I can't think of a way at the moment to prove that this can't be the case. I haven't given it much thought. However, one definition of a GTO strategy pair (or Nash Equillibrium) is two strategies such that no player has an incentive to change, i.e., no player can unilaterally gain EV in any way.

Example,

SB opens to 3bb

BB 3-bets to 9bb

If we fold more than 2/3 of the time, BB can profitably 3-bet any two cards.

I think it is very reasonable to assume that if both players were playing perfectly, the correct play for BB would be to fold 72o. If 3-betting 72o becomes +EV for BB, then he obviously has an incentive to deviate from GTO and therefore SB's strategy can't be GTO.

I think this proves that folding more than 2/3 of the time in this scenario with these bet sizings, cannot be GTO.

P.S. Sorry if I'm butchering some of the terminology/definitions. Regardless, I think the basic logic holds.

what if GTO strategy for player IP is so much ahead, so the GTO for OOP player is to fold most of his hands? if he defend more so he can't be exploited by any two(or thats what we think) he would actually lose more.
i don't say this is true, or that you are wrong.
we just can't know what would real GTO model looked like.

We don't need to consider this possibility. I'll try to word it differently...

-Assume that BB is playing GTO (whatever that may be), and SB is playing an unknown strategy which may or may not be GTO.

-I assume that the GTO play for BB with 32o facing a 3bb open, is to fold.

-We know that if BB ever has an incentive to deviate from GTO, SB's strategy cannot be GTO

-If SB starts folding more than 2/3 of his opening range to a 9bb 3-bet, BB has an incentive to start 3-betting 32o because this now becomes +EV which is better than the 0 EV achieved by folding

-Therefore, a strategy that includes folding more than 2/3 of the time to a 9bb 3-bet after opening to 3bb, cannot be GTO.

You are most likely correct that 27o isn't in the GTO defend range BB vs SB. However, here are some points:

1) Because of position, folding 27o is only slightly better in EV than 3betting against an optimal opponent (my estimation- just as you have estimated preflop pseudo optimal strategy).

2) Because of blocker effects, when facing SB open and we 3bet 27o, we would get a bit less than 68% folds from SB (SB's folding range has a LOT of 2x and many 7x)- so although it's probably true that the theoretical value of defending % in the SB should be below 66% against 27o, snowie could be at worst be folding 2-3 hands incorrectly which would amount to a pretty small mistake preflop (or maybe get some frequencies wrong on borderline hands). This only seems huge since you can recognise it as a human using "trickery".

3) The "edge" you gain here from being able to play 27o profitably rather than fold is no where near as big as the edge you gain from forcing villain to only bet halfpot, pot and 2x pot postflop (since mistakes postflop happen every hand in every situation, and are compounded over multiple streets). Also indeed even if we assuming that snowie plays the game from this restriction perfectly (obv this is no where near true), it's possible that with this handicap BB can indeed 3bet atc profitably.

Also snowie is not GTO, and nor do/should they claim otherwise, even for their abstraction of the game into specific betsizes.

assume SB defend 1/3 so BB can't 3bet 32o and show Immediate Profit.
than that range because it's too wide and OOP get crushed by value part of bb's 3beting range so hard that leting BB 3bet any two is actually less costly.

again i don't claim this is the case, just consider it as possibility in some spots.

You need to prove this. What if gto includes not folding anything in the bb to a 3x open? I'm not saying it does I'm saying that's where the logic flaw in your post is. Obviously if you can prove that then the rest of your post does follow logically.

Yeah, the whole thing kind of hinges on this assumption. Obviously I cannot flat out prove this is true mathematically. However, I thought most people shouldn't have a problem accepting it, as virtually every single good player will have a folding range from the BB vs. a 3x SB open when SB is decent.

I think it's easy to imagine how a basic tight/aggressive strategy from the SB could exploit a no-fold strategy from the BB. I mean, his range is going to be so weak and wide (obv as weak as it gets) and he will be forced to call down with a lot of weak hands.

Yeah this is just a bunch of baseless statements. What if SB minraises preflop, what if SB 2.5x and what about 2.9x? What's so special about 3xing at 100bb deep (or whatever stackdepth it was) that means BB can't defend atc profitably?

4 years ago many winning regs defended less than 50% vs a minraise HU. So virtually every single good player back them would have been making huge mistakes.

Hi guys, lmk if i am missing something, but if BB 3betting over sb because sb fold 2/3 times to 3bet can't be GTO cus GTO player would never adjust and is not exploitable (100% def bb obv can be exploited)?

There is nothing special about a 3x open. That is just the sizing I use in my example. It also happens to be the most common SB open sizing.

Where is the cutoff for when BB can no longer profitably defend 100%? Can BB even defend 100% vs. a min-raise? I don't know, and I haven't claimed to know or even guessed at where this cutoff is. I am just guessing that he can't do it at 3x.

I think your point here is that just because good players do something doesn't mean it's correct. Let me respond.

1)In this HU situation, it's not so clear to me that defending less than 50% is a mistake. Yes, it lets BTN autoprofit, but since he has a positional advantage, he may be entitled to autoprofit. I don't play HU so I don't know what a common defense frequency vs a minraise is nowadays. Either way, this scenario is certainly less clear than 72o vs a 3x SB open.

2)Theory has advanced a lot in the past 4 years. And as time goes on, players are playing more and more balanced and closer to GTO. Therefore, what winning players are doing today is more likely to be correct than what players were doing 4 years ago.

3)When virtually every single winning player (not "many" or "most" or "80%" but practically every single winning player) does the same thing in a particular situation (e.g., fold 72o vs a 3x SB open), then I think it is very likely for this to be correct. Just like it is very likely that open raising AA UTG (as opposed to limping) is correct.

4)I'll elaborate on my last point in my previous post. Think about the consequences of defending 100% of your range from the BB vs a 3x open. As part of a GTO strategy, you cannot allow villain to profitably tripple barrel with his entire range on average. Therefore, you have to call down with a certain percentage of your range on average. And since your preflop range is so weak, you're going to have to call down with a lot of bad hands, which, I would imagine could easily be exploited by a standard value-oriented strategy. I mean, you're basically just a calling station.

OK I'm not sure how much serious hu poker you have played or followed. But defending less than 50% oop vs a minraise is a pretty huge blunder (since it happens every other hand). Also BB can defend 100% profitably vs SB minraise 100bb deep if he is IP for sure. Just to put it into perspective, many top players (if we are talking about highstakes then it's "virtually all") defend close to 90% vs button minraise OOP (e.g. even like 2 years ago sauce defended 92% vs 100% button open), and most people defend > 60% vs button 3x.

I never argued for it being GTO, but defending 72o is closer to actual GTO in EV than you think, and I would not be surprised at all if it's +EV or 0EV to do so in GTO (e.g. we 3bet some % of 72o, 32o, 62o 93o etc). Defending >50% vs button minraise is much clearer to be GTO than folding 72o vs 3x bvb not the other way round.

The statement "you cannot allow your opponent to profitably triple barrel on average" is a variation of "it works 60% of the time every time". Basically all you are saying is- his range feels too weak, so it must be too weak, so it must be exploitable to barrels etc without any way of knowing.

Finally, autoprofit is a useless tool for GTO unless it's the river. The reason being you only consider the difference between betting and open folding. And there is no hand in poker where the EV of checking is zero postflop before the river. I agree that it can't be GTO for villain to profit whilst triple barreling his entire range, but I don't see why defending 100% preflop would allow SB to do so.

Anyway like I said in my first post- GTO or not, 3betting 72o vs a SB open cannot be a big mistake.

oh boy

I guess it mut be reminded for some that the BB calling the raise does not expect to gain money for the call to be ev+. She just expect to lose less than 1.0 bb.
This said, I think that for 20bb deep it can be shown through simulation that it is a mistake to call a 3bb raise with 72o, I'm not sure about 3betting it, a non zero percentage of time.

i just played around with the free trial and it seems like snowie doesn't approve of sb limping strategy. isnt snowie supposed to learn from the hands that its users import, so when it sees that it's viable it'll stop telling me to not limp?

Snowie DOES limp the SB sometimes, in 6-max at least. It's done this since the AI got updated about a month ago.

If it marked your limps as errors, it's probably because you picked the "wrong" hands to do it with, or you're playing HU 100bb deep, a format in which Snowie doesn't limp.

FWIW, I think Snowie needs to do more training of its limping strategy, because there are some contradictions in its limp-calling/limp-folding/limp-reraising strat.

As I understand it, it doesn't learn from imported hands. It mostly learns by playing versions of itself.

It learns by playing against other opponents not by playing itself, though it also would play itself.

In fact the opponents are trying to come up with exploitative strategies which snowie learns to defend against which should result in gto when all possible strats have been learned.

Obv it has not been trainings against everything.

Apparently, it's a work in progress.

I read a newsletter recently (subscribed a long time ago but didn't pay for the long term)... it made an update to a rather terrible mistake in which it folded AK in a situation that can't fold against a person who is shoving correctly.

I'm not sure it's 100% but it's probably getting better, making these updates as it goes.

It's got to be able to adjust to limps even if limping isn't optimal. If it plays badly against limps, then it's still not perfect.

It would probably do better playing versions of itself than it would other players. I don't agree with matching it up against humans since humans are naturally not good at this sort of thing.

By teaching it how to play against "exploitative" players, aren't you just teaching it a million different ways to play badly?

I don't know, makes no sense to me. I wouldn't trust the program completely if it's learning from bad players. Seems weird.

Why is everyone so hell bent on proving the software wrong? All the great poker minds should come together and solve it once and for all, and charge up the butt for the software is what I say, rustybrooks u mad bro?

Gto is about finding a strategy that is profitable against any and all other strategies, including bad ones.

The concerns about an optimal bot killing holdem are very interesting. As some say, it may well be inevitable.

There are already some microstakes games that a basic bot can beat. Sealswithclubs, for example, you can just play tight and overbet the nuts and get paid off plenty. I could imagine a bot could easily win a BI per session on SWC .02-.04 simply by waiting for AA and sets.

But LIVE poker, may have a different fate than chess/backgammon due to luck/variance/tilt/psychology, no? Especially tournaments with fast blind levels where even optimal play might only get your money in at less than 2 to 1. Really fun, still +EV for pros and amateurs still have a chance. I don't see those dying off from bots. But I might be naive.

Is this a good software if I want to deepen my gto play for specific situatuions?
I have developed a close to gto style in basic scenarios (like preflop standard situations, cbets, defend v cbet..etc) mostly using Janda's materials.
Will pokersnowie help me in more non-standard things like play vs 3bettors who cbet than cr on turn, or srp vs cbet-cbet-cr...etc ? Or will it draw my attention to things like if I go to the river with a gto checkcall range but I still lose vs his range in the long run ,its because my preflop range is weaker?

thanks

@Tschinga-Tschanga You should download the free trial and give it a whirl, but you sound to me like the sort of person that would find the software very beneficial, or at least "interesting".
FWIW, I got into it around the same time as reading and viewing Janda's stuff, and was actually pretty surprised at how Snowie contradicted a fair bit of what Janda said. That just made me more intrigued by the whole idea of GTO poker.

Since Snowie doesn't "explain" why it chooses certain ranges or frequencies (it just chooses the most +EV option based on its database), it can be quite tough to use as a learning tool, but it can be very rewarding if you study its ranges carefully and think about them while studying other "GTO-style" players/coaches.
Unfortunately, Snowie isn't "programmable" (by which I mean you can't tell it to play like a typical aggro reg at your limit, in order to find out the best ways to beat such a player) but it does a pretty good analysis of your hand histories, which should help you spot tendencies in your play (such as a lack of balance in 3-bet pots, or too much/not enough river betting). You can set up scenarios like you described, but it will still only recommend actions based on "Snowie ranges", not the actual ranges played by specific exploitable villains. For that, you might prefer to try GTOrangebuilder, as I think that allows that sort of customization.

Like I said, give it a try to see how it works out.

Thanks for your detalied answer.
Unfortunatly I cant try the trial version because they dont send out any emails.