Game Theory Optimal Strategy in Poker

Game Theory Optimization (GTO) in Texas hold 'em poker is a strategy that employs game theory, a branch of mathematics. It refers to a situation where two perfect players cannot successfully make an exploitable play against each other. Poker is an unsolved game and as a result, there is no true game theory solution.^[1] However, a game theory optimal play does exist, and can be used to capitalize on players who are inexperienced with the strategy.[1]

History

Game theory optimal play in poker has its roots in mathematical models. Game theory is the study of exchanges between two (or more) rational decision-makers. ^[2] Originally, it belonged to zero-sum games, but now exists as an umbrella term for study of logical decision making between humans, AI, and animals. Its proof was first formulated by John von Neumann, a mathematician and physicist. He used used the Brower fixed point theorem, which was the foundation bedroom of the theory. In 1944, the book Theory of Games and Economic Behavior expound on idea of cooperative games amongst several players. In 1950, game theory was analyzed further by scholars such as Jean Tirole and John Maynard Smith. Both these individuals went on to win awards for their respective fields.

Understanding GTO and its Limited Applications

Near the early 21st century, GTO gameplay has been a staple amongst the vernacular of poker players. Only a quasi-GTO gameplay exists for poker, because true GTO solutions only exists for solved games. For example, take the the game Rock, Paper, Scissors:

The GTO percentage to throw each option would be 33%--that is, Rock 33%, Paper 33%, and Scissors 33%.^[3] Two perfect players would be virtually unexploitable if they knew exactly what the other player was thinking. In the long run, a player would not win as there is no exploitation of mistakes. To do so, requires the deviation of two imperfect players.

The existence of optimal solutions (or Nash Equilibria) is something of particular importance to poker. However, poker is a game that is far too complex to be solved by today's computers, and thus, true game theory optimal play serves little use to players. Players are still able to benefit the fundamental rules by studying game theory for poker, but its true workings are simply too complex for the poker table. Due to this, many players have simply named is "psuedo-optimal" play, as the exact solution is yet to be solved. Many approaches to this game theory applications in poker remain highly theoretical.

Pros of GTO Play (With Regards To AI)

Difficult to exploit

The point of a true GTO play is to be unexploitable as one assumes the role of an omniscient perfect player. In a hypothetical situation where took two perfect AI players (programmed with data that contained solved poker), neither player would be able to exploit each other. For example, take a solved game like Connect Four. If one took two perfect players, who ever drops the disc first, will inevitable win. However, no exploitation exists since both players are perfect, and therefore, the first-to-act player will simply win due to the nature of the game.

Profitable against weaker opponents

While GTO play is something many don't have mastery over in the lower-stake games, it serves as a strong tool amongst nosebleed tournaments (high-stakes) and cash games. In 2017, two Carnegie Mellon researchers built an AI that defeated four top players in a game of poker. In this example, because the AI has immense computational power, there simply is no way an unassuming human player can profitably win.

A great defensive strategy

This works especially well when one plays with another player of whom they know nothing about. Much of poker relies on exploiting the opponent's tendencies whether through bet-sizing, physical tells or limps (that is, when the player elects to just call). Such exploitation cannot exist if one is playing a GTO theory as there will be no weakness to gain from.

Cons of GTO Play

Hard to fully compute

Whenever a player makes a move on the felt, there exists a complex decision tree. As a result, no player will be able to fully use a GTO play without computer assistance. The closest players can get is to emulate GTO play based on theoretical concepts.

Sacrifices profits against stronger opponents

Most money can be won by playing against stronger opponents as they are usually equipped with a deep stack (a wealth of chips). Because GTO play is the balanced in its offence and defence, it can sometimes sacrifice the most +EV decision for a more balanced one.