the time.

Hey Spladle, I really hate to interrupt your headsup with kaby but when you say:

are you implying that a max exploit strategy from SB wont be able to increase his EV by opening 100%? In other words, a BB strategy which requires to fold >50% vs openraises will have a greater EV than one which defends at least at thresholds?

...

I never said that one should bet his bluffcatchers! I only said that now he can bet an very unbalanced range by expanding at maximum his bluffing range ie bottom equity hands (no sdv, no real draws - hands that otherwise would check/give up a decent %), because by doing so he will add more EV to the strategy.

How do you think the term "balanced" is defined then? I agree that a raising range of only 8x and 4x would be very unbalanced.

Of course. I do suspect that you'd advocate raising too infrequently though.

Imagine, for a moment, that your options for continuing on the flop are restricted in one of two ways - either you are forced to call with your entire continuing range, or you are forced to raise with your entire continuing range. It should be intuitively obvious that the former strategy will allow you to continue more frequently than the latter against the NE - some hands are profitable calls but not profitable raises, and some hands are profitable raises but not profitable calls, but the former should usually outnumber the latter. It should also be obvious that there are some boards for which the gap between these ranges is much larger/smaller than others.

My claim is that boards where the gap is larger should be check-raised less frequently than boards where the gap is smaller. In extreme cases, I believe that some boards should not be check-raised at all (because the gap is very large, which implies that check-raising your strongest hands will radically diminish the profitability of otherwise borderline calls, forcing you to continue much less frequently), while on others, almost every hand that can be profitably called can also be profitably raised. For this not to be true, we'd need to make some pretty strange assumptions about equilibrium play that I find to be unrealistic.

What I think this implies about actual play is that boards where this is true should be check-raised much more aggressively than is currently considered fashionable. As I've stated elsewhere: "At every single decision point in the game tree, you want to have as wide a raising range as possible. The only reasons to refrain from having a [wider] raising range in certain spots are defensive - that is, if by raising [more] hands you diminish the strength (and therefore the profitability) of your calling range (because range strength, like position, is a component of ex-showdown equity) by so large an amount that it outweighs the gains to your raising range, then calling [more] of your continuing range can be better than raising." But if there are few hands you call with that wouldn't make profitable raises themselves, then raising a seemingly absurd fraction of your continuing range can be correct, because calling (rather than raising) more frequently does not allow you to continue with many additional hands. Therefore, it seems likely that raising a sizable fraction of thin value hands is correct, as otherwise you cannot semi-bluff as often as you'd like. Of course, when a substantial fraction of your raises are for thin value, it becomes necessary to usually check the turn after being called. So if you want to barrel often after check-raising and are uncomfortable with frequently taking a "check-raise, check" line, then raising a much narrower range (and never 4x, which should rarely bet again after having a check-raise called) is better.

Another way of making the argument: I think check-raising 4x results in an immediate win 30-40% of the time and winning a check-down 20-30% of the time when called. I think check-calling results in winning the pot 55-65% of the time but that 25-35% of these wins come from the turn/river getting checked down, meaning that the pots won will on average be smaller. The EV of both options seems pretty close, and so I'm inclined to take both actions some non-zero % of the time (usually raising because of reasoning outlined in the paragraph above this one).

Not sure if serious, but obv I think that's way too small.

If BTN 2barrels 75% of the time at equilibrium, then 2 and 3 are true by definition.

The reason I think the BTN should barrel so aggressively is a corollary of the fact that I think he should be checking back on the flop a lot because so many of the BB's hands play best as check-raises rather than check-calls (leading many of the SB's hands to play better as checks than c-bets). On boards where I c-bet the flop less, I tend to 2barrel more, and vice versa.

I'm not clear on what "c/c ch ch" means, but assuming it's that the flop c-bet was called and the turn went check-check, the answer is that I call sometimes if the BB bets the river.

Hope this post made my thinking more transparent. If you spot a flaw in it please do let me know.

Your use of the phrase "[i]n other words" is confusing here, as these two sentences suggest opposite things. If the SB should open less than 100%, then the BB should defend often often enough to prevent the SB from profitably opening any two cards. If the BB does not defend often enough to prevent the SB from profitably opening any two cards, then the SB should open 100%.

Leaving this aside, I happen to believe that the SB should not open 100% and that optimal BB defense will prevent the SB from doing so, but there is nothing inherent in the nature of games which makes this necessary or important - it is simply a coincidence. There are many situations in other forms of poker where a player can profitably raise 100% of his hands on the first betting round and his opponent cannot continue often enough to prevent him from doing so.

But if you want to check bluff-catchers, then obviously you must also check other types of hands as well, because if you don't then they cannot actually serve effectively as bluff-catchers. After all, if your opponent knows that your entire range will call a turn bet, then he has no incentive to bet the turn, does he? So you must check some hands that plan on folding to a turn bet as well. And if you're checking some very weak hands, then you must also check some strong hands too, or else you will not be able to effectively bluff with the very weak ones.

Well at this point it doesnt matter anymore because we've made all our bluffs +EV while he cant do nothing anymore with his [bluffs]! So what happened was him folding so much to cbets took him in a worse spot ott after we check back flop, where his whole range is beaten - ie he cant bluff profitably anymore therefor smaller overall EV for him.

If you argue that the EV of betting 100% of bluffs otf vs him is smaller than the EV of let him bluff ott after we check, i have some big doubts thats the case.

It did, ty.



I'm surprised you're looking at this so binary (profitable/not profitable). I think raising 4x on this board should be profitable vs NE, and that calling should be profitable too. I think calling should be significantly more profitable though - I think that's what we fundamentally disagree on.

This was a an inexcusably awful typo, and I apologize for any confusion it may have caused. What I meant to say is that if your opponent knows that your entire range will call a turn bet, then he has no incentive to bet the turn as a bluff (unless you will over-fold the river after calling the turn). Obviously, knowing that you will always call a turn bet provides him with an enormous incentive to bet the turn for value.

This is simply wrong. The fact that a strategy allows every hand you hold to be +EV and prevents your opponent from betting the turn OOP without some threshold level of equity against your calling range does not demonstrate that the strategy is optimal or unexploitable. In fact, after being called pre-flop, every single hand you can hold will be +EV against the NE on almost all flops regardless of the strategy you employ. So this isn't a high bar to clear - in fact, it's not even a bar at all.

It should be obvious - and I'm not sure why it isn't - that by calling the turn 100% of the time and preventing your opponent from bluffing profitably, you render yourself vulnerable to exploitation by someone who refrains from semi-bluffing and instead bets the turn exclusively for value after seeing you check back. Furthermore, if the range you check back is so strong that you really shouldn't ever fold with any part of it, then your c-betting range will be weaker than is optimal. And although c-betting ATC should probably be profitable at equilibrium, human opponents are under no obligation to refrain from attempting to exploit perceived imbalances. If your c-betting range is too weak, then not only may betting ATC not be profitable, but the BB may actually be able to check-raise ATC profitably. If, in order to prevent this from happening, you defend against check-raises more loosely, you will wind up putting too much money in the pot with hands that are too weak and render yourself vulnerable to exploitation by someone who weights their check-raising range more towards value.

All of these are concepts I covered earlier in the thread; I encourage you to go back and re-read it if you're interested.

The only way BB's whole range can be beaten after SB checks back the flop is if he checks back exactly and only 88. Otherwise the BB can easily hold plenty of hands that are ahead of the SB's range and play accordingly, value-betting when appropriate and checking otherwise.

I've outlined the costs of preventing the BB from semi-bluffing the turn a few paragraphs above.

Okay, well your doubts are unfounded. Again I'll point to the best HULHE bots, which are radically close to playing GTO. After checking behind the flop, they sometimes fold to a bet on the turn, even though betting the flop would have been immediately profitable. I've explained why checking weak hands that will fold to a turn bet is important in the last paragraph of post 114, which I'll quote (with some additional words) here:

But if you want to check bluff-catchers, then obviously you must also check other types of hands as well, because if you don't then they cannot actually serve effectively as bluff-catchers. After all, if your opponent knows that your entire range will call a turn bet, then he has no incentive to bet the turn as a bluff, does he? And if 100% of the BB's bets are for value, then it clearly can't be right for the SB to call 100% of his range, because many of his hands will be -EV calls against the BB's (all-value) betting range. So the SB should fold some. But once the SB starts folding occasionally, the BB has an incentive to start semi-bluffing sometimes in addition to betting for value. This is what equilibrium play looks like.

So you must check some hands that plan on folding to a turn bet as well (because otherwise the BB can exploit your never-fold range by never bluffing). And if you're checking some very weak hands, then you must also check some strong hands too, or else you will not be able to effectively bluff with the very weak ones after facing two or three checks.

Robust checking ranges look somewhat similar to robust c-betting ranges - they contain some strong hands, some medium-strength hands, and some weak hands. Overall, they should usually be a bit weaker and more weighted towards medium-strength hands than c-betting ranges, but failing to check enough hands of each type is an exploitable mistake.

(This is in stark contrast to HULHE, btw, where the best bots almost never slowplay/check behind a very strong hand. I'm pretty sure that can't be right in NLHE though due to the possibility of over-betting.)

I hope I didn't give the impression that I'm incapable of distinguishing degrees of profitability and deciding that one profitable option is more profitable than another profitable option (if nothing else, the discussion itt about checking back when betting ATC would be profitable should dispel that notion). The post you're quoting from was my attempt to explain the method by which I try to figure out how many of the hands that can be profitably raised are likely to be most profitably played by raising. On boards (like 884r) where I believe the answer is very large (for reasons outlined above), I believe that raising strong but vulnerable hands can make a lot of sense. Almost every hand that c-bets and folds to a check-raise has >20% equity against 4x, so folding out these hands is a significant win, and yet we still have >50% equity when called or raised . . .

I don't really care to re-litigate the issue though. I wouldn't be very surprised to learn that I was wrong about this.

One factor I haven't discussed at all - but which I believe to be quite important - is bet size. On some boards, I believe there should be a linear relationship between the bet size you face and the frequency with which you check-raise (when continuing) - that is, against smaller bets you check-raise more, and against bigger bets you check-raise less. On other boards (like 884r), I believe the relationship is very different - against smaller bets, you should continue more frequently but check-raise less frequently. As bet size increases, you should fold more often but check-raise a greater proportion of the hands you do continue with. As bet size increases still further, though, the relationship switches again, and check-raises should become less frequent.

In practice, what this means is that I'd be much more likely to call 4x against a smaller c-bet and raise it against a larger one (within the normal range). Food for thought!

Spladle i agree 100% with everything you said if we are talking about exploitative strategies but apparently we both lost the hypothesis from which our discussion begun:
"A GTO strategy should defend ~ thresholds of the bets it is facing."
- which you disagree with.

The BB's GTO strategy is fixed because it is designed as a best response strategy vs an single unexploitable strategy so BB wont "adjust" so it wont switch to leading turns with only value (instead of a balanced/unexploitable range of a GTO strategy), therefor we can exploit it by cbetting flop 100% of bluffs therefor folding more than thresholds isnt GTO to begin with.

Heres an example:
hunl, 100 bb, minraised pre, BB called.
BB is playing the "said" GTO which requires folding ~50% vs 1/2pot cbets.

BB checks
Opponent_1 is playing GTO and he is cbetting a balanced range {value, good draws, some% of low equity hands}.
Opponent_2 is playing exploitative and he is cbetting {value, good draws, all low equity hands}

How can BB have 2 different lead ranges ott after encountering a check back otf in a srp pot? How can it be unexploitable vs both opponents?

So it will! If BB turn lead its only value then SB defend should be top x% of his range where x is ~threshold.

Lets see what happens: BB leads turn with only value which is no more then 20% (top pairs+) - SB will have to defend some %, lets round it up to pot bet and 50% defend, to not make BB bluff all his hands. And I suppose BB will also barrel river close to 100 % where SB folds another 50%. The rest 80% when BB doesnt leads the turn, they see a river and basically SB wins around 70% of the time (obv quite simplistic but it will do the job).

So we have:

EV_SB_whenBBleads= timesBBleads * (timesSBdefendOTT*amoutlostOTT + timesSBdefendsOTT*timesSBdefendsOTR*amountlostOTR)
EV_SB_whenBBleads= 0.20*(0.5*(-4) + 0.5*0.5*(-12)) = 0.2*(-5)= -1

EV_SB_whenBBchecks= timesBBchecks * equity * pot= 2.24
EV_SB_whenBBchecks= 0.80*0.70*4= 2.24
---------------------------------------
EV_SB= +1.24



some nice stuff here

PREFLOP
Yeah I agree that it's impossible to determine with anywhere close to certainty what is the correct play preflop.

So it seems to me that what you're saying is that you're "bluffing" type hands realize their EV by getting our opponent to fold. Similarly, some of our stronger hands realize their EV when our opponent calls and if we're 4-bet are likely close to 0 EV at that point. I think this is all fine and true.

I would make the same argument that some of our hands are going to work best as a 3-bet because of a combination of the reasons above AND they'll be able to check-call postflop.



I'm sure you're being sarcastic. But another way of putting it is that even if you only 3-bet KQ+, then you're opponent would be able to likely 4-bet ~11% of hands. In other words, by adding KJ to your 3-bet range, you only add an additional 1% of a range to your opponents 4-bet range. It's just not drastically different when you add KJ.


Well let's say that you're 3-betting KQ+, so KQ is the bottom of your "value" range, I'm guessing that you'd be able to bet flop, turn and river over 50% of the time when you hit (assuming the flush never gets there and not any other terrible run out). And if this is the case, it seems that one of two things are then true:
1) you could either 3-bet KJ for value
or
2) you should 3-bet KJ so you can have hands which will sometimes check-call in a 3-bet pot.


POSTFLOP:
The BB will have ~9% of the hands that are 3 of a kind or better. Even if we're being generous and giving you a 3 to 1 bluff to value ratio. At most you'll have a 36% check-raising range, and then a pretty close to 0% check-calling range. I'd be surprised if the BB could defend more than 40% of the time.

If this is true, I don't understand how you could think that this flop is a "good flop" for the BB OR easy for the BB to defend.

It's going to be very profitable for the SB to be betting his entire range on this flop regardless of what the BB does, imo.


The BB is going to want to defend as little as possible because the wider he defends the thinner the SB will be able to value bet. Now the BB doesn't need to defend enough so that the BB cannot bet any two cards, he just needs to defend enough so that the SB has both a betting and checking range. In other words, when the SB checks-back even with his lowest EV hand, this hand will always be +EV. So it's not a problem is we fold so much that the SB can bet any two cards profitably. And really the hand(s) which differentiate between the betting and checking range will be stronger than his weakest EV hand, so it's not necessary for the BB to defend so much that the SB can't bet any two cards, instead just enough so that the right hand(s) are probably indifferent between betting and checking.

But I wasn't only talking about exploitative strategies. What seems apparent to you isn't true. Furthermore, I feel like you must have either not read or failed to understand the following from post 114:

Put another way, there are some situations in poker where a player should be able to bet profitably (or raise on the first round of betting) with blank hole cards at equilibrium, and the player facing the bet or raise should fold sufficiently often (at equilibrium) to allow this. There are other situations in poker where a player should not be able to bet profitably (or raise on the first round of betting) with blank hole cards at equilibrium, and the player facing the bet or raise should not fold sufficiently often (at equilibrium) to allow this.

It is absolute nonsense of the highest possible order to claim that a player facing a bet or raise in all situations in all games should prevent the player making the bet or raise from doing so profitably as a pure bluff (i.e. having 0% equity when called). There is no reason to think this whatsoever and in fact we know with 100% certainty that this is not the case.

Whether equilibrium play entails continuing against flop bets after calling a raise from the SB out of the BB in HUNL with sufficient frequency to prevent the SB from betting profitably with ATC is not yet known, but regardless of the answer, we do know for a fact that continuing with this particular frequency has absolutely no importance whatsoever in and of itself. If continuing more frequently than this threshold is correct, that is a coincidence. If continuing less frequently than this threshold is correct, that is also a coincidence. The threshold is irrelevant.

The above paragraph is complete nonsense. It has precisely the same form as "2 + 2 = 4, therefore the the moon is made of cheese, therefore the elves and underpants gnomes are engaged in an epic struggle to the death in order to decide which will get to take Halle Berry out on a date."

"[True statement], therefore [craziness], therefore [craziness]."

By definition, a single strategy will have only one range for any given action sequence.

Any equilibrium strategy will be unexploitable against all possible opponents.

It is possible for a game to have more than one Nash equilibrium though.

Don't wanna argue anymore and this is my final post on the subject but as long as you don't have any proof whatsoever in one direction or the other (+/- thresholds) how come it doesn't makes sense to begin constructing your ranges around this thresholds?

P.S.
Its sad how none of the other [many] bright minds of poker that hover above this forum doesnt jump in to make a stand.

Spladle provided good logic as to why your idea doesnt make much sense, he doesnt have to disprove it. Rather, you should provide insight as to why you think we should design our strategy around these thresholds. How did you come up with this idea?

Because it's a totally arbitrary number, any advanced poker mind realizes that.

Rather than anchoring yourself on a number for no good reason (or to say even more: for demonstrably irrelevant reasons) and waiting for your arbitrary number that happens to sound correct to novice poker minds to be disproved, you'd be better off looking for what a better number might be given a certain situation.