Von Neumann proved that there exists an unexploitable strategy for any zero sum game, where playing that strategy gives you the best possible outcome if your opponent knows your strategy and can play perfectly against it. Poker players refer to this strategy as "Game Theory Optimal". It is not necessarily "optimal" in the sense of making the most money in real life, EG if your opponent always folds to big bets then you should bet big more often than a GTO strategy would.

Over the last 15 years or so high level poker strategy has increasingly focused on approximating GTO play, and people are moving away from any type of exploitative play, whether that's psychological tells or adjusting to weaknesses like an opponent folding too much. So a GTO player actually will bluff quite frequently, but it's due to the math indicating that it's an advantageous spot to do it, not because of anything he's observed about his opponent.

That said, there's still room to adjust to exploit an opponent, and the weaker the opponent is the more profitable it can be to deviate from "correct" play.

> but it's due to the math indicating that it's an advantageous spot to do it, not because of anything he's observed about his opponent.

I wonder about this distinction. This seems it would make sense if all the players played the GTO strategy. Suppose one agent were to play the GTO strategy, but an other player was vulnerable to bluffing. It seems reasonable to "tune" the bluffs to that player.

In an extreme example, suppose every time a certain player would fold 100% of the time when another player played a certain way. It seems it would make sense for that other player to play that way when they wanted that player to fold, even under normal circumstances that play would be suboptimal.

That is absolutely correct. If everyone plays 100% GTO, then no one makes any money except the house. In order to actually profit, you need to deviate from the GTO strategy in order to exploit your opponent's mistakes.

Playing GTO against a poor player will make you money. This isn't the case in every game (rock paper scissor is the canonical example), but it is true in poker.

Perhaps, but much less money than exploiting the poor player's many mistakes.

Correct me if I'm wrong, but isn't GTO only valid for 2-player games - i.e. no Nash equlibria for 3 or more player games exist? If so, then "solving" poker by finding good enough approximation of GTO strategy only works for heads-up poker, which is a variant almost no one plays nowadays. Of course, in multiplayer games GTO is extremely useful where there's only two players left in the pot (you can view the remainder of the hand as a two player game and find GTO strategy for that game), but you still need a strategy for the remaining situations.

It's complicated. The short version is that a Nash equilibrium exists for multiplayer games, so there is a GTO strategy for multiplayer poker, but it is not as useful in theory or practice if pots are frequently multiway post flop.

This article explains it better than I could:

http://blog.gtorangebuilder.com/2014/03/gto-poker-outside-of...