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# A Basic Guide to Game Theory

## Background

Game Theory was developed during the Second World War by John von Neumann, a mathematician, and Oskar Morgenstern, an economist, and developed by US mathematician John Forbes Nash Jr. In a 1951 article on Non-Cooperative games, Nash stated that at least one ‘Nash Equilibrium’ is present in any mixed strategy game with a finite set of actions. In relation to poker, it means that there exists an equilibrium called game theory optimal (GTO).

## Nash Equilibrium

A Nash Equilibrium is defined as a situation in which players’ strategies result in the best possible decisions, taking into account the decisions of others. Taking the game of poker to the stage where players are in Nash Equilibrium results in maximum expected value (EV) play for every decision the player makes assuming he faces perfect opponents. The principles of Game Theory detail the process via which you reach Nash Equilibrium and hence a more profitable level of play.

## Strategy

Game theory is an optimised strategy which is intuitive and simple to understand. It is a purely mathematical model that is independent of opponents’ skill and playing style. In the simplest terms, GTO strategy provides the best decision at a given moment for a poker player by taking into consideration what your opponent's best strategy is.

## Example

Taking the example of bluffing: should you bluff for £50 when attempting to win a £200 pot? If you always bluff, your opponent should always call with his semi-weak hands. And if you never bluff, your opponent should never call with his semi-weak hand. Of course the player shouldn't bluff all of the time, but must bluff some of the time to improve his EV. But more importantly, he must consider his opponent's options. If he has a weak hand does this mean a bluff will succeed? What if he raises? Should he just give him the pot, or should he re-raise? Through Game Theory, players can determine how often they should bluff, and how often they should take any other poker actions. Following GTO strategy allows players plenty of opportunities to collect positive EV from opponents that make GTO mistakes.

## Advantages & Disadvantages

Critics have argued that Game Theory is very defensive, and prioritises not losing over attempts to win. It’s true that Game Theory does not necessarily mean the most profitable play in a certain situation: it simply means making a decision that will show a profit – no matter what your opponent does (profit can also mean losing as little as possible, e.g when playing in the Blinds). Opponents are still liable to make mistakes, meaning a loss in EV, while those employing a GTO approach will never hand out EV to their opponents.

Game Theory centres on maximizing profit, and making the decision that will profit the most. To that end it is unexploitable, and can be viewed as being without risk. The one acknowledged deficiency of the strategy is that it doesn’t maximise profit against weak opponents. When facing such opponents, alternative strategies (such as Heads-Up Displays, or HUDs) can yield greater returns.

## Comments

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