Introduction

When you play poker, you’ve probably heard terms like “GTO” and “game theory.” Because poker is a game where players compete for chips, it has a deep connection to game theory. In this article, we’ll look at how game theory was born, how it developed, and why it matters in poker. Whether this is your first time encountering game theory or you became curious through poker, we hope this helps you build a solid foundation.

1. What Is Game Theory?

From the name “game theory,” many people imagine recreational games like cards or board games. But in academia, the “games” studied in game theory cover a much wider range. A “game” refers to any situation where multiple players make decisions while considering each other’s actions, aiming to gain some kind of “payoff” (such as points or profit). As a result, game theory applies not only to entertainment like board games and card games, but also to competitive bidding, price competition between companies, international negotiations, and even biological evolution.

Game theory mathematically models these strategic situations. It expresses players’ strategies and payoffs using formulas, then searches for optimal strategies and equilibrium states. While it uses advanced mathematical tools, the theory itself was built by brilliant mathematicians in the early 20th century. Two names you can’t avoid in the history of game theory are John von Neumann and John Nash, giants who shaped many fields.

2. The Early Days: von Neumann’s 1928 Paper

When you trace the history of game theory, the first name that comes up is John von Neumann. In 1928, von Neumann published a groundbreaking paper in German titled “On the Theory of Parlor Games,” where he used mathematical analysis to model situations in which multiple players exchange points. Von Neumann was a true 20th-century genius: he helped formalize the mathematical foundations of quantum mechanics, conceptualized modern computer architecture, and even contributed to nuclear weapons development. Among his many achievements, he also established the foundations of game theory.

In 1928, von Neumann organized probabilistic games (like roulette or rock-paper-scissors, and even simple card games) into a mathematical framework and clarified key terminology and concepts. Terms like “strategy” and “payoff,” which remain fundamental in game theory today, were already being discussed at this stage. However, his ideas were so far ahead of their time that they didn’t attract much attention in academia. Some say that simply hearing “studying games with mathematics” made many researchers dismiss it as not worth serious effort. The fact that the paper was written in German also limited its spread, especially in the English-speaking world.

3. Theory of Games and Economic Behavior: The Landmark 1944 Book

More than a decade after von Neumann’s initial insights, game theory reached a major turning point in 1944 with the publication of Theory of Games and Economic Behavior, co-authored with economist Oskar Morgenstern. This massive work exceeded 600 pages, and von Neumann and Morgenstern argued that problems of interaction in economics can be analyzed mathematically through the lens of game theory.

Economists had already tried to express markets and competition using equations, but those approaches struggled to directly handle “strategic interaction,” where players influence each other’s decisions. In contrast, von Neumann and Morgenstern presented a systematic framework that began with a simple model called a “zero-sum game,” where two or more players compete over points or money, and then expanded the discussion to “non-zero-sum games.” Terms and theorems still used today, such as “zero-sum game,” the “minimax principle,” and “expected payoff,” appeared at this stage. As a result, game theory rapidly spread through economics and established itself as a major academic field.

4. Nash and the Rise of “Nash Equilibrium”

When people think of game theory, many immediately think of “Nash equilibrium.” This concept was established by John Forbes Nash in a 1950 paper. Nash, a young mathematical prodigy, proved during his PhD studies that in any finite game with any number of players, at least one equilibrium point must exist as a combination of strategies for all players. This is what we now call a Nash equilibrium. In a Nash equilibrium, if each player assumes the others’ strategies are fixed, no one can improve their expected payoff by changing their own strategy. In other words, everyone is simultaneously playing a best response, and no one has an incentive to deviate.

What made Nash’s achievement revolutionary was that he proved an existence theorem: an equilibrium always exists. Even in simple games like rock-paper-scissors, where outcomes can be perfectly balanced, it’s a separate and difficult question whether you can mathematically claim that “every game has some equilibrium.” Nash solved this challenge by using an advanced tool called a fixed-point theorem. This theorem is often associated with major contributions by Japanese mathematician Shizuo Kakutani, and it’s said that Nash realized he could complete the proof if such a theorem were available, and Kakutani’s work provided it.

5. Applications in Evolutionary Biology and Deeper Economic Theory

As game theory gained attention in economics, researchers began applying it across many other fields. One especially notable area is biology. From around the 1970s, scientists increasingly used game theory to analyze conflict and cooperation among organisms, as well as strategies among males competing for mates. This field became known as “evolutionary game theory,” and it introduced new concepts such as the Evolutionarily Stable Strategy (ESS). An ESS describes a form of evolutionary stability: when a population mostly adopts one strategy, a small number of mutants using a different strategy cannot defeat it. Organisms don’t act rationally in the human sense, but game theory fit extremely well as a way to mathematically model how “strategies” become refined under selection pressure.

Meanwhile, economics continued to develop around Nash equilibrium and non-cooperative game theory, building tools to analyze complex market competition and design auction mechanisms. Researchers who won the Nobel Prize in Economics for auction theory relied heavily on game theory at its core. It’s no exaggeration to say that game theory also powers modern systems like e-commerce bidding and online advertising auctions.

6. Poker and Game Theory: The Keyword “GTO”

When you hear “game theory,” you might also think of games like chess or shogi. These are “perfect information games,” where both players share full knowledge of the board state and build strategies from complete information. Poker, on the other hand, is an “imperfect information game.” You can see your own hole cards, but you can’t see your opponent’s. This information asymmetry forces you to infer ranges, predict actions, and choose bet and raise sizes accordingly. Players bluff, counter-bluff, and calculate expected value using probability, which creates a much wider strategic landscape.

In imperfect information games, one major mathematical goal is to find a strategy that cannot be exploited. In poker, players often call this GTO (Game Theory Optimal). Strictly speaking, “GTO” is not a formal game theory term. Instead, poker players use it as a practical label for “Nash equilibrium strategy” in a two-player zero-sum setting, from the player’s perspective: a strategy that an opponent cannot exploit.

The Foundation of GTO: Two-Player Zero-Sum Games

In poker theory, “mastering GTO” ultimately resembles “internalizing Nash equilibrium as your own strategy.” If you assume poker is a zero-sum game where two players fight over chips, then a Nash equilibrium strategy profile must exist. And if one player follows it, the opponent cannot increase expected value by deviating. However, real poker often involves multiple players, such as 6-max or 9-handed games, where Nash equilibrium analysis becomes far more complex. Many aspects of two-player zero-sum theory do not transfer directly. Still, in practice, understanding heads-up (one-on-one) GTO provides a strong foundation that you can often apply approximately in three-player or multiway situations.

7. The Rise of CFR: A Practical Way to Compute Nash Equilibria

After Nash proved that Nash equilibria exist in the 1950s, many mathematicians spent decades tackling a different problem: how do you actually compute a Nash equilibrium? As games become more complex, with more players or an enormous number of possible actions, finding the equilibrium becomes extremely difficult even if you know it exists in theory.

A major breakthrough came around 2007 with a method called CFR (Counterfactual Regret Minimization). CFR is an iterative algorithm that looks back at each decision point and asks, “What if I had taken a different action?” (this is the “counterfactual” part). It then improves the strategy in the direction that reduces regret over time. A key advantage of CFR is that in two-player zero-sum games, it is theoretically guaranteed to converge toward an “epsilon Nash equilibrium” (a Nash equilibrium with a small error). This made CFR extremely useful for fast poker simulations, especially in heads-up scenarios, and it became a critical ingredient in poker AIs that could beat human players.

8. Advances in AI: Libratus and Pluribus

The Shock of Libratus

In 2017, the poker AI “Libratus,” developed by researchers at Carnegie Mellon University, drew major attention. In heads-up no-limit Texas Hold’em, it faced top human poker pros and won. AI had already surpassed humans in perfect information games like chess, shogi, and Go, but creating an AI that could defeat professionals in poker, an imperfect information game, was a landmark achievement for both game theory and AI research.

Libratus built on CFR-style methods and used massive computational resources while gradually abstracting the strategy space. Poker includes an almost infinite number of bet sizes and situations, so Libratus grouped together spots where fine-grained differences had little impact on expected value, reducing computational load. At the same time, it calculated key situations in greater detail. This approach allowed it to search through an enormous game tree and produce strategies closer to Nash equilibrium within limited time.

The Evolution of Pluribus

Then in 2019, the same research group introduced “Pluribus,” which played 6-max no-limit Texas Hold’em and dominated professional players. Six-player poker is far more complex than heads-up. The theoretical guarantees of two-player zero-sum games no longer apply, and even running CFR extensively does not guarantee strict convergence. Despite that, Pluribus demonstrated experimentally that it could outperform top human pros. Some poker players argued that the opponents were not truly the absolute best, but the impact was still enormous: it showed that even in multiplayer poker, applying existing AI methods could surpass human performance. In fact, many pros began to believe that humans might no longer be able to beat AI.

9. Game Theory Is Still an “Unfinished” Field

As you’ve seen, game theory has already produced many results and has been applied widely, from poker and chess to economics, auctions, and evolutionary biology. But that doesn’t mean game theory has explained everything. Modern game theory still faces major challenges, including the following.

1. The nature of Nash equilibrium in multiplayer games
   In two-player zero-sum games, once you find a Nash equilibrium, playing it protects you from being exploited and guarantees a certain baseline expected value. But with three or more players, Nash equilibrium becomes much more complicated. Multiple equilibria may exist, and comparing which one is “better” can be difficult. Many aspects remain theoretically unresolved, and computing equilibria in practice requires enormous effort.

2. Fully solving imperfect information games is extremely hard
   Poker is a flagship example of an imperfect information game, and the rise of CFR-based AI might make it feel “solved.” In reality, researchers analyzed it step by step under constraints such as heads-up formats, limit betting, or fixed stack sizes. The more constraints you remove, the harder computation becomes. And as Pluribus illustrates, when non-zero-sum elements and multiplayer interactions enter the picture, we still lack strong theoretical guarantees. In many cases, we are simply producing AIs that are “empirically strong” without full theoretical backing.

3. Humans are not always rational
   Game theory assumes that each player acts rationally to maximize payoff. But real humans do not always behave rationally. Psychological biases, loss aversion, and other non-rational factors often shape decisions. These elements may sit outside classical game theory, but in recent years, behavioral economics has advanced efforts to quantify how people deviate from rational behavior.

10. Summary and Outlook

The history of game theory began with von Neumann’s 1928 paper and expanded dramatically with the 1944 publication of Theory of Games and Economic Behavior. In 1950, John Nash proved the existence of Nash equilibrium, creating a powerful foundation for mathematically analyzing strategic decision-making among multiple players. After that, applications spread beyond economics into evolutionary biology, political science, and more. In the 21st century, game theory merged with AI, leading to computers that can beat top human pros even in imperfect information games like poker. Behind these breakthroughs are algorithms like CFR and implementation techniques that cleverly manage large-scale computational resources.

Even so, game theory is not a universal tool that solves every strategic problem. As the number of players increases, as cooperation enters the picture, and as human irrationality becomes more important, the theory grows more complex and computational difficulty rises sharply. That’s why many researchers still push forward, asking how to solve larger games faster and more accurately.

In the poker world, interest in learning and applying GTO strategy has spread widely, and many top players use solvers or CFR-based study tools in some form. This is especially true in online poker, where high-stakes situations often resemble heads-up play or short-handed formats, making AI-style study increasingly essential. In real games, players also adjust based on opponent skill: they mix in exploitative lines to target weaknesses, or they shift closer to GTO to avoid being exploited themselves. Perfect GTO play requires massive computation and repetition, so humans can’t reproduce it 100%, but GTO has clearly become a practical learning framework.

This trend is a strong example of how game theory has moved beyond academia into real-world use. It applies not only to gambling and casinos, but also to everyday life. Price competition between companies, bidding systems, daily negotiations, and even social media behavior can all create “game-like situations” where multiple players pursue payoffs. In a sense, we may be using game theory intuitively more often than we realize.

Final Thoughts: How to Use Game Theory

Looking back at the history of game theory, it started with insights from a small number of genius mathematicians, then transformed economics, advanced biological theory, and even reshaped poker and AI research. What began as classical theory has now entered an era where supercomputers refine strategies through massive simulations. But humans don’t only play “games that theory can fully describe.” Where theory is incomplete, there is often the greatest room for research and innovation. As AI continues to advance, it may open new frontiers we can’t yet predict. For example, AI could intervene in situations shaped by psychological bias, or in imperfect information environments where multiple conflicting interests overlap, potentially creating new strategies for multiplayer games.

Even within poker, many open questions remain: How far can we compute in games with 6+ players? Could approaches beyond Nash equilibrium produce even stronger strategies? If supercomputers become more powerful or new mathematical breakthroughs emerge, we may eventually compute precise equilibrium strategies quickly even in larger multiplayer imperfect information games.

Some people may find “game theory” sounds unusual or overly academic. But at its core, it reflects a simple mindset: trying to understand mathematically a world where multiple players influence each other. In business, politics, social issues, and ecosystems, you can view countless situations as “games.” Applying game theory can reveal surprising insights and help you appreciate the depth of human strategy and interaction.

If learning about game theory sparked your interest in poker, consider giving poker a try. Poker isn’t just about luck. It’s full of human dynamics, strategic thinking, and probability-based decision-making. At first, learning hand strength and basic bet sizing is already fun. As you start to understand bluffing frequency and the core ideas behind GTO, the game becomes even deeper.

If you want to explore game theory academically, you can also read original works by Nash and von Neumann and challenge yourself with textbooks used in university economics or mathematics courses. You may see pages of abstract equations, but once you understand them, you’ll likely feel inspired by how mathematics can model real strategic interactions across society.

Game theory remains an evolving, unfinished field. But by following its history, you can see how much of our world is shaped by strategy and interaction. You might even start noticing moments in daily life where you think, “This feels like a game theory situation.” When that happens, simply recalling something like “What does Nash equilibrium mean again?” can broaden your perspective and make the world more interesting. That’s one of the real pleasures of game theory.