Game Theory & Decision

Basic

Expected Value

Probability-weighted average outcome of a decision.

Formula

EV = \sum_i p_i x_i

Variables

EVExpected value

p_iProbability of outcome i

x_iPayoff i

Example

50% win $100, 50% lose $40: EV = $30

Did You Know?

Rational players choose the option with the highest expected value — the foundation of decision theory.

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More in Game Theory & Decision

Kelly Criterion

Optimal fraction of bankroll to bet for long-run growth.

Expected Utility

Weighted average of the utility of outcomes, not just their cash value.

Payoff Comparison

One strategy dominates another if its payoff is always higher.

Minimax Value

Best worst-case payoff a player can guarantee.

Mixed Strategy (Indifference)

Probability that makes an opponent indifferent between their options.

Bayes' Theorem

Update a belief's probability given new evidence.