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What is the difference between a pure strategy and a mixed strategy?
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game theory
Table 1
The normal-form table illustrates the concept of a saddlepoint, or entry, in a payoff matrix at which the expected gain of each participant (row or column) has the highest guaranteed payoff.
In game theory, the distinction between pure and mixed strategies lies in how a player selects their course of action:
- Pure Strategy: A player chooses a single, specific action or move consistently. When a game has a saddlepoint, a pure strategy exists that represents the best possible choice for each player.1
- Mixed Strategy: A player chooses from a set of available actions according to a specific probability distribution. This approach is used when no single best strategy exists, as it prevents an opponent from exploiting predictable patterns in behavior.1
In many games, such as rock-paper-scissors, a mixed strategy is necessary to reach a Nash equilibrium, as choosing any single option consistently would allow an opponent to gain an advantage. The minimax theorem establishes that every finite, two-person constant-sum game has a solution involving either pure or mixed strategies, ensuring that players can enforce an optimal expected payoff.21