## Introduction

In the world of poker, there has always been a recognition that skill plays a crucial role in the game. While luck can certainly play a part in the short term, it is the long-term success that separates the skilled players from the rest. If you’ve ever wondered why some players consistently come out on top, it’s not just luck – it’s their mastery of the game’s optimal solution.

### Recognition of Skill in Poker

What sets apart those players who seem to win consistently? Are they simply the luckiest individuals on the planet? Well, we now have compelling evidence to prove that, although luck does play a role in the short term, poker is ultimately a game of pure skill.

Over a significant sample of hands, a skilled poker player will consistently emerge victorious when playing against weaker opponents. This revelation has dispelled the notion that poker is solely a game of chance, highlighting the importance of skill in achieving long-term success.

Skilled poker players engage in a high-stakes game, relying on their expertise and strategic thinking to outperform their opponents.

### Long-Term Success in Poker Through Skill

Like many other games of skill, poker has an optimal solution. This means that there are objectively right and wrong answers to the tough decisions we encounter at poker tables. Achieving long-term success in poker requires understanding and implementing this optimal solution.

To grasp the concept of an optimal solution, we need to delve into the realm of game theory optimal (GTO) strategies. Game theory is a branch of mathematics that deals with calculating strategies for competitive situations, including poker. When a poker decision is game theory optimal, it means that it is mathematically the best possible decision when facing a perfect opponent.

### Optimal Solution and Game Theory Optimal (GTO) Concept

In the poker community, an optimal solution refers to a mathematically-perfect game theory optimal (GTO) strategy. When a player follows a perfect GTO strategy, they become unbeatable. Even against advanced opponents who are also using a GTO strategy, the worst-case scenario is breaking even. Against unskilled opponents, a perfect GTO strategy can yield significant profits.

Imagine a scenario where every decision you make at the poker table is backed by mathematical precision, making it impossible for your opponents to exploit your play. That’s the power of GTO poker. However, it’s important to note that achieving a complete GTO solution for popular variants like NLHE and PLO is currently beyond reach. The vast number of possible actions, boards, hands, and bet sizes in these variants make it impractical to generate a comprehensive GTO solution.

Nevertheless, we can still make highly accurate estimates of what GTO poker looks like by utilizing simplified game trees. By employing commercially-available GTO poker software, known as solvers, we can approximate GTO solutions for specific game trees. These solvers provide valuable insights into GTO strategies without the need for complex solver analysis.

Understanding the concept of GTO poker is a powerful tool in your poker arsenal. It enables you to recognize the mistakes your opponents are making and develop strategies to exploit those weaknesses. While playing perfect GTO poker may not be realistic or necessary, having a deep understanding of GTO concepts can dramatically enhance your overall poker strategy and help you dominate the majority of opponents.

By incorporating GTO principles into your game, you’ll gain a competitive edge and improve your long-term profitability at the poker table.

Every decision at the poker table requires careful consideration. Skilled players analyze their hand and the situation to make the optimal move.

## Understanding GTO

When it comes to poker, there is an undeniable allure to consistently winning and outperforming opponents. That’s where understanding Game Theory Optimal (GTO) strategy comes into play. GTO refers to the mathematically-perfect solution in competitive games, such as poker. It represents the objective right and wrong decisions we face at the poker tables.

Imagine a scenario where you face a perfect opponent. If your poker decision is GTO, it means you have made the mathematically best possible decision in that situation. Following a GTO strategy ensures that you cannot be beaten in the long run. Even against advanced opponents using GTO strategies, the worst-case scenario is breaking even, while significant profits are made against weaker opposition.

### Game Theory and its Relevance to Poker

Game theory, a branch of mathematics, is integral to understanding GTO poker. It involves calculating strategies for competitive situations, including poker and other strategy games. By applying game theory principles to poker, we can determine optimal strategies in various scenarios. This helps us make informed decisions, maximizing our profitability while minimizing potential losses.

Poker, like chess or other complex games, has an enormous game tree representing all the possible actions, boards, hands, and bet sizes. While generating a complete GTO solution for popular poker variants like NLHE and PLO is currently unattainable, we can still make highly accurate estimations using simplified game trees.

### Benefits of Following a GTO Strategy

Now you might be wondering, why should you bother exploring GTO poker if playing perfect GTO is nearly impossible? The answer lies in the numerous benefits it offers. By delving into GTO concepts, you gain a better understanding of poker strategy and can dominate the majority of your opponents.

One crucial point to remember is that the goal of learning GTO poker is not necessarily to play GTO poker itself. Instead, the objective is to identify and exploit the mistakes your opponents make. Exploitative play, which takes advantage of opponents’ deviations from GTO, can be even more profitable than rigidly adhering to GTO strategies.

The game tree in poker represents the vast number of possible actions, boards, hands, and bet sizes, adding complexity to the game and making it challenging to achieve a complete GTO solution.

### Profits with GTO Strategy against Weaker Opposition

One of the significant advantages of adopting a GTO strategy is its effectiveness against weaker opponents. Over a large sample of hands, a skilled poker player employing GTO tactics will consistently win against weaker opposition. By making mathematically-optimal decisions, you exploit their mistakes and increase your profits.

For instance, let’s consider a scenario where you face an unskilled opponent who consistently makes suboptimal decisions. By utilizing GTO strategies, you gain a substantial edge, making significant profits in the long run. The more you understand and implement GTO principles, the better equipped you become to exploit opponents’ weaknesses and maximize your earnings.

GTO poker provides you with a strategic framework to consistently make optimal decisions. While achieving perfect GTO play may be unattainable, the knowledge and application of GTO concepts give you a competitive edge, enabling you to outperform weaker opponents and increase your profits in the long run.

## Limitations of GTO in Poker

While Game Theory Optimal (GTO) poker is a powerful concept, it is important to recognize its limitations. One significant limitation is the incompleteness of the GTO solution for popular poker variants like No-Limit Hold’em (NLHE) and Pot-Limit Omaha (PLO). As of now, a complete GTO solution for these variants is not known, nor is it expected to be discovered in the foreseeable future.

The vast number of possible actions, boards, hands, and bet sizes in NLHE and PLO make it extremely challenging to generate a comprehensive GTO solution. Even with powerful modern computers, the game tree (representing all possible game states) is too vast to allow for a complete GTO solution.

GTO poker software allows players to approximate GTO solutions for specific game trees. It offers valuable insights into optimal strategies without the need for complex solver analysis.

### Complexity of the Game Tree and Its Impact on GTO Solutions

To better understand the complexity of GTO poker, let’s delve into the concept of the game tree. A game tree is a diagram that encompasses all possible actions, boards, hands, and bet sizes in a particular game. In complex games like poker, the game tree can become enormous.

Considering a simplified example, let’s imagine a heads-up poker game where players have limited options, such as betting half-pot, checking, or calling at every decision point. In this case, it becomes feasible for an amateur player with a basic laptop to calculate the full GTO solution using specialized GTO poker software.

### Introduction to GTO Solvers and Their Role in Estimating GTO Poker

GTO solvers, also known as game theory optimal solvers, are commercially available software tools that provide an estimation of the GTO solution for a given simplified game tree. These solvers are widely used in the poker community to gain insights into optimal strategies.

It’s important to note that GTO solvers do not provide a complete GTO solution for complex games like NLHE and PLO. However, they do offer valuable estimations of what GTO poker looks like in simplified scenarios. Most GTO solvers come with user-friendly interfaces that allow players to construct and configure their preferred game trees.

Our objective is to teach you valuable GTO poker concepts without requiring you to run complex solver analysis. However, if you are interested in diving deeper into some of the concepts we discuss, you may consider purchasing a commercial solver. For those interested, you can find the same solver we use for our postflop solves, along with a comprehensive training course on using it effectively.

By understanding the limitations of GTO poker, the complexity of the game tree, and the role of GTO solvers, you can gain a better perspective on the practical application of GTO strategies in your poker game.

GTO poker enables players to make mathematically-optimal decisions, leading to long-term profitability. Understanding GTO concepts gives players an edge and helps them dominate their opponents.

## GTO Solvers and Software

When it comes to mastering GTO (Game Theory Optimal) poker, GTO solvers play a crucial role. But what exactly are GTO solvers? GTO solvers are computer software programs designed to calculate optimal strategies for a given game tree in poker. These solvers utilize advanced mathematical algorithms to analyze various factors, such as different actions, boards, hands, and bet sizes, to determine the best possible decision in a game.

### Availability and Commercial Use of GTO Solvers

The availability of GTO solvers has revolutionized the way poker players approach the game. These solvers are now commercially available to anyone interested in improving their poker skills. Whether you’re a beginner or an experienced player, GTO solvers can provide valuable insights into optimal strategies and help you make better decisions at the tables.

By investing in GTO solvers, you gain access to cutting-edge technology that was once limited to only a few elite players. With these solvers, you can now analyze complex game trees and develop a deeper understanding of the game’s intricacies.

### Role of Solvers in Constructing and Configuring Game Trees

Game trees in poker represent all the possible actions, boards, hands, and bet sizes that can occur during a game. GTO solvers allow you to construct and configure game trees to analyze specific scenarios and decisions. By inputting different variables and parameters, you can simulate various situations and study the optimal strategies recommended by the solver.

The flexibility of solvers enables you to customize game trees based on your preferred betting structures, hand ranges, and other variables. This customization allows for a more accurate representation of real-world poker scenarios and helps you make informed decisions based on GTO principles.

You are also able to put in an estimate of your opponent’s flawed strategy and solve for what is optimal against them in particular.  This is dangerous in that your estimate might be wrong, but when you are right, it will show you what is best against flawed opponents that you actually play against.

### Optional Use of Solvers for Deeper Analysis and Training

Utilizing GTO solvers for deeper analysis and training can be highly beneficial. These solvers provide a comprehensive understanding of optimal strategies, helping you identify mistakes and weaknesses in your opponents’ play.

With a GTO solver, you can study specific hands or situations and evaluate the optimal decisions according to GTO principles. By exploring different variables, bet sizes, and hand ranges, you can gain insights into the effectiveness of different strategies and develop your own exploitative approaches.

Moreover, some solvers offer complete training courses to help you navigate and utilize the software effectively. These courses provide in-depth knowledge of GTO concepts, enabling you to enhance your overall poker strategy.

By using GTO solvers for deeper analysis and training, you can refine your decision-making skills, exploit opponents’ mistakes, and ultimately improve your profitability at the poker tables.

Remember, GTO solvers are tools that supplement your poker knowledge and understanding. While they offer valuable insights, it’s important to balance GTO principles with exploitative play to maximize your profits.

GTO solvers provide comprehensive analysis and estimation of optimal strategies in poker. They help players refine their decision-making skills and develop a deeper understanding of the game.

## Complexities of GTO Poker

When it comes to the complete GTO solution in poker, we are faced with an overwhelming challenge. The size of the game tree, encompassing all possible actions, boards, hands, and bet sizes, is so vast that generating a full GTO solution becomes an unrealistic endeavor. Even with powerful modern computers, it would take an impractical amount of time to calculate every aspect of the game.

Just imagine, if a futuristic alien dropped the complete GTO solution onto our desk, we would be confronted with several trillion pieces of paper. The sheer magnitude of the full GTO solution is immense, making it difficult to comprehend and implement.

### Challenges in executing the complex GTO strategy

The complexity of the GTO strategy poses another significant challenge. It goes beyond making simple decisions like calling, folding, or raising at the right time. GTO poker involves utilizing mixed strategies, which require us to take differing actions at specific frequencies.

For instance, imagine a hand on a given board that needs to raise 17.4% of the time, call 37.8% of the time, and fold 44.8% of the time. These frequencies change with every hand we are dealt, on every street we play, and against every bet size we face. Tracking and executing these complex frequencies over tens of thousands of hands is beyond the mental capacity of humans.

### Use of mixed strategies in GTO poker

Mixed strategies are a cornerstone of GTO poker. They involve utilizing specific frequencies to balance our decision-making process. Instead of taking actions with 100% frequency (pure strategies), GTO poker necessitates a calculated mix of actions to achieve an optimal approach.

For example, when facing a bet, GTO poker might require us to call 70% of the time and raise 30% of the time. These mixed strategies are designed to prevent opponents from exploiting our tendencies and maximize our long-term profitability.

### Mental limitations of humans in tracking complex frequencies

While machines or savants may possess the ability to accurately execute the full GTO strategy, humans face inherent limitations. Our mental capacity restricts us from effectively tracking and implementing the intricate frequencies required by GTO poker.

Even further, randomizing decisions is difficult.  Just try and make a list of 100 coin-flip results.  Most people make a list that someone skilled in statistics will easily identify as human-generated vs true random flips.

Attempting to execute the complete GTO solution would likely lead to mistakes and suboptimal play. However, this does not diminish the value of learning GTO poker concepts. Understanding GTO strategy allows us to recognize and exploit the mistakes our opponents make, enabling us to dominate the majority of players at the table.

The complexities of GTO poker are multifaceted. The enormous size of the full GTO solution, challenges in executing the complex strategy, the use of mixed strategies, and the mental limitations of humans in tracking complex frequencies all contribute to the intricacy of GTO poker. While implementing a perfect GTO strategy may be unattainable, learning GTO concepts empowers us to make better strategic decisions and capitalize on the mistakes of our opponents.

The complete GTO solution for poker is extremely complex and challenging to execute. Its sheer size makes it unrealistic for human players, but learning GTO concepts still enhances strategic decision-making.

## Importance of GTO Poker

When it comes to achieving perfect GTO (Game Theory Optimal) poker, it’s important to set realistic expectations. While a complete GTO solution theoretically does exist for complex games like No-Limit Hold’em (NLHE) and Pot-Limit Omaha (PLO), implementing it accurately as a human player is nearly impossible. The sheer number of variables and possibilities in these variants makes it impractical for us to execute the full GTO strategy. However, this doesn’t diminish the significance of exploring GTO poker concepts and incorporating them into our gameplay.

### Value of Understanding GTO Concepts for Strategic Improvement

Understanding GTO concepts can have a profound impact on our overall poker strategy. It allows us to enhance our thinking process and make more informed decisions at the tables. By delving into GTO principles, we gain insights into optimal strategies and learn how to navigate various scenarios effectively. This knowledge empowers us to make better-informed choices, adapt to different opponents, and optimize our overall gameplay.

For example, let’s consider the concept of mixed strategies. In GTO poker, a mixed strategy involves taking different actions at certain frequencies. By incorporating mixed strategies into our decision-making process, we can become less predictable and exploit our opponents’ tendencies. For instance, when facing a bet, GTO poker might dictate that we call 70% of the time and raise 30% of the time. This balanced approach prevents opponents from easily exploiting our playing style and keeps them guessing.

### Exploiting Opponents’ Mistakes for Profitability

One of the key advantages of learning GTO poker is the ability to recognize and exploit our opponents’ mistakes. While striving for perfect GTO play may not always be feasible, exploiting the strategic errors made by our opponents can be highly profitable. By gaining a better understanding of GTO concepts, we can identify when our opponents deviate from optimal play and capitalize on those deviations.

For example, if we notice an opponent consistently over-folding in certain spots, we can adjust our strategy to bluff more frequently and extract extra value. Conversely, if an opponent tends to overvalue hands and call too often, we can tighten our range and focus on value betting. These exploitative adjustments can significantly increase our profitability and give us an edge against less skilled opponents.

As a simple rule, if you can confidently say a player “always” or “never” does something in a situation, then it is virtually certain they are deviating from proper play.  When they deviate from proper play, there is an exploit you should take.

### Comparison to Rock, Paper, Scissors as a Solved Game

To illustrate the relevance of GTO poker, let’s consider the game of Rock, Paper, Scissors (RPS), which is a solved game. In RPS, the optimal strategy is to choose each option (rock, paper, scissors) randomly exactly one third of the time. This balanced approach ensures that, in the long run, we win one third of our games and tie one third, regardless of our opponent’s strategy.

Similarly, in poker, playing perfect GTO poker against another perfect GTO opponent will result in a long-term break-even outcome. However, the beauty of GTO poker lies in exploiting opponents’ mistakes. Just as we can deviate from the optimal RPS strategy to exploit an opponent who consistently chooses “rock,” we can adjust our poker strategy to exploit the weaknesses and errors of our opponents.

By recognizing the parallels between RPS and poker, we can appreciate the value of GTO poker as a foundation for strategic improvement and exploiting our opponents’ mistakes to maximize profitability.

Remember, the goal of learning GTO poker is not necessarily to play perfect GTO poker but to understand our opponents’ mistakes and capitalize on them. This exploitative play can often generate more profits than rigidly adhering to a GTO style of poker.

Next, we will explore the significance of keeping score in poker and how expected value (EV calculations can help us make informed decisions and maximize our long-term profitability.

GTO poker involves intricate decision-making processes, such as utilizing mixed strategies and tracking complex frequencies. Understanding these complexities enhances strategic thinking in poker.

## Keeping Score in Poker: Understanding Expected Value (EV)

In poker, keeping score is crucial for making strategic decisions. One of the fundamental tools for measuring and assessing the potential profitability of a decision is expected value (EV). Expected value represents the average outcome of a particular action over the long run, taking into account all possible scenarios and their respective probabilities.

To calculate the EV of a decision, we multiply the potential outcomes by their probabilities and sum them up. If the result is positive, it indicates a profitable decision, while a negative value suggests an unprofitable one. By understanding EV and incorporating it into our decision-making process, we can make more informed choices and increase our overall profitability.

GTO solvers help players analyze game trees and make informed decisions based on optimal strategies. Utilizing these tools can improve decision-making skills and increase profitability.

### Applying EV Calculations to Poker Scenarios

Let’s consider a simple example to illustrate the application of EV calculations in poker. Suppose we’re playing No-Limit Hold’em and facing a bet on the river. To decide whether to call or fold, we need to evaluate the potential outcomes and their probabilities.

If we estimate that our opponent’s range consists of a value hand 70% of the time and a bluff 30% of the time, we can assign probabilities accordingly. Let’s say the value hand beats us 80% of the time and loses to us 20% of the time, while the bluff loses to us 100% of the time.

Folding now has a zero EV, always.

Calling and losing will happen 70% of 80% or 56% of the time

Calling and winning will happen the other 44% of the time.

This looks bad for us since we lose over half the time.  However, the risk of the bet compared to the size of the pot will dictate if we should call.  For a pot sized bet, we would only need to win 33% of the time.  Even though we will lose frequently, against a pot sized river bet, we should call.

By consistently evaluating EV in different poker scenarios, we can make better decisions that align with our long-term profitability goals.