What Is the Difference Between Pure and Mixed Strategy Under Game Theory?


Martha Robinson

Game theory is a fascinating area of study that deals with the analysis of strategic interactions between individuals or groups. At its core, game theory explores how people behave when they are faced with choices that depend on the choices of others.

One of the most fundamental concepts in game theory is the distinction between pure and mixed strategies. Understanding the difference between these two types of strategies is essential for anyone interested in game theory.

Pure Strategy

A pure strategy in game theory refers to a specific course of action that a player takes in a given situation. This course of action is determined entirely by the player’s preferences and does not depend on any random factors or uncertainty.

For example, imagine you are playing rock-paper-scissors with a friend. If you always choose “rock,” regardless of what your friend chooses, then you are using a pure strategy. You have made a deliberate decision to always choose “rock,” and this decision does not depend on any external factors.

Mixed Strategy

In contrast, a mixed strategy involves randomizing your choices based on probabilities. With a mixed strategy, each possible choice has some probability associated with it, and you select one of those choices at random according to those probabilities.

Continuing with our rock-paper-scissors example, if you decide to choose “rock” 50% of the time and “paper” 50% of the time, then you are using a mixed strategy. This means that sometimes you will choose “rock” and other times you will choose “paper.”

The Key Differences

The key difference between pure and mixed strategies lies in their level of determinacy. Pure strategies are entirely determined by the player’s preferences, while mixed strategies involve some element of randomness or uncertainty.

Another important difference is that pure strategies tend to be easier to analyze than mixed strategies. Because pure strategies involve only one possible course of action, it is often possible to determine the best strategy for a player in a given situation. In contrast, mixed strategies can be more challenging to analyze because they involve probabilities and randomness.

When to Use Which Strategy?

The decision of whether to use a pure or mixed strategy depends on the specific situation and the preferences of the player. In some cases, a pure strategy may be more effective because it allows the player to make a clear, decisive choice based on their preferences. In other situations, a mixed strategy may be more effective because it can introduce an element of unpredictability that can be advantageous.

Ultimately, the choice between pure and mixed strategies is one that must be made carefully and thoughtfully. By understanding the differences between these two types of strategies, however, you will be better equipped to make informed decisions in game theory scenarios.


In conclusion, pure and mixed strategies are fundamental concepts in game theory that help us understand how people behave in strategic interactions. Pure strategies involve making deliberate choices based on preferences, while mixed strategies introduce an element of randomness through probabilities.

By understanding these concepts and their differences, you will have a better appreciation for game theory and its applications in fields as diverse as economics, political science, and psychology.