Expected Utility Calculator - Risk Decision Analysis

The expected utility calculator summarizes a decision with uncertain outcomes by combining each outcome’s probability and utility. Utility is a decision-specific measure of value or satisfaction; it does not have to equal money. An investor might assign utilities to portfolio outcomes, a manager to expansion scenarios, or a household to insurance choices. Probability weighting produces one comparable expected utility while preserving the decision maker’s chosen scale. For discrete outcomes, expected utility equals the sum of each probability multiplied by its utility. Probabilities are entered as percentages and must total 100. The calculator also computes probability-weighted variance and standard deviation around the expected utility. These dispersion measures describe how widely outcomes differ from the average, which is important because two choices can share the same expected utility but expose the decision maker to very different downside and upside ranges. The optional risk-tolerance factor ranges from zero to one, with 0.5 treated as neutral. The expected utility calculator applies an explicit comparison adjustment: expected utility plus (risk tolerance - 0.5) × two × standard deviation. A lower factor penalizes dispersion, while a higher factor rewards upside variability. This is a practical sensitivity score, not a universal law of expected utility theory. Formal analysis normally captures risk preference inside a concave, linear, or convex utility function before probabilities are applied. Use the outputs to structure conversations, compare alternatives on one utility scale, and test how conclusions change when estimates move. Build outcomes that are mutually exclusive and collectively exhaustive, document the evidence behind each probability, and avoid double-counting consequences. Sensitivity analysis is essential: uncertain probabilities or utility judgments should be varied across plausible ranges rather than hidden behind a single precise result. The method cannot make an uncertain decision objectively correct. Probabilities may be biased, rare outcomes may be omitted, and utility assessments can change with wealth, time, or organizational priorities. Expected utility also does not show liquidity constraints, irreversible consequences, or ethical considerations unless those factors are represented in the utility values. Use the expected utility result as a transparent decision framework, then combine it with scenario narratives, risk limits, expert review, and updated evidence before making a consequential commitment.