When I learned about GTO I quickly jumped to the conclusion that it isn't concerned with its opponent's strategy - the only things that matter to it are positions and the price being layed. However in another thread some knowledgable posters showed me that defending optimally in spots does require assumptions about opponent's range: that MDF is calculated only from the part of your range that can bluffcatch (and to know that you obviously need to know what your opponent's bluffs look like).

So it seems possible that the process of finding GTO is not an isolated one where you are concerned with your own holdings only; it is one where you search for optimality for your position and your opponent's, and then balance one range against the other until you reach Nash. For example I can safely assume that my opponent has AA in his preflop 3bet range, because if he doesn't then he is losing enough money to me anyway, and I won't be exploitable by such a deviation.

By definition it would not be making any assumptions about the opponent's range. A nash equilibrium would be reached in the situation in which the both players have no incentive to adjust their strategy--neither player can increase their EV by doing something else.

When people use solvers to identify a nash equilibrium and input constraints such as ranges/sizings/flops/etc. it's essentially done to limit the size of the game tree such that is solvable. Specifically, if you were to solve for nash in a heads up game including all preflop and all sizings and all stack depths etc. the game tree would be more or less infinite. By adding in various constraints you make it possible to solve. In the real "GTO" sim with all possibilities being allowed then any deviation by our opponent should result in hero having equal to or greater than the EV of nash. Hero's EV can only remain the same or increase.

Multiway games/situations are a bit different, though, and aren't necessarily as clean of an answer.

Nash Equilibrium doesn't care about Villains range in the sense that it's a static strategy that shouldn't be affected by shifts in villains own strategy.
It does care about a Nash opponents range when calculating itself, as every action must be >= 0EV vs that opponent

Well I do understand that the GTO strategy in on itself just is and doesn't make assumptions, was just wondering about how I can attempt to find it.

So would I be right in saying that once Nash is reached you are playing GTO? Because according to their definitions, Nash Equilibrium and GTO sound like the same thing, but I also have a feeling that there's a difference.

Yup, this was basically my question. So this is the standard way to approach situations in a GTO way, good to know.

Not the first time I'm hearing this, can you expand a bit? I watched a Triton Poker interview with Trueteller and Rui Cao, and Trueteller said that Nash equilibrium doesn't exist multiway (but Rui Cao disagreed), is this related to your point?

Yeah this is basically what I was asking. The word equilibrium of course infers a balancing act between two things, I simply thought that maybe GTO and Nash were slightly differing things.

This is something that really interests me: does every action really have to be +EV on its own? What I mean is if I have value hands, I can include bluffs to balance them out. But if every hand is plus EV, then am I balancing out so much or just stuffing a range with overall good holdings? I had the impression some actions will be -EV on their own but +EV for your entire strategy.

This is a quite common misconception and I thought that for a long time as well, but GTO never sacrifices EV in a specific area to gain EV in another one. It always tries to maximize EV with every single combo in every single situation.

Really good to know.

But can one know, without a solver, which bluff is >=0EV and which is -EV? It's easy to intuit which bluffs are better than the other bluffs (because of blockers, unblockers, etc.), but it seems difficult to know if they are +EV in the first place.

And another super important question: shouldn't the EV of your bluffs be directly related to the amount of bluffs in your range? For example you arrive at a spot where your range has a bunch of bluffing candidates that are pretty much identical (none of them are blocking anything for example). So if they are all close in EV, and you end up bluffing them all, surely that overall will result in a minus EV strategy since you're overbluffing?

Then you should stop caring about GTO/Nash Equilibrium for a while until you've nailed down EV

The easiest way to intuit NE is to Imagine you were forced to use a completely fixed strategy. Your opponent knows your strategy exactly and is allowed to adjust to exploit it. The optimal fixed strategy will be GTO. So it's not concerned with the villain's exact range, rather it's concerned with their "potential" range.

Very nice, I'll try it

In a practical sense, I don’t think it’s really a misconception. Imagine a player playing against a GTO bot, and specifically playing against a specific hand in the bot’s range rather than the range as a whole, as if that single hand were the entire range. For example, maybe this player plays a strategy as if they’re playing solely against a hand that bluffs often, and they “exploit” that by being a station and calling all the time. Then that bluff will lose EV for GTO bot, but that will be made up by the value part of the GTO bot’s range, which will gain EV against a station.

This is, in fact, how bad players tend to play, who say things like “I put you on Ace King” or “I put you on a missed flush draw.”

The GTO bot only maximizes EV of every hand when playing against other GTO players, not against non-perfect players.

This is the problem with playing your hand in a vacuum. It's very easy to be profitable against one part of a GTO strategy, at the expense of losing more money against the rest of the strategy.

If the fish calls too wide they will over-profit against GTO's bluffs, and lose more money against the rest of the strategy. If they call anything that isn't at least a mixed call in NE, then they will lose money overall.