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