Game Theory & Decision

Advanced

Bayes' Theorem

Update a belief's probability given new evidence.

Formula

P(A|B) = \frac{P(B|A)P(A)}{P(B)}

Variables

P(A|B)Posterior probability

P(B|A)Likelihood

P(A)Prior

P(B)Evidence

Example

Updating the chance of a disease after a positive test.

Did You Know?

Bayes' rule powers spam filters, medical diagnosis and the reasoning of modern AI systems.

game theory bayes probability decision

Share this formula

More in Game Theory & Decision

Expected Value

Probability-weighted average outcome of a 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.