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GTO in Poker: The Science of winning Poker (1/3)
Gto poker strategy explained: theories, solvers, and Nash equilibrium to become an unexploitable player and maximize your profits
14.5.2024
Article written by Gandalf, Spin & Go and GTO specialist, co-founder of Poker Sciences.
What does gto mean?
GTO is an acronym that means: Game Theory Optimal.
What is GTO in poker?
Game Theory
Game theory is a branch of applied mathematics that analyzes strategic situations where the choices of each participant depend on the actions of others. This theory is used to study various fields such as economics, politics, biology, and of course, games like poker.
The objective is to predict the behavior of players assuming they act rationally to maximize their gains or minimize their losses, according to the rules and objectives of the game.
Game Theory and Poker
In the context of poker, game theory helps understand how players interact, make decisions, and what strategies they might adopt to achieve the best possible results against opponents who are also trying to maximize their gains. A key concept here is the Nash equilibrium, named after mathematician John Nash.
Drawing in tribute to John Nash (credit: MemreSoyak)
A Nash equilibrium occurs when no player can profitably deviate from their strategy if their opponents maintain their unchanged strategies. In other words, it’s when each player optimally exploits their opponent.
Nash Equilibrium and the Ice Cream Vendor Example
To illustrate game theory and Nash equilibrium, we can draw a parallel with an ice cream vendor. Imagine two ice cream vendors on a beach:
Initially, the two ice cream vendors share the clientele equally.
Initially, they share the beach fairly to maximize their customer coverage. There are as many customers going to the red vendor as to the blue vendor since each covers the same area on the beach.
However, we cannot talk about Nash equilibrium because both vendors can change places to increase their gain.
Indeed, when one vendor moves towards the center, they increase their market share because they cover a larger area.
The blue vendor covers more area than the red vendor. The red vendor must react to maintain their revenue.
Here, the blue vendor thinks he will cover a larger area by moving to the left, which will increase his revenue as more customers will come to buy ice cream.
Therefore, to restore his revenue, the red vendor must adapt by moving to the right.
This movement continues until both vendors find themselves in the center.
Each vendor has found the optimal strategy. They are unexploitable because they are at equilibrium.
We then talk about equilibrium because both vendors no longer have an interest in moving.
Although this strategy potentially reduces their overall revenue because customers at the beach's ends might choose not to walk to the center, this arrangement represents a Nash equilibrium : neither vendor can improve their situation without a coordinated change in strategy.
<span class="inarticle_section">♠️ In poker, GTO (Game Theory Optimal) is a strategy that aims to achieve this Nash equilibrium. It involves playing so that no deviation by opponents can systematically be profitable against it, exactly like in the ice cream vendor example.</span>.
In other words, GTO is an unexploitable strategy. By strictly following this strategy, for example, staying in the center for the blue vendor, no one can be better than you in the long run, regardless of the strategy used. In the ice cream vendor example, the red vendor has no more profitable spot than the blue vendor because the blue vendor has a GTO strategy.
How is the GTO strategy determined?
Solvers and their role in the development of GTO strategies
GTO in poker is determined using computer programs called "solvers". These solvers simulate thousands, even millions of different game situations to determine the most effective actions to take in each possible situation. These actions are calculated to maximize gains or minimize losses, regardless of the opponent's moves.
GTO Wizard is an example of a popular GTO solver
Can Solvers play GTO?
It is difficult to answer this question absolutely. Technically, GTO is too complex to be perfectly solved by current computers. Solvers, in practice, only approximate the GTO strategy. For example, most solvers use static bet sizes determined by the user, which is a computational limitation and can vary from solver to solver. However, the approximations made by solvers are considered very accurate.
For practical reasons, poker players therefore consider that solvers offer gameplay equivalent to GTO gameplay.
Basics of Applying GTO in poker
How to play GTO in Poker?
As explained earlier, playing GTO means adopting a play style where, even by revealing your strategy in advance to other players, no one can take advantage of it to beat you in the long run. In practice, this means making strategic choices that perfectly balance bets and bluffs to remain indifferent to opponents' actions.
<span class="inarticle_section">ℹ️ For example, if during a hand you decide to raise with a certain hand and simply call with the same hand in other situations, you create a mixed strategy that makes it difficult for your opponents to predict your actions and exploit them..</span>
To know how to make these right decisions of frequencies and actions, a substantial off-table work is necessary using a GTO solver (such as GTO Wizard).
To play “GTO”, poker players work on their game using solvers
The importance of frequencies
In GTO poker, understanding and applying the right frequencies to your actions, such as raising, calling, or folding, is crucial. These frequencies determine how you should play certain hands in order to remain unpredictable and effective.
<span class="inarticle_section">ℹ️ For example, choosing to bluff with a certain hand 20% of the time and play for value the rest of the time will optimize your gains and minimize your losses, while making it difficult for your opponents to adapt or exploit your choices.</span>
Should we play GTO?
Adopting a GTO strategy is not always necessary and may not even be optimal in all situations, especially against opponents who make predictable mistakes that you could exploit. For casual players or those playing at stakes where mistakes are frequent, an exploitative approach could be more profitable. However, understanding the principles of GTO can be extremely useful for developing a solid foundation and improving your overall strategy.
Can we play GTO?
In theory, playing perfectly GTO is impossible as it is beyond the reach of human players, mainly due to the immense amount of calculations and scenarios to consider. As explained earlier, poker solvers themselves can only approximate GTO strategies. For players, approaching the GTO strategy can be a goal, but exactly reproducing a perfect GTO strategy is not achievable.
What does gto mean?
GTO is an acronym that means: Game Theory Optimal.
What is GTO in poker?
Game Theory
Game theory is a branch of applied mathematics that analyzes strategic situations where the choices of each participant depend on the actions of others. This theory is used to study various fields such as economics, politics, biology, and of course, games like poker.
The objective is to predict the behavior of players assuming they act rationally to maximize their gains or minimize their losses, according to the rules and objectives of the game.
Game Theory and Poker
In the context of poker, game theory helps understand how players interact, make decisions, and what strategies they might adopt to achieve the best possible results against opponents who are also trying to maximize their gains. A key concept here is the Nash equilibrium, named after mathematician John Nash.
A Nash equilibrium occurs when no player can profitably deviate from their strategy if their opponents maintain their unchanged strategies. In other words, it’s when each player optimally exploits their opponent.
Nash Equilibrium and the Ice Cream Vendor Example
To illustrate game theory and Nash equilibrium, we can draw a parallel with an ice cream vendor. Imagine two ice cream vendors on a beach:
Initially, they share the beach fairly to maximize their customer coverage. There are as many customers going to the red vendor as to the blue vendor since each covers the same area on the beach.
However, we cannot talk about Nash equilibrium because both vendors can change places to increase their gain.
Indeed, when one vendor moves towards the center, they increase their market share because they cover a larger area.
Here, the blue vendor thinks he will cover a larger area by moving to the left, which will increase his revenue as more customers will come to buy ice cream.
Therefore, to restore his revenue, the red vendor must adapt by moving to the right.
This movement continues until both vendors find themselves in the center.
We then talk about equilibrium because both vendors no longer have an interest in moving.
Although this strategy potentially reduces their overall revenue because customers at the beach's ends might choose not to walk to the center, this arrangement represents a Nash equilibrium : neither vendor can improve their situation without a coordinated change in strategy.
<span class="inarticle_section">♠️ In poker, GTO (Game Theory Optimal) is a strategy that aims to achieve this Nash equilibrium. It involves playing so that no deviation by opponents can systematically be profitable against it, exactly like in the ice cream vendor example.</span>.
In other words, GTO is an unexploitable strategy. By strictly following this strategy, for example, staying in the center for the blue vendor, no one can be better than you in the long run, regardless of the strategy used. In the ice cream vendor example, the red vendor has no more profitable spot than the blue vendor because the blue vendor has a GTO strategy.
How is the GTO strategy determined?
Solvers and their role in the development of GTO strategies
GTO in poker is determined using computer programs called "solvers". These solvers simulate thousands, even millions of different game situations to determine the most effective actions to take in each possible situation. These actions are calculated to maximize gains or minimize losses, regardless of the opponent's moves.
Can Solvers play GTO?
It is difficult to answer this question absolutely. Technically, GTO is too complex to be perfectly solved by current computers. Solvers, in practice, only approximate the GTO strategy. For example, most solvers use static bet sizes determined by the user, which is a computational limitation and can vary from solver to solver. However, the approximations made by solvers are considered very accurate.
For practical reasons, poker players therefore consider that solvers offer gameplay equivalent to GTO gameplay.
Basics of Applying GTO in poker
How to play GTO in Poker?
As explained earlier, playing GTO means adopting a play style where, even by revealing your strategy in advance to other players, no one can take advantage of it to beat you in the long run. In practice, this means making strategic choices that perfectly balance bets and bluffs to remain indifferent to opponents' actions.
<span class="inarticle_section">ℹ️ For example, if during a hand you decide to raise with a certain hand and simply call with the same hand in other situations, you create a mixed strategy that makes it difficult for your opponents to predict your actions and exploit them..</span>
To know how to make these right decisions of frequencies and actions, a substantial off-table work is necessary using a GTO solver (such as GTO Wizard).
The importance of frequencies
In GTO poker, understanding and applying the right frequencies to your actions, such as raising, calling, or folding, is crucial. These frequencies determine how you should play certain hands in order to remain unpredictable and effective.
<span class="inarticle_section">ℹ️ For example, choosing to bluff with a certain hand 20% of the time and play for value the rest of the time will optimize your gains and minimize your losses, while making it difficult for your opponents to adapt or exploit your choices.</span>
Should we play GTO?
Adopting a GTO strategy is not always necessary and may not even be optimal in all situations, especially against opponents who make predictable mistakes that you could exploit. For casual players or those playing at stakes where mistakes are frequent, an exploitative approach could be more profitable. However, understanding the principles of GTO can be extremely useful for developing a solid foundation and improving your overall strategy.
Can we play GTO?
In theory, playing perfectly GTO is impossible as it is beyond the reach of human players, mainly due to the immense amount of calculations and scenarios to consider. As explained earlier, poker solvers themselves can only approximate GTO strategies. For players, approaching the GTO strategy can be a goal, but exactly reproducing a perfect GTO strategy is not achievable.
References
Some links if you want to learn more:
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