I took some years off of the game because, yeah... life stuff. Anyway, I've come back to a world where AI touches everything. I mean, I've always had HUDs, solvers, and Nash; but now it feels like the AI landscape has changed enough(DeepMind/AlphaGo/etc,) that people are looking up to computers, and trying to reverse engineer the way the machine thinks. I'm worried that extending this courtesy to poker is not completely, but largely unfounded. Sorry, I digress.

We were always hunting for equilibrium back in the day, so the concept of GTO is a completely understandable evolution from that, but there is great concern about GTO never taking into account how many games are actually going on within the confines of one table. Supposing the primary, umbrella game is to win the most money-- Say, for example, there is a whale at the table that you wish to target: perhaps you are in the pot with a good player, who you want to minimize loss/variance against, and the hand comes up in such a way that a conservative line is most optimal for the "game" of that one hand vs. the reg, but what if by showing down a stronger hand on a passive line, you cost yourself money against a whale who now will give you far less action? Possibly now you will have to sacrifice some optimization and show a bluff or be aggro in a different hand to regain GTO of the larger, umbrella game of extracting the most money you can from the whale.

so you have all these games running at each table:
hero image vs. each individual x 5 (lets just call it 6max for ease)
hero image vs. table as a whole
hero image vs. community as a whole

Plus maybe a few more just for the sake of leveling or networking, and these games are all layered over and intertwined like a cloud, and competing with each other for priority, and often it will be required of us to sacrifice optimization in one to gain it in another. I've accepted GTO as an abstract concept like happiness, that we can never crystallize, only indefinitely pursue.

I tried to sort this myself on wiki, but it seems mostly over my head. So, again I'm sorry for the digression, but here is my question:

I've been wondering where the science stands(or just what are peoples' personal experiences) on looking at GTO from the top down(big picture meta is static, takes priority, individual hands serve as pawns,) or bottom up(meta completely dynamic, constantly adjusts to minutiae.) Yes, I'm sure that obviously to some degree they will always react to each other, in some sort of reflexive, ying-yang situation, but can't seem to find any commentary toward a mathematical representation of this, not to mention how to predict other GTO players' adjustments, and preempting them. Does this material exist anywhere?

The science is almost entirely focused on AI and poker is just the ‘playpen’ that computer scientists use to test the AI.

Way back in the 1950’s the best mathematicians recognized the future of the science was computers, not to mention the good paying jobs therein.

Computer scientists will make more money and have a lasting legacy of accomplishment that far exceeds the world of poker. This leaves us poker players out in the cold, looking in the laboratory window trying to catch a glimpse of true GTO.

The material you are seeking is not written, because the potential authors are not interested in writing it, and the potential audience to read it is very very tiny.

As for the answer to your last paragraph, my personal opinion is the top down static GTO. The whales and regs will either have the correct ranges or not, and will profit or lose accordingly. This opinion is debated here in the theory forum from time to time. If you would like some math analysis to support my position, a specific hypothetical hand with ranges and bet sizing will be required, imo.

I have made several post on this topic that might be helpful to you.

I don’t think you’re understanding what GTO is. GTO does not consider Metagame concepts like image at all.

Oof, that's too bad. Thanks for the comprehensive reply.

TY, I found the simulation/gto/ai and hints for a returning player threads very interesting.

Oh yes, I most definitely think that I do not. In this case, image refers to my set of ranges, for purposes determining what actions would be optimal for villains. Not sure if that helps.

I think the first thing to consider is that although the "O" in GTO stands for "optimal", it does not mean "optimal" in the most common usage of the word. It does not really mean "the best thing to do"

GTO means "unexploitable" - it means you're playing the Nash Equilibrium. Unless your opponent is ALSO playing GTO, it is not usually the line that will make you the most money. You could make more money by exploiting the player. But exploitative deviations from GTO are, by definition, no longer GTO.

Which is fine. You don't want to play GTO against someone who is exploitable, unless you are also worried about being exploited.

Solid op, nice replies. Thread has potential.

I tried to draw a line in the sand between the difference between Nash Equilibrium and gto here in the theory forum. There were mixed replies. Here's what I took away from it:

Until someone deviates from Nash equilibrium, there is no difference between gto and Nash.

Once someone deviates from Nash equilibrium, there is a difference between gto and Nash. While Nash is unexploitable, it is not necessarily maximally exploitive vs the opponent's best counter strategy going forward after the deviation. Gto, however, is necessarily maximally exploitive vs the opponent's best counter strategy going forward after the deviation.

Correct Rusty, but there are exceptions I think: for example if I'm on the button vs a very tight small blind and an expert big blind, I'm still going to raise some extra hands to exploit the small blind despite the threat of counter exploitation from the big blind in the form of less folding and more 3 betting. I'm going to attempt to play solid poker vs the big blind, considering my adapted range and how the expert should play vs me. I think that in this case the most profitable line isn't Nash, but it's a sort of post deviation gto vs gto battle.

There's a Rounder's reference in there somewhere "you see all the angles; you just don't have the stones to play em."

I think you're better off choosing another term. I think it's a really interesting course of discussion, way more so than finding actual GTO lines. Understanding GTO to me seems like a good way to recognize imbalance, but the point of recognizing it is to exploit it. I think possibly you can also use it to find lines that exploit, while minimizing their own exploitability.

As Sun Tzu said, fight the enemy where they are not. Gto can show you where opponents are being exploitable and you can fight them there.

Is there a nicer way to talk about "maximally exploitative counterstrategies?" Is there a term for talking about optimizing our meta-strategy the way OP is talking about? Maybe we should come up with the terms ourselves.

A Bayesian Nash Equilibrium is a strategy pair that is informed by the frequency of an opponents strategy over sequences of opportunity to alter strategy. This requires a number of observations to be statistically significant.

Curious what you mean by "nicer" here?

Maybe you find this intersting

https://www.youtube.com/watch?v=2dX0lwaQRX0
Its about AI that first beat humans and GTO.
As others said GTO just makes up unexploitable.It wins vs every player but there is strategy that can make more EV vs non-optimal opponent.

I assume he means something shorter that rolls off the tongue/keyboard better

ggto: gambit game theory optimal

there's an important difference between gambit game theory optimal and unnecessary unexploitability, the latter of which is what happens when we make unprofitable calls with bluffcatchers and the weaker draws vs players that don't bluff as much as they should,* for example, or if we make unprofitable bluffs with low equity hands** vs players that don't fold as much as they should, etc.

*I have a particularly hard time vs those players that err on the tight side preflop because of this effect. I win more than my fair share of free showdowns, which supposedly counteracts the loss, but if they let me off cheaply on the flop and turn, I often find myself facing a range that is both tight and properly polarized, or tight and just slightly value heavy range. This is a tough spot for bluffcatchers on the river.

**high equity draws will be profitable as bets up to certain betsizes, no matter the opponent's calling frequency, depending on the strength of the draw, which will depend on the strength of the ranges in question.

this

GTO is a purely mathematical description and does not need the players to be defined