What are “Solvers” in poker?

Poker Solvers they are software tools that calculate theoretically optimal solutions in a variety of gaming situations. The mathematical aspects of card games have become available to a wide public, and interest in probability theory in the context of games with incomplete information has grown. Players who are able to apply the calculated values in practice win in game scenarios.

With the advent of online poker, tools for strategy development are developing. Despite the existing powerful equity calculators, many decisions in the game remained at the level of intuition. With the advent of GTO solvers, a revolution has occurred that allows you to analyze strategies in detail at all stages of the game and evaluate the expected profit (EV) from each action.

 

Basics of work:

The principle of operation of any solver is based on assessing the profitability of each action and its impact on the overall benefit of the strategy from the flop to the river. Various algorithms are used for this:

1. CFR (counterfactual regression). This method involves multiple repetitions of the same situation, in which the profitability of various actions is evaluated. Counterfactual regret is the difference in profitability between these actions. By performing a large number of iterations, solver seeks to optimize the strategy when faced with an opponent using the same algorithm. This leads to the formation of an equilibrium strategy.

2. The Monte Carlo method. This is a simplified version of CFR, characterized in that it does not analyze all possible distributions, but conducts a selection of them. Although this reduces the accuracy of calculations, this method significantly reduces the requirements for computing power.

3. Linear programming. The program formulates the search for the optimal strategy as a system of linear equations and inequalities, solving the problem using mathematical methods. This algorithm was relevant in the early stages of GTO, but now it is inferior to the more advanced CFR and Monte Carlo models.

 

Game Theory Optimal (GTO)

The idea of Game Theory Optimal (GTO) originated long before the first solvers appeared and covered zero-sum games in various fields. Despite the fact that the search for optimal strategies in various fields began in the XVIII century, the concept was developed in the 1950s after the publication of an important dissertation on game theory. The name of its author, mathematician John Nash, became famous in the poker world because the basic idea of this discipline was called “Nash equilibrium”.

In the early 2000s, the theory received a new impetus when many professional players decided to develop the idea of a mathematically balanced strategy that could not be exploited. GTO, as a theoretically optimal game, has become a counterweight to exploit – a strategy based on exploiting the weaknesses of the opponent.

In 2014, one of the most important books in the history of poker was published – “A Guide to the theoretically optimal Game” by Matthew Janda.

From that moment on, the question of the need to study GTO was resolved: the poker community realized the deep mathematical foundations of Hold’em and similar disciplines.

The main idea of GTO is a balance that makes the strategy indifferent to the decisions of the opponent. Two players following an equilibrium strategy will play zero in the long run. Deviation from the GTO provides the opponent with opportunities for adaptation and creates an advantage.

Today, poker is about finding a compromise between GTO and exploit. Theoretically, an optimal game serves as the basis of a defensive strategy, and identifying and exploiting the opponent’s weaknesses gives one player an advantage over another. However, it is incorrect to say that GTO will not bring profit. A strategy based on it makes a profit when rivals make mistakes. In fact, both concepts work together, taking the initiative from each other in suitable situations.

 

The goal is to reach a solution

The main goal of Game Theory Optimal (GTO) is to achieve a strategy that is not exploitable, corresponding to the Nash equilibrium. In fact, poker solvers do not use this term; their goal is to maximize the benefits of each specific action.

Depending on the type of software, you can set a different number of “opponents” with their own ranges, bet sizes and decision options on all streets. Each side tries to exploit the others by analyzing the different complexity of the game tree from several thousand to hundreds of billions of hand simulations. Each such cycle is known as an iteration.

The parties continue to exploit each other until they reach a point where neither of them can increase the total expected profit (EV) of the strategy. This moment corresponds to the achievement of equilibrium in terms of John Nash.

 

Initial parameters

GTO-solvers are mathematical algorithms that require a clear formulation of the problem. To calculate optimal solutions, the user must determine the parameters that form the distribution structure:

• Bid sizes and available actions. Each bet size on any of the streets leads to the creation of a new branch of calculations. The totality of all possible lines is usually called a game tree.

• Target accuracy of calculations. This represents the level of acceptable deviations from the optimal strategy, below which the solver stops computing.

• Initial bank and stack sizes. They determine the SPR (the ratio of the pot size to the remaining chips of the opponents) and affect the degree of aggressiveness in the hand.

• Initial ranges. The wider the opponent ranges, the more complex the iterations become and the longer the computational process lasts.

• Common cards on the flop. The structure of the board determines which parts of the ranges the solver will use in different lines.

• Additional factors. Among them: rake and cap — for cash games, ICM — for tournaments.

 

 

Calculation results

The results of calculations are usually ranges where each particular hand is divided into different branches of the decision tree according to the optimal strategy.

These results are limited by the initial conditions set by the user. If the program is provided with an unlimited number of betting options, it uses almost all of them in most situations, just with different frequency.

Unlike human thinking, which tends to simplify, solvers more often distribute starting hands along different lines with different frequency. This is the main reason that the strategy of the program will always be more balanced than the game of even the most experienced poker players.

 

Software Limitations

Solvers represent the pinnacle of poker software development, opening up new opportunities for learning strategy. Nevertheless, these programs place high demands on the computing power of the equipment, since they use all available processor and RAM resources during calculations.

Even owners of powerful personal computers are often forced to limit the number of betting options in order to reduce the complexity of the game tree and get acceptable results in a reasonable time.

Loading PC components also increases power consumption. Therefore, some players prefer to purchase ready-made calculations or rent powerful servers for quick analysis of complex game trees.

 

Collection of poker solvers

The first software for studying the optimal game based on the Nash equilibrium was created in 2013 by Oleg Ostroumov, but it remained available only to a small circle of high rollers of that time. Within a few years, other programs have appeared, and by 2023-2024, players can choose from various products according to their basic requirements.

 

Simple Postflop

Simple is a versatile software from Russian—speaking developers that provides virtually unlimited opportunities to study preflop and post-flop strategies in most poker formats. In the free version, users can perform calculations for the turn and river. Ready-made sets of strategic solutions are also available for purchase.

In addition to the basic free version, two plans are available to poker players Simple Postflop: Standalone за $299 и 50 Preflop Points за $1,499.99 The software is designed for professionals, and the price is due to the flexibility of the program settings for the needs of players. For calculations, you can use both the resources of your own PC and the cloud servers of Simple itself.

In addition to the solver itself, the creators of the program offer a high-quality simulator for practicing strategy.

Any additional functionality it is purchased for a fee.

 

GTO+

The most democratic version of the software. At one time, it became a real gift for players of medium and low limits who do not find the opportunity to give a significant part of the bankroll to more expensive programs. User-friendly interface with good performance even on budget PCs does the job in GTO+ no less comfortable than in Simple.

In addition to intuitive control of the tree, the software has a Nodelock function and placing the turn and river in a separate window for quick recalculation with adjustments. The price of the program is $75 for one computer, for the second you need to add $ 40. Since the software was developed by the same people as CREV, the owners of this utility can get GTO+ with an additional payment of $ 50.

 

 

Types of solvers in poker:

In addition to the calculation algorithms, the programs differ in their implementation. This applies not only to the external interface, but also to methods for obtaining the necessary information. Most programs are installed on personal computers and use their computing resources to solve game trees. However, some developers have chosen a different approach, providing access to ready-made calculations through subscriptions on the Internet.

Traditional – These are classic programs designed to develop optimal strategies in accordance with the specified parameters. They use the processor and RAM of the computer to perform iterations. As a result, the user receives a unique solution based on their own ranges and rates, and can also make adjustments and supplement them.

Browser – The solvers presented through the browser formally remain so. They are a tool for studying ready-made solutions. Developers carry out all the necessary calculations on powerful servers, and use their websites as an interface for interacting with the finished material.

Examples of such solvers are GTOBase and popular GTO Wizard. In addition to learning strategy, these websites allow you to upload your own hands for analysis depending on the texture of the board.

 

How to choose a poker software?

To determine which program is suitable for a particular player, it is necessary to take into account the initial data: the level of knowledge, preferred limits and bankroll. For example, allocating more than $1,000 for a purchase Simple Postflop for a player starting with NL10, it can be considered an overkill. Many experienced regulars prefer this software, also paying extra for other products from the same developers.

It cannot be said that some software is overrated or undervalued. The cost is formed by the market, so it is important to set specific goals and gradually move towards achieving them.

In the early stages of studying GTO, it is recommended to choose programs such as GTO+ for installation on a PC and GTO Wizard to study ready-made solutions in the browser. As the bankroll grows, other software options can be considered, although many successful players at the highest limits also use these programs.

 

Limiting the use of software in real time

Despite the importance of a GTO-style game and programs for its calculation, it is important to remember that strategy development should take place outside the gaming tables. Poker solvers should be considered as a means to gain knowledge, and using them in real time in a game against live opponents violates the rules of poker rooms and the ethical norms of the poker community. It is important to emphasize that the ban does not apply to the programs themselves, since they are not able to provide a solution in a limited time. However, scammers can create software based on calculation trees that analyzes the situation at the gaming table. Poker rooms consider such violations as a serious crime, and sanctions, if discovered, usually include not only account blocking, but also confiscation of funds in the account.

Poker rooms themselves provide built-in security programs in their software, which determine the status of open auxiliary software.

Even using the program Flopzilla during the hand, it may cause temporary closure of access to the account until the player provides an explanation of the circumstances.