Poker solvers aren't the end all be all in poker. Reminds me of the zone defense in the NBA

But the equilibrium is computed given assumed hand ranges (perfect information). When those ranges change, doesn't the equilibrium and the strategies defined by it change too? For example, let's assume the solver picks a bluff combination on the river partly because it blocks some of the opponents value range. What if that value range isn't even in the opponents hand range (it pure folds pre)? Isn't the solver then making an error?

Yes, it is only an equilibrium under the given assumptions (ranges/bet sizing). This is referred to as unsafe subgame solving. There has been some work on safe subgame solving but it turned out to not really be necessary. It turns out to be quite difficult to exploit unsafe subgame solving if the root of the subgame is at the start of a round.

Yes, the maximum EV strategy will change. But that doesn't mean that the equilibrium strat becomes -EV. Thats why I say it depends on how you define mistake.

Only in the sense that if the solver knew that villain couldn't have specific value hands, it may bluff more often and value bet other hands more aggressively and for larger sizes, with would increase its EV. But the solver is still going to be balanced with bluffs/value and put villain in an indifferent spot. Its going to make a 0EV bluff at worst, not a -EV one.

So this is more what I mean. In the first photo, we've computed an equilibrium using an assumed 3bet range from our opponent and the solver tells us to do this facing a 1/3 pot cbet:

Now just imagine that our assumptions about our opponent are wrong, and his 3bet range is not that but more looks like this:

We re-compute the equilibrium for his actual range while keeping ours fixed and this is our new response to a 1/3 cbet:

We can see in this second image that our response differs significantly based on our changed assumptions. Not only is our ev lower across the board, there are quite a few hands that originally mix in the first equilibrium that now pure fold. A pure mistake in this case would be to take an action the solver never suggests. If the action had the same ev as folding, the solver would mix, and because the solver doesn't mix on these combos we can safely conclude that taking the original raise/call mixed actions are not 0ev, but -ev instead (JJ,TT,77-22, etc). This is what I mean by assumptions being wrong messing with the whole model. Different equilibriums will be generated from different assumptions (including preflop ranges), so I don't see how playing like a GTObot can't result in -ev decisions when our assumptions are wrong, at least sometimes or on some combinations. I'm open to being proven wrong of course.

Ok I see what you are saying. Maybe specific nodes of the game tree can become -EV, but the entire strategy (sum of all nodes) will still be 0EV at worst.

now how does villain's strat change effect other parts of the game tree. I would imagine that if you are getting 3bet less, then the hands that you do play become higher EV pf, and the EV of the IP player in single raised pots will increase as well.

Oh for sure well if villain's moving 8% of his 'should 3bets' into his call range or not defending wide enough as well, then we either make more money IP vs. a wider calling range or steal his blinds more often, which makes up for our reduced ev in 3bet pots. 100% with you

Thank you for this I have never heard of it and will look into it.

the EV loss from the player not 4 betting everytime they have the pure 4bet hands is going to essentially be larger than the mistakes the solver made on subsequent streets

but yes naturally a solver will punt money in some later part of the game tree if earlier part of the game trees assumptions are off, if it never did it would mean its exploiting perfectly every opponent

Yep.

GTO is a wonderful tool to teach equilibrium strategies. Every serious player should understand it. It is very powerful tool and if a player understands WHY a particular play is made by GTO it helps them become a better poker player.

However if you are playing in a game where you are not considering exploitative strategies that deviate from basic GTO at least 50% of the time when you have real decisions them you suck at game selection.

Poker is and will always be an exploitative game. If a player is not thinking in exploitative terms, they are either at the wrong table or they are playing wrong.

this part is a little shortsighted, you can be playing at 6max table with 4 excellent players and 1 mega whale and you will want to play the least exploitatively possible against the 4 excellent player, this is the main reason people learn GTO, it's when you play pots reg vs reg, sure you might find some leaks here and there but they are usually much less apparent and might become moreso when you actually have a good idea of what equilibrium looks like

I agree and disagree with this. I understand what you are saying, but even in this case your actions should be exploitatively isolating the mega-whale where possible. Also, it is my experience if 5 very good players are trying to take advantage of a whale while playing GTO against each other, it quickly devolves into an unspoken agreement where they just soft play each other. Why play GTO, which gives no actual advantage against another GTO player while drastically increasing variance rather than just soft play and reduce variance against the other good players? Basically play revolves less around GTO and more around each player trying to exploitatively isolate the whale while minimizing variance against everyone else.

Basically poker is played until the whale folds and then it is unspoken softplay afterwards.

It is a grey area and I am sure you can come up with examples of where GTO is the smart play, and I could come up with counter-examples where exploitation or unspoken softplay is the smart play.

The whole purpose of this exercise is the 5 players trying to exploit the whale.

If the collection of strategies is such that no player gains an advantage by deviating, then the game is playing at Nash equilibrium.

The "soft play" state by the five good players is an equilibrium state. There is no incentive to deviate. They are playing GTO.

Not sure why the regs would soft play each other after the whale folded. Regs arent incentivized to softplay in a 4 handed reg war why would it be any different if the whale folded utg or something? Theres no extra downside to getting stacked reg v reg, you just reload.

Also, even the biggest whales notice when they are being picked on. If the regs go to battle with the whale at every opportunity but soft play each other otherwise, then the whale is more likely to leave before getting stacked.

If you are in a tournament and there is a big whale at your table and a bunch of other regs, then that may change things. There actually is a downside to getting stacked... you dont get to play with the whale anymore, and even if the whale notices whats going on he cant just pick up and leave or get a table change.

I think the understanding is the regs are of somewhat equal skill. So, if 5 equally skilled reg players and a whale are playing against each other, by definition when the regs play against each other postflop they are not increasing their win rate, they are just increasing their variance.

Getting stacked reg vs reg has huge downside when variance is considered. Reducing variance with no drop in win rate is huge for a reg.

When it is 5 regs and a whale, it is natural for the regs to start to softplay each other. It reduces variance. Why wouldn't they want to reduce variance?

Note, softplay doesn't have to be extreme. It doesn't mean always checking it down if the whale isn't involved. Also, it us unspoken. If some regs do not participate then the others are savy enough to pick up on that and play back. It just means less bluffing, smaller bets,etc. Why play hard in situations that by definition you are EV neutral and are just increasing rake and variance?

Fundamentally the game hasn't changed in all eternity. The mark(whale is ID'd) stacked or gets a heater either way all the big $ is made there and very little should be made from those of equal skill.

GTO has solved HUs AFAIK but not 6 Max. At this point in history at least when it does then we stop playing on-line poker right?

You can quit if you want but no matter how good the bots get we humans will always be flawed and have leaks to exploit