Expected Payoff Matrix Calculator

About this calculator

In game theory, a payoff matrix lays out the outcome for every combination of two players' strategies. When each player mixes their strategies with certain probabilities rather than committing to one choice, the expected payoff is the probability-weighted average across all four cells: it sums each payoff multiplied by the joint probability of the row and column strategies that produce it. This calculator takes a 2×2 matrix plus the row and column probabilities and returns that expected value, alongside the best and worst outcomes under pure strategies.

This calculation underlies mixed-strategy Nash equilibrium analysis, taught in economics, game theory and decision science courses to model situations like pricing competition, auctions or the classic matching-pennies and battle-of-the-sexes games. Analysts and strategists use the same expected-payoff logic outside the classroom too — in negotiation modeling, risk assessment and any decision where outcomes depend on an opponent's or counterparty's uncertain choice.