Expected Value Calculator
Expected Value Calculator
Enter a comma-separated list of possible outcomes (values) and a matching comma-separated list of their probabilities. This calculates the expected value — the probability-weighted average of all possible outcomes.
Expected value is how you compare bets, investments, or decisions with uncertain outcomes on a level footing — a lottery ticket, an insurance policy, or a business decision with several possible payoffs can all be reduced to a single expected-value number. It's important to remember that expected value describes the long-run average across many repetitions, not a prediction of any single outcome: a game with a positive expected value can still lose money on any individual play, and your list of probabilities should sum to 1 (100%) for the result to be meaningful.
- Formula: E(X) = Σ (value × probability) — sum each outcome multiplied by its own probability of occurring.
- Probabilities should sum to 1: a valid probability distribution across all listed outcomes should add up to 100% (1.0).
- Not a prediction of any single outcome: expected value describes the long-run average across many repetitions — a single trial can land far from it (e.g. a lottery ticket's expected value is usually negative even though the winning outcome is huge).
What does a negative expected value mean?
It means that, on average across many repetitions, you'd lose more than you gain — common in gambling and insurance from the customer's side, where the "house" or insurer sets it up so their own expected value is positive.
Do the values and probabilities lists need to be the same length?
Yes — each value must be paired with exactly one probability, so the two comma-separated lists should contain the same number of entries in matching order.
Expected Value Calculator
Enter a comma-separated list of possible outcomes (values) and a matching comma-separated list of their probabilities. This calculates the expected value — the probability-weighted average of all possible outcomes.
Expected value is how you compare bets, investments, or decisions with uncertain outcomes on a level footing — a lottery ticket, an insurance policy, or a business decision with several possible payoffs can all be reduced to a single expected-value number. It's important to remember that expected value describes the long-run average across many repetitions, not a prediction of any single outcome: a game with a positive expected value can still lose money on any individual play, and your list of probabilities should sum to 1 (100%) for the result to be meaningful.
- Formula: E(X) = Σ (value × probability) — sum each outcome multiplied by its own probability of occurring.
- Probabilities should sum to 1: a valid probability distribution across all listed outcomes should add up to 100% (1.0).
- Not a prediction of any single outcome: expected value describes the long-run average across many repetitions — a single trial can land far from it (e.g. a lottery ticket's expected value is usually negative even though the winning outcome is huge).
What does a negative expected value mean?
It means that, on average across many repetitions, you'd lose more than you gain — common in gambling and insurance from the customer's side, where the "house" or insurer sets it up so their own expected value is positive.
Do the values and probabilities lists need to be the same length?
Yes — each value must be paired with exactly one probability, so the two comma-separated lists should contain the same number of entries in matching order.