GTO stands for “game theory optimal” and it is the holy grail of poker. We know that mathematically there is a solution to No-Limit Texas Hold’em but no one knows what it is. This is the game theory optimal solution for the game. The actual GTO solution for poker is unknown and will not be figured out anytime soon. When we say GTO Poker we refer to an approximation of a GTO strategy we obtained from running simulations using a solver.
The GTO solution to rock paper scissors
To give you an introduction to a GTO strategy in action let’s take the game of rock paper scissors. For those unfamiliar with the game, it is played by two players. Each player chooses one of rock, paper or scissors. If both players choose the same thing then the game is ended in a tie. Otherwise, rock beats scissors, scissors beats paper and paper beats rock. The GTO solution to this game is simple, you just pick each option one-third of the time. Doing this means you will be guaranteed to never lose over the long run (although of course, you can absolutely lose in the short term).
Imagine if your opponent in this game was a child who absolutely loved choosing rock. They have a pet rock called Mr Rocky. Rock is their favourite thing ever and they will never deviate from this choice. The optimal play for you is to always pick paper and you will always win. If you did use the GTO strategy you would only ever break even with the child over a large number of attempts. When you pick rock you tie, when you pick paper you win and when you pick scissors you lose. By always choosing paper you are playing what is called the maximally exploitative strategy.
Rock paper scissors is not a very complex game. Eventually, even a child will realize they are being exploited. They will soon get sick of losing and soon outgrow Mr Rocky. The child will start always picking scissors to beat your paper. You being an adult will realize very quickly the child has changed his strategy and start going rock yourself to beat their scissors. On and on the cycle will go. Of course, at some point, you will both realise that in order to trick the other opponent you need to sometimes choose rock, sometimes paper and sometimes scissors. If you each continue adjusting to exploit the strategy of the other, eventually you both will settle on the equilibrium strategy of choosing each option a third of the time. At that point, there is nothing either of you can go within the rules of the game to improve your strategy. This adjustment backwards and forwards is how poker solvers reach a state of equilibrium.
How does a solver help you play GTO Poker?
The truth is it doesn’t, at least not in a mathematical sense. A solver is simply a model of an unbelievably complex game. It does not allow us to play GTO poker but rather gives us a solution to a particular model of the game. In poker we don’t just have three options like in rock paper scissors, we have 1236 combinations of starting hands, 19600 combinations of flops, every bet size between 1bb and all in per street, not to mention the turns and rivers. There is no computer in the world that can solve such a complex game but what we can do is create a model of the game by limiting the bet sizing options on each street.
Where our models differ from many others is we map out more of the game tree. Our models are more complex, using much more RAM than most people have. The reason many people do not see flop overbets on boards like AK2 in their sims is that they simply do not add that option to their model! The benefit to having more RAM is you can easily discover interesting bet sizes people have not considered before.
How do I use the results of a solver to play better poker?
You shouldn’t be aiming to play as the solver plays exactly, but rather you should be trying to understand why it does what it does. It’s just not possible for a human to memorize everything a solver does but if you start understanding the reasons behind the results of the model you can greatly improve your poker playing ability.
Through the understanding of why solvers do what they do, you will develop a more fundamentally strong base strategy you can use when you know nothing about your opponents. Exploitative poker should not be thought of as opposed to a GTO style of poker. In fact, they complement each other. If you have good GTO fundamentals, then you can more easily spot the mistakes of even strong opposition. For example, in the BB vs BTN c-bet guide, we indicated that on A72 BTN vs BB the BTN should not c bet their entire range. However, many people will do so anyway, and the reason is it just tends to work. The reason it works is they know that most BB’s do not check-raise enough. The way to exploit this is to simply check-raise more often. Without knowing though the optimal c-bet frequency on that board you may have missed that exploit. To give another example on 654 we observed the BB will have a large donk betting range against the BTN. If you see your opponent does not do this now you have recognized the mistake and know that you should check back more often since the opponent’s checking range is really strong.
There will be times where using a solver like a strategy is foolish. In rock paper scissors if our opponent only ever picked rock we wouldn’t use the GTO strategy for the game. We would always pick paper. To give a practical example in poker, if you are playing a live game against a recreational player who rarely raises without a very strong hand but will call large bets with weak holdings, then the correct play is clearly to always fold to his raises unless we also have a very strong hand and bet very large for value when our hand is strong. Our play can be exploited because we are overfolding against his raises and when we bet small or check back the flop our range is very weak. The important part though is that the recreational player will likely not be able to exploit us very easily. It would take a lot of time and thoughtful consideration to do so and by their nature recreational players are playing for fun. They aren’t thinking about the game on that level.