Hi, I hope you're having a nice day.

This question must have been asked a billion times in the following form or another but please help me on this.

Let's say I want to play GTO. On the flop, I know which range I gonna check, which range I gonna bet etc.

Now let's say that when I bet on the flop, vilain raise me every single time. If I understand correctly, while playing GTO, I should remove my opponent from the equation, but then, in this case what should I do, call/3bet only with the hands that correspond to the "you get reraised on the flop" range?

Another way of asking the question would be: is there some cases in which you cant play GTO because your opponent play is so out of line that it becomes impossible not to play exploitative or do I simply do not understand GTO play? Do you have to have your opponent range as input for playing GTO?

Hopefully that makes sense and thanks you for your time in advance.

GTO effectively means building optimal ranges that cannot be exploited for every situation. This doesn't take into account any tendencies of a villain, and doesn't need to to be profitable. Therefore if you somehow managed to play perfectly GTO, you would play the same against any villain and be profitable against all of them, regardless of how they act. As you mention earlier in your post, this would require sorting through your flop c-bet range and forming a further range vs a reraise consisting of hands that fold, call or 3bet at certain frequencies to become truly unexploitable (ie. there is nothing the villain can do to profit vs you).

GTO is effectively a theoretically consistent profitable style of play however vs villains that make mistakes/have certain tendencies is not the MOST profitable style. In this case, given that you have observed villain has a high flop check raise frequency, it would be MORE profitable to call/3-bet his check raises wider as you have identified them as weaker than optimal (ie. play an exploitative style). Understanding GTO ranges helps serve as a foundation to which you should build ranges however to maximise profit you should deviate from this foundation depending on villain tendencies.

If you played GTO perfectly you would make a modest profit vs everyone. Unfortunately, no one plays truly GTO (we all make mistakes). So it's important to maximise the edges you can get from your opponent by exploiting and adjusting to their mistakes as they will be trying to exploit your mistakes too.

Great answer really I think I got it.

From what I understand then, there is two ways of making money, 1) by making a clearly exploitable move that beat/exploit an opponent mistake (example: shove any two hands preflop knowing vilain never calls), 2) the opposite, play closer to GTO to beat yet again an opponent mistake (example: call some mediocre value GTO that beat an opponent heavy bluffing).

Well, I guess it's called playing exploitative vs playing GTO... It's super interesting. In every situation now, I can ask myself which one is "+EV", what are my chances of executing each one, etc. That's core. Exactly what I was looking fore. Thanks so much again MedicMan.

I play a very GTO oriented play style. I think the best way for me to exploit my opponents IS to play balanced. While I can exploitively take advantage of my villains mistakes, if I play GTO, villain HAS to make a mistake vs us no matter who they are. While I do take exploitive lines, I do that exclusively on the river. I will play a fish and a reg the exact same way upto the river.

As to your original question
If villain raises every hand, we can just fold all of our bluffs and continue with our highest equity draws and strong made hands. Villain will win more pots, but more small pots, and we will be showing up to the turn in larger pots with much stronger ranges to still bluff and value bet vs villains very weak ranges

I strongly disagree with this. Although we don't even look like what GTO looks like (or exists, in other than heads-up), we do know that some of the best players got absolutely mauled by Libratus. It beat them by something like 10bb/100 over 100k hands in symmetric hands (i.e. reduced variance).

That's far more than a modest winrate. Imagine what the winrate would be against regular opponents instead of world class humans. The EV of not making mistakes/blunders is enormous.

Yes agreed perfect GTO would crush. The point I was trying to make but perhaps oversimplified is that vs certain opponents there are exploits you can make that will make you more +EV than a human attempting to play GTO (obviously no human attempting to play GTO would be anywhere near Libratus in terms of winrate). So although GTO is an effective strategy vs all villains/when you lack any hand history or reads, you can improve your win rate by deviating in certain situations especially if villain is exceptionally unbalanced.

I agree with that.

Do we know that Libratus always played the Nash equilibrium strategy? (Honest question, I have no idea.) I would think it rather kept track of how the villain played hands, and using a learning strategy, calculated an exploitative mixed strategy to maximize win rate.

You'd make a profit against everyone provided the population is deviating from GTO, correct? If everyone played perfect GTO, then everyone would be a small loser in raked games, and break-even in non-raked ones.

Correct. The other equilibrium strategy would break even vs us in non-raked games and each strategy would lose money to the rake in the raked game, but break even vs eachother.

That just shows that even the best humans are not able to get very close to GTO. The Libratus team said they think the bot was itself about 10bb/100 from GTO so in reality the humans were probably 20bb/100 from GTO

There is (as a live player who thus cannot track or randomize well) a real question of which approach is easier to implement to PRACTICALLY gain our max edge over the field. Some people are simply quantitative by nature and are better off thinking mathematically even knowing they will be 20bb/100 or more from GTO. Most people are not realy mathematical thinkers and thus will get closer to their likely max profit by focusing on exploitation. Whatever approach, or combination, works best is often based on the individuals ability to implement more than the theoretic differences.

Libratus switched from a multi-opening size pre-flop strategy to a single -sized pre-flop strategy after a few days. That already rules out it being GTO. I do think it strived to play GTO-like. On the turn it would solve the entire game tree, being GTO within the ranges that it estimated based on the pre-flop and flop action. Those ranges would not be fully accurate of course, but apparently accurate enough to **** the humans up.

I also believe the Libratus engine studied the hands vs the humans at night. I suspect the main goal was to get a better grasp on their ranges, but I don't think the night training was ever quantified by the developer.

Interesting conclusion.

You are half right (and half wrong).

Jason Les tweeted about this after the match concluded.