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🎲 Expected Utility Calculator

Calculate the expected utility of a risky choice with two possible outcomes, using a standard risk-averse utility function.

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What is expected utility?

Expected utility theory, a cornerstone of decision theory and economics, weighs the desirability (utility) of each possible outcome of a risky choice by its probability, rather than just its dollar value.

The formula

Expected Utility = Σ (Probability of Outcome × Utility of Outcome). This calculator uses the common square-root utility function (U(x) = √x) to model a risk-averse decision-maker, where each extra dollar adds progressively less satisfaction. The certainty equivalent is the guaranteed amount that would provide the same utility as the risky gamble.

This is a simplified educational model of a much richer field of decision theory.

Last reviewed August 2026