I was mostly just creating an example of where GTO doesn't care enough about board coverage anyways. But as it turns out there are no Ax that check back 11bb vs a limp either :P They all ISO (though not always all-in--a couple NAI sizes are used by some of them too).

He can't exploit us by definition since we are x/r a near-GTO range :P All he can do is defend all hands that are better defended then folded and 3b all hands that are better 3b then flatted or folded. He can use GTO frequencies with indifferent hands if he's worried about us changing from a near GTO x/r range to some other range.
GTO is a well-defined mathematical concept. It is often also called Nash equilibrium. It is defined by a a set of strategies, one for each player, such that if all players use their GTO strategy then if any individual player changes their strategy their EV cannot increase. In HU zero-sum play it reduces to the minimax solution which ends up being stronger because if both players play GTO then deviations from GTO by one player cannot lower the other player's EV (in multiplayer games a unilateral deviation cannot increase that player's EV, but it can sometimes decrease the EV of another player in the game). The mathematician John Nash proved that every finite game that allows mixing has at least one Nash Equilibrium solution. Do some wikipedia reading :P

In any case it's not a computer program, or a set of EVs (though you can think of it as being equipped with EVs since the strategy set also generates GTO EVs for each player)--it's a strategy for each player. You can compute this strategy using computer programs, but a strategy is also a well-defined mathematical object--it's as a decision rule for each node in the game.

As for its relation to balance, most players use "balanced" as "near-GTO". It's usually used in reference to betting ranges, and is sometimes used to to describe some restricted part of near-GTO--for example you could claim a range is balanced vs 3b AI, but not balanced vs 3b NAI which is the same as saying it's GTO when your opponent is restricted from being able to 3b NAI. Mostly people use it in the case of polar ranges to identify the concept of betting value hands together with air hands in a specific ratio. However, it's not a very precise term which many people use differently (for example your view of "balance" is clearly very far from the unexploitable/GTO view and so is very non-standard and created a ton of confusion in this forum) which is why I don't like it. It's not the concept, but the lack of clarity.

But as far as I can tell the general unifying concept of the poker community's view on balance is almost always based on the concept of being "unexploitable" in some way, while an unbalanced range is "exploitable". Unexploitable is supposed to mean that no matter what your opponent does your strategy behaves "well". But all these terms are also undefined! Instead unexploitable in HU translates well in my mind to "no matter what villain does, if I play this strategy I am guaranteed a certain amount of EV, and there is no strategy that guarantees even more EV then this one" which is equivalent to the Nash condition for two players--ie to me an unexploitable strategy is exactly the same as GTO.

GTO is the mathematical solution concept that captures the concept of exploitability, and the concepts you mention about regulating frequencies and mixing actions, as specific strategies that satisfy the Nash condition of no increases with unilateral deviation (or maximum EV guarantee), so really balanced should equal unexploitable which should equal GTO and suddenly everything is defined precisely since it relates to the mathematical GTO definition. This equality is generally the accepted definition of balance and unexploitable nowadays.

So yeah, GTO certainly has an accepted definition, so you should be careful using very specific terminology like GTO and balance without knowing the accepted meaning. Maybe invent some new term for what you mean by balance (Range awareness?) and define it precisely. I think this is what Kobmish was reacting to when he said you were misleading others since you were using accepted terms in completely different ways, which can create a lot of confusion and statements that become false to others who are using accepted definitions.

Coffeeyay writing Will Tipton's third book with all these long strat posts

Flying today and then the all-star break is over so back to the MLB betting grind but before I stop posting I want to clarify how GTO relates to 3-betting. If GTO is just a collection of EV from each hand, and each hand stands alone would what would be the incentive to 3-bet non-monsters? The obvious answer is that if you only 3-bet big hands then they can just safely fold to most of your 3-bets, but that would make the small hands "loss leaders" which you say is never in GTO. By 3-betting 84s and AA I expect to make my AA a lot more profitable long term because they can't just fold confidently, but I wouldn't expect to show a profit from the 84s.

Well, thank you. I am not sure which of the several meanings of this phrase you refer to, since I am not a native speaker. It was never my intention to post more than 1-liner as a strategy on 2p2. I do my best though the 1-liner to be correct in terms of do or do not do this.

Else when someone is clearly completely ignorant, but gives advice as though he has God on a direct line, I may indeed talk out of my ass, again whatever meaning you put into this.

I mean, you wrote this guy half a book and his answer is still pretty much "balance though".

Also as a very small example that pretty much everything he says is horribly wrong - he advocates to check call entire range (or almost entire) vs aggressive opponent. I am sure you know, but the correct adjustment to that is often to check raise your entire range (depending on a few factors of course, again won't go into detail). Let alone that he calls his groundbreaking strategy of calling entire range balance, which you tried to explain him with half novel that is wrong.

Btw report me, Jimmy will be happy to ban me, I am sure.

U mad bro?

This after Mark Twain brings your intellectual level down, I am afraid. It's a solid argument though, can't argue with that.

You told me you can tell what's bad from your "6th sense". If you don't want to contribute anything that's fine but there is no need to engage with you like a real person if you don't post anything that could actually be of interest

Sounds like you're still missing it. GTO is a fixed, always the same, strategy. Each strategic choice is choosen because it has the highest EV. GTO 3-bet bluffs because the EV of 3-bet bluffing is equal to or better than other options for that hand. The incentive is always the same--max EV given that villain is playing GTO. The reason for EV of 3betting being equal to or better than folding/flatting is because a GTO villain folds just enough and 4b just little enough to make it the EVs come out that way.

I'd strongly recommend learning more about GTO because right now you have a lot of misconceptions and are displaying flawed thinking as a result. Will Tipton's books, Expert No Limit Hold'em, are a great resource to help you to understand GTO (ie balance) a lot more precisely

Working on my HU guide vid-pack which is kind of like Tipton's 3rd book so a lot of this stuff is fresh in my head

Thank you, that actually clicked a lot better for me. The fold % the villain plays factors in what else you are 3 betting with, so it is connected to what else you are 3 betting but the hand can still stand alone as +EV. When the grind of betting MLB ends I will definitely read that book. I really appreciate your willingness to share some great info with me and the community.

Glad I could help clear up some of the confusion

Me too . I was thinking about it too much as 3 betting low hands to set up big hands, but course by 3 betting big hands it also sets up the bluffs.

I didn't make my point clearly but this is actually what I was getting at when I said thought of it like a computer program where your opponent can see the code.

What I was not understanding was that in doing that it's actually maxing the EV of each hand and not having loss leaders to set-up other hands. As a result I am sure I have been over-using certain concepts such as board coverage.

I'd rather iso or shove him preflop if he has tendency of over-limping, rather than check/raising this exact flop. I would never x/r this flop, not even when eff stacks are deeper. Just try not to make much of plays like this one, x/r only top pairs for value or some strong flushes/draws.

This hand plays way too good post to iso shove it pre imo. If you never x/r such hands on these dry flops that players tend to overcbet on, you're letting villain exploit you.

I've said iso OR shove, not iso shove. That's true but if player limps too often and u don't iso him with such hands he's also exploiting you.