It used to be this way. If I may make an analogy: Much like how I am not defined by my anger, yet I do exhibit anger from time to time; gto is not defined by balance, yet gto exhibits balance from time to time.

Balance is a byproduct of good poker; Good poker is not a byproduct of balance.

Including value hands and bluffs at 100% frequency may in fact make a hand or two in your opponent's range indifferent. However, true indifference means something else. When two equilibrium strategies face off against each other in a heads up situation on the flop or turn, for example, we will see many combinations within those ranges using a mixed strategy at different frequencies. This is precisely because the opposing equilibrium strategy makes those combinations indifferent; the ev will be identical whether the equilibrium strategy chooses to bet or check those combinations.

The fact that the opposing equilibrium strategy is constructed in such a way that these combinations are indifferent to a bet or a check is exactly why a mixed strategy is necessary. If the opposing strategy isn't an equilibrium strategy, then the equilibrium will cease to function; in this case those hands that were indifferent under the conditions of the equilibrium will now have a clear maximally exploitive choice, which will be a pure, unmixed strategy. This pure and maximally exploitive strategy will give a higher expected value than the equilibrium strategy both for individual hand combinations, and as a whole.

Is there such a thing as an unbalanced GTO strategy for a game of incomplete information?

I can think of games of complete information in which balance disappears, but that's because the value of deception is completely gone.

This reminds me a the "shania" conversations that date back to who knows when. (I think 2+2 still had wood paneling at the time.)

You're right here. Merely having a balanced range does not immediately equate to good poker. Otherwise, raising 72o UTG because you also raise AA UTG would always be considered good poker. But I will say that sometimes raising 72o sometimes in addition to raising AA is probably better poker than only raising AA.

The obvious questions that come up would be things like "Why 72o? Why not some other hand?" And this is where Fret's approach at least has the advantage of moving players into a new level of understanding of GTO poker. It's not GTO. As you've stated, nobody actually knows what that is. But it seems unnecessarily restrictive to deny that it's moving in that direction.

The idea of making categories for hands that create balance begins the process of understanding how range vs range works instead of thinking in terms of hand vs range. There's very little natural intuition for that sort of thinking, and without a systematic approach, there's no good way of moving forward.

This is also true, but it's also not new. But where does one even begin to think about calling with such-and-such a hand 30% of the time and raising 70% of the time? And with which hands? Again, Fret's approach creates a baseline to begin starting the process of thinking about it.

The bolded statement isn't true, unless by "cease to function" you mean "is no longer the most profitable." But that would have less to do with GTO strategies and more to do with implementing exploitative strategies.

GTO is its own thing. It is independent of what your opponent does. And GTO does not imply "mixed." When HU limit was solved a few years back, some people were surprised that AA was raised 100% of the time. Don't you need to mix it up sometimes? No. You don't. Rather than raising less frequently with AA for deception, it was determined to be better to just raise more hands!

Gto takes some actions at 100% frequency.

AA is limped a small fraction in huhu.

By function I meant that neither strategy is maximally exploiting the other, which they do at equilibrium.

I just got both of Phil N's books (great sale at the 2+2 bookstore). Doing a little bit of reading in those. For high level strat, I usually just pester AvoidThe9to5 or DonJuan or Rodeo.

Is that a "rounding error" in a bot that found near-perfect strategy hill climbing or is that an actual finding that even AA should be limped sometimes in a perfect strategy?

Not sure about the rounding error or perfect strategy, but Cepheus took a big pot from me by limping AA on the button. So I did the query the bot thingy and sure enough AA gets limped sometimes.

You have issues with convergence in anything that self-learns. Is limping AA 0.1% (you pick the number our of air) much different than not ever limping it? How big a sample do you need to never do X or Y vs. doing them at tiny frequencies?

It can be hard to divine intent in a machine that self-learns. They drew a circle around perfect and said "if our machine gets this close or closer, we'll call it perfect". It went and did whatever it did. The quality of play as judged by minimum regret was inside the circle. Machine is "perfect". However, you have the size of the circle to deal with in learning exact things. It could be that perfect poker is actually a bit simpler than looking at the stopping point of the bot, because it only got close enough. I guess it could also be much more complicated, again just got inside the circle. Does it know that spades are the best suit?

It makes it hard to say perfect strategy is never this while only looking at the frequencies of a robot. If someone has another way to say "you must limp AA sometimes if you have a limping strategy", that would be a different thing.

If I remember correctly, the bot also 4 bets T9s in position preflop some small fraction, but calls the 3 bet with everything else.

Well, I had to look it up.

http://poker.srv.ualberta.ca/preflop

AA-
Raise: 99.49%
Call: 0.51%

It was KK that was raised 100% of the time.

There's a smattering of 4-bet hands. None of them with frequency greater than 0.06%. (See "Bet, Raise" tab, which is "raise, 3!".)

A few things come to mind:

Gto is the strategy that maximally exploits gto.

Mixing vs gto is both necessary and maximally exploitive.

Mixing vs non gto strategies is non exploitive.

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I'm not sure where this leads the conversation, but those statements just came to mind.

I'm a little bit hesitant to go with this. I'm not sure how you're using the language.

GTO can't be exploited. If you play the best counter-strategy to GTO, you minimize your losses. If you do something differently, your losses go up (or at least stay the same). So I think saying that GTO maximally exploits GTO is a little bit fuzzy on the language.

It's unclear to me what "mixing vs GTO" actually means. Against GTO, you can't do any better. So mixing strategies doesn't help. Maybe you move around in the space of counter-strategies with equivalent expectation, but it's not clear how "maximal exploitation" occurs.

It's also unclear that mixed strategies against non-GTO is somehow not exploitative. When I think of exploitative strategies, I think of doing things specific to the errors that we see our opponents making, and we do these things knowing that we are opening ourselves up to being exploited ourselves. But using a mixing strategy can cause our opponents to extend their errors longer.

For example, if you thought your opponent was bluffing way too often, you could call down every single hand. But then your opponent might recognize this and bluff less frequently. So you might have a mixed strategy where you don't call down with A-high 100% of the time on similar boards, just so that your opponent will continue to think that he can get away with bluffing.

<3 flashback humor.
For sure. It's about as good as we can do within the confines of the English language to describe what happens when equilibrium strategies face off heads up.

Sorry for the poor wording. It should read "non maximally exploitive."

You may exploit a little bit with a mixed strategy vs a non equilibrium strategy, but this mixed strategy will not be max ev, thus it's not maximally exploitive.

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I don't like using Rock Paper Scissors as an analogy for poker, but the most simple example I can think of for exploiting a non equilibrium strategy is a RPS example:

My opponent throws 60% rock, 30% paper, and 10% scissors. My maximally exploitive strategy will be to throw paper 100% of the time. Any other strategy will not be as exploitive. Of course this opens us up to counter exploitation, which is why it's important to exploit exclusively on the margins in real games.

I think it is helpful to use the word "adaptive" to talk about strategies that are changing. It's different from "fixed" and "mixed" (which could also be called "non-probabilistic" and "probabilistic").

The alternative is "meta-game strategies" for "adaptive" but that's even worse.

Got it. I agree with this.

Here's where I think the extra language is helpful. It's not maximally exploitative against non-adaptive strategies. But if your opponent adapts, you can have a better long-term expectation by playing a mixed strategy because it can prevent them from adapting to a better strategy.

I like "highly explosive love poker" which is the best autocorrect ever in these forums imo. I also like to think of exploitive adaptations as "strikes." There are soft targets and hard targets. In no limit holdem, the room for error on your hard targets is quite small, relatively; you can lose your whole stack to an exploitive strike. In limit holdem, the room for error on your hard targets is much larger; the effect of exploitive strikes is more limited. We were talking about this the other day in the theory forum and came to an agreement about the difference between river exploitation and the play of the earlier streets. Here's a clip:



Back on topic from Aaron:
This is what gtorangebuilder does. It finds the two near maximally exploitive strategies for a given set of ranges and predetermined betsizes. The strategies are not max ev though, unless they face each other. The guy that wrote the program hangs out in the theory forum from time to time.

Also, the bold brings up the topic of leveling wars, which I try to avoid in general. Of course there are special situations where I'll go into the exploitive deep end. I once won a ~40 big bet pot with just AA unimproved vs a maniac; more than 3/4 of the money went in on the big streets. He had TT. Besides the exceptions, I just think about maximizing my ev in this spot on this street in this hand vs this opponent. Sometimes I run into nits that lol calldown with quads three ways and doesn't even raise the river?! Sometimes I run into maniacs that would've gone many bets with an inferior hand. Most of the time, my opponent's play at least follows the law of subjective rationality. The game makes sense to them in their mind; they 10 bet TT unimproved on the turn because it's an overpair. That's a good enough reason for some people.

Ok I'll stop rambling now. Your post really got me thinking so I went with it. I'm glad we're not quitters.

You could get into minimally exploitative play. There's a video on GTO range builder about the idea.

when i watch replays of big tournaments (like WSOP) i often see people raise garbage like 10-4o (not even suited) from time to time. For example in bvb situation they 3bet on BB. I think the main idea: hands like 76s playable and 10-4 is not...and it's great (fun?) to steal pot with a "dead" hand.
Maybe it works because they do it once a day.

There are some NL concepts of guys only being able to call or re-raise monsters. You're making moves with hands with little equity because you're snap folding to further action? Still, seems like you'd take better hands out of your folding range than T4o as choices for bluffing. Could also be soul-reading live players, where they at least think that the guy won't ever call and they don't care about their own hand. You have sample bias for what they show on TV with the fact that most live MTT players are horrible at poker. There's a tiny chance it was expert, but doubtful.

I would x/c flop with the intention of x/c'ing down unless I improved.

I've been deep down the bluffing range construction rabbit hole. Here are some relevant links; I haven't been living up to my reputation of the most self referential poster around so here are some clips and links:

http://forumserver.twoplustwo.com/33...dem+discussion

http://forumserver.twoplustwo.com/15...14/?highlight=

http://forumserver.twoplustwo.com/15...46/?highlight=

http://forumserver.twoplustwo.com/15...00/?highlight=

http://forumserver.twoplustwo.com/53...minds-1516480/

In conclusion: Now, I'm thoroughly convinced that our opponent's potential non optimal strategies perform worse vs my strategy that maximizes draw equity when called than the non optimal strategies perform vs other, potentially equilibrium, strategies that build bluffing ranges in other ways. For example, you could build a profitable strategy that includes bluffing the T4o preflop, but this strategy will perform poorly compared with the strategy that builds a bluffing range with the best draws at high frequency and the worst draws at low frequency.

Oh good morning.