Should hero bet this flush-completing turn given the high hand bonus implications?

Respectfully, you should work on not over-explaining things.

Again, I understand the meaning of "polarized".

My issue was with you describing yourself as being "fully" polarized. You said this in support of using a LARGER bet size on the turn, rather than a SMALLER bet, or CHECKING:

I took "FULLY" polarized to mean you're only betting the pure nuts or nothing, whereas I think we could be betting a more linear range here, even as the PFR who c-bet the flop. I think I was pretty clear about that:

I also think you've proven that you like using solvers to support your opinions or actions in game. But as I seem to recall someone else in these forums saying, "you're using solvers for evil" (or something to that effect).

It seems to me that you're either using solvers to say, "my action is solver approved at equilibrium, and therefore correct, all arguments to the contrary be damned", or "using these assumptions, my action is solver approved (all opposing views be damned)", but you're inputting assumptions that support your conclusion, without those assumptions necessarily being an accurate reflection of how live humans actually play, nor giving anyone else's opinions enough consideration to build a solve around them.

It's hard to imagine a solver preferring a check back on turn to a small bet, at equilibrium, much less if we node-lock it to more closely approximate a human opponent's actions leading up to action checking to us on the turn.

Regardless, I and Omahadonk said you should bet SMALL. I said around 40% pot. OD said around 1/2 pot. You responded that you should bet larger than that, because you were "fully" polarized.

I gave you logical reasons for betting small, and then you used a solver, which apparently also said you should bet small (or check, which seems impossible if your inputs are realistic).

Like I said, we don't NEED a solver to figure this out. But if you WANT to use a solver, by all means, go ahead. I would only suggest you take what others are saying about actual live play into consideration when setting up the parameters for your solve, rather than using inputs which support your initial conclusion.

Otherwise, you're not likely to improve, only likely to become more entrenched in your views, be they right or wrong.

It's becoming increasingly apparent that you may be more interested in arguing or trying to prove others "wrong" than you are in actually improving. Case in point, in the midst of posting several different EV comparisons, and arguing that there's little to no difference between checking, betting small, or betting big (yet also arguing checking is clearly the best option), you say this:

This is EXACTLY what I'm talking about. Most human opponents aren't calling a BIG turn bet with 9x, or TT/JJ, and probably not much Qx. Few opponents are getting to the turn with all those hands. If you truly believe your V is really that bad, then you should node-lock the solver to make V call a BIG bet with all those hands, and then re-solve to see what size bet the solver prefers.

If you haven't done that, then your suggestion that V is calling a big bet with all those hands is BS, as is your earlier argument in favor of a big bet, because you're "fully polarized" here.

For whatever it's worth, I don't think a good V is calling any bet, even a small one, with 9x, JJ or TT very often. Maybe not even Qx. I think he's mostly continuing with AdQx, JdTx, AXdd, and made flushes. V would have to be pretty bad (or your table image pretty fishy) to call even a SMALL bet with all those 1P hands that you said would call a BIG bet.

If you have the solver set up so V folds all those weak 1P hands to a small bet, that may explain why it prefers a check back. But there again, that's an example of you using a solver to "prove" someone else is wrong. How can you say V will call a big bet with all those 1P hands, then set up the solver to to fold those hands, even to a small bet?

A hand's polarization can be determined by the action of the current and previous streets, because in general hero should be betting a polarized range from the flop forwards. If he checks at any point, for example on the flop, or on the turn after betting the flop, in theory his range becomes capped. In this hand, hero has iso-raised preflop, then bet on the flop and the turn. This means that his betting range is as polarized as possible. If hero had checked back the flop and then bet the turn, the betting range would still be polarized, but it would be less polarized than when he bets both flop and turn. The most polarized a range can be is when it 3bets preflop from a position that uses polarized 3bets (button and big blind) and then triples off on flop, turn and river. The decision point we are looking at in this hand is on the turn. When hero bets the turn his betting range is as polarized as it can be, or "fully polarized", because he has bet the flop and the turn.

When a range is polarized on the turn/river it should use larger sizes because it contains nutted hands and air. Using a large size means that the nutted hands get maximum value and the air gets maximum fold equity. It does not make sense to use a small size with a polarized range, because your nutted hands do not get as much value, and your bluffs do not get as much fold equity.

I use solvers to see what game theory equilibrium looks like for hands. As is well known, this is rarely 100% applicable to how one should play live low stakes poker, but it's a very useful tool/guide. I don't always agree with/advocate for the solver output, as you can see in this thread for example:

https://forumserver.twoplustwo.com/170/l...

It's not possible for me to "input assumptions" in a solve. I enter ranges, stack sizes and a range of reasonable bet sizes for each street, and the solver outputs a perfectly balanced strategy.

I didn't say the solver prefers a check back to a small bet. I said that when the high hand bonus EV is added to hero's options on the turn (i.e. betting or checking) that checking becomes clearly the highest EV option because it captures the most of the high hand bonus EV.

The solver output that I posted was independent of any high hand bonus EV calculations:

Potsize is 175

Bet 219: 288.70
Bet 116: 293.05
Bet 44: 293.79
Bet 18: 293.47
Check: 291.26

As you can see, the EV is almost identical for betting 66% pot, 33% pot and checking. This is not uncommon on the turn. (Or, at least, it's not uncommon for the EVs to be very close). Your suggestion of betting small on the turn is fine; it has an equal EV to that of betting larger (66% pot) and checking. The point that I'm making is that hero is polarized and therefore should prefer a larger size if he's going to bet. And that is of course only if we are ignoring the high hand bonus. If we include the high hand bonus then there is zero question that hero should check the turn, because then the EVs are as follows:

Bet 219: 296.41
Bet 116: 304.105
Bet 44: 308.47
Bet 18: 311.68
Check: 313.26

You could clearly benefit from a solver, because your natural conclusions were wrong. For one thing, you completely ignored the high hand bonus EV factor, and how it influences strategy, when you made your initial post. If you were used to working with solvers and looking at the EV of different decisions you would have realized how much of an impact 5bbs in bonus EV can have on a hand.

It's literally impossible for me to "use (solver) inputs which support (my) initial conclusion". Even if that was possible, I would have zero desire to use a solver that way, because my interest is in improving at poker, and solvers have assisted me in doing that to an immeasurable degree.

When I said :

"There are plenty of worse hands with which villain can call a large bet on the Q947 turn. You have to remember that this is live low stakes poker - people don't like to fold, and their limping can get wacky. For example, he can have Qx, 9x, JT, JJ, TT, flushes, Adx, a small amount of AA and KK, etc"

it was in response to your post:

"What the hell can an opponent have that will call a big bet here, when all your opponents limped in pre? You're basically hoping to get called by J8dd".

Obviously hero has a value bet here on the turn if the high hand bonus is not in play, and I made that clear in the post to which you were responding:

If you and/or the players in your games are folding Qx/TT/99 (and to a lesser degree 9x) with a diamond on this turn to a 66% pot bet then you are overfolding and giving up EV to your opponents. Those hands have a profitable call at equilibrium:

I don't need to node-lock the solver to do that, because it calls these hands already and understands that its opponent is going to have plenty of bluffs on the turn that these hands beat, or that their diamond draw is live, etc. It's honestly pretty incredible that you "don't think a good V is calling any bet, even a small one, with 9x, JJ or TT very often. Maybe not even Qx". Any player who plays that way is giving up EV and is going to get run down in any tough, aggressive game. If you only continue with "AdQx, JdTx, AXdd, and made flushes" then you're automatically getting exploited by any player who fires a second barrel when the flush draw completes on the turn. Are you really going to make the assumption that the turn bet is never a bluff and that therefore your pair is never ahead?

Lol no I obviously did not have the solver "set up so V folds all those weak 1P hands to a small bet" - on the contrary, you can see that it's calling with those hands in the image above. So I'm obviously not "using a solver to "prove" someone else is wrong". I have zero interest in doing that. I have no idea how you got it into your head that I "set up the solver to fold those hands, even to a small bet" - I hope you can now see that that's not the case.

I honestly think saying you are arrogant is the understatement of the century. But IDK man maybe im just another glue sniffing moron who didnt pay enough attention in debate club. Maybe you need a computer to tell you whether youre arrogant or not since you dont seem to put a lot of value in the opinion of humans so IDK man, let chatGPT run an analysis of your posts and let me know what it says as far as your arrogance percentile.

I even did the solve myself. Didnt give as many bet sizings because its sort of irrelevant (66 OTF, 25 and 66% ott, 10, 25, 66, and 125 OTR). All I did was create a mixing error fo V on the turn. I nodelocked such that any hand that GTO check raises at least 5% of the time, I set as a pure raise, and any hand that GTO calls at least 10% of the time i set as a pure call. The EV change to V is zero if you just blindly look at the EV of these individual decisions after all. I forgot to nodelock the river or the checking profit would be far lower.

with that simple change, KTdd is earning 587 with a 66% pot bet and only 500 with a check, making the $22 irrelevant. Feel free to check it yourself and come back and let me know what your guarantee is worth to me.

"You can name any ranges and whatever bet sizes etc from flop to river that you want" is what I said. I'm talking about equilibrium. Obviously you can manipulate EV if you nodelock (and the output then becomes biased and absurd). Of course the EV of hero betting is going to go sky high if you nodelock villain to check raise 100% of the time instead of 5%. See if you can achieve the same result without nodelocking.

good post too tbh

You're fond of these intellectually weak ad hominem responses.

See if you can achieve the same result without nodelocking.

You dont see the irony at all do you?

Id have to write a novel to explain how ridiculous this comment is, and if i spent time writing it, you wouldnt understand it, and assume thats my fault.

So you can't prove your point without nodelocking, got it.

If we're going to discuss how high hand bonus EV impacts strategy then of course equilibrium has to be used.

Well, good job, youve successfully baited me into one more response, but i really am about at the end of my rope on this thread, and im reasonably inclined to never read one of your posts again after this unpleasant interaction.

Your recommended strategy involves changing your own strategy to no longer be at equilibrium, but you dont think V can be afforded the same luxury. Further, you never nodelocked to check to see how such a strategy would actually affect your EV.

My whole point was that whether checking or betting the turn is EV+ depends upon V’s tendencies, but you find my simulation of a V tendency to be irrelevant to MY point. This is because the only point of view you acknowledge is your own. Youre too busy jerking off to the sound of your own typing to take the time to try and understand what anyone else is saying.

You believe your conclusion to be beyond reproach because you refuse to acknowledge the possibility that a lowstakes live player may be imbalanced such that the EVs could change, or is capable of adjustment to your strategy such that they are able to exploit your adjustment.

Are you able to figure out how you ought to adjust to the population not betting any of their sets or straightflush draws until the river?

This interaction became unpleasant because you got emotional and started making childish comments and using ad hominem attacks (like calling me arrogant etc, which is whatever lol and completely irrelevant to anything being discussed) instead of simply exchanging logical points of view in a civil way. There was obviously no need for it to go down that path, but that's what you chose.

My recommended strategy in the thread above does not involve changing my strategy to no longer be at equilibrium. When the high hand EV is added to the various options available to hero on the flop/turn, it has the effect of checking becoming the highest EV option available - which means that hero should choose it every time (all else being equal) when he has a straight flush draw.

Villain can of course be afforded the same luxury of adjusting his strategy for the high hand bonus (and presumably would, for example if he had a high hand draw himself). But you did not explain why you believe your suggested adjustment that "any hand that GTO check raises at least 5% of the time pure raises, and any hand that GTO calls at least 10% of the time pure calls" is a fair and reasonable counter-adjustment for villain to be making - and on the contrary, it's a massive adjustment in comparison to hero pure-checking only three combos in his range in comparison to equilibrium.

Sure, the EV of checking or betting depends upon villain's tendencies (like it does on every street of every poker hand). The problem is that we do not know what villain's tendencies are. Some may play as you indicated, some may play other ways, etc. It's absurd to argue that because villain playing a certain way makes checking lower EV for hero that the argument that hero should check with a high hand bonus hand is no longer valid. It's very simple to disprove that, because we could equally say that other villains can play in a way that makes it even higher EV for hero to check in the same situation. So, at least as far as I can see, the only fair way to approach it is to do so from a point of view where villain is balanced.

I already mentioned earlier in the thread the extent to which I believe the high hand bonus factor would impact strategy (but I believe it to be minimal as it applies to such a small fraction of the ranges in play:

"Another interesting question is how this would impact hero's turn strategy (although admittedly it's probably not by much) because it would mean that all straight flush draw combos would be checking, i.e. KT, KJ, JT, J8. This would very slightly reduces the semi-bluff portion of hero's turn betting range, making him fractionally more value-heavy if he changes nothing else, and I assume meaning that he has to bet a slightly tighter range (less value as well, in order to compensate). Also, it means that if hero does bet turn and gets called and the river completes a straight flush draw, then villain could in theory get ultra-aggressive because hero can never have a straight flush after he bets the turn. So I guess this would mean that hero would have to balance in some way and bet each straight flush combo a fraction of the time, in order to avoid this exploitative play from villain".

But n.b. this is just shallow speculation and I have not checked it with a solver etc.

Since you still dont see the irony. This you? Im blocking you now. Bye bye have a nice life.

Lol okay dude, whatever you like. Always Fondling has a history of trolling my posts; if he's going to act like an idiot then he's going to get treated like an idiot.

I'm honestly not surprised that you are reluctant to get involved in a debate on this, and can only assume it's because you know your arguments are weak - otherwise you could respond intelligently, and without the need (yet again) for strawmen and ad hominems.

Take care and enjoy yourself 🙂