Expected Value Calculator
Enter up to three possible outcomes and their probabilities to find the expected value.
Probabilities should be entered as decimals (e.g. 0.5 for 50%) and ideally sum to 1.
How expected value is calculated
Expected value is the sum of each possible outcome multiplied by its probability: EV = Σ(outcome × probability). It represents the long-run average result you'd expect if the same scenario were repeated many times.
The probability sum shown helps you check your inputs — for a complete, valid set of mutually exclusive outcomes, the probabilities should add up to 100%. If they don't, you may be missing an outcome or have entered a probability incorrectly.
Frequently asked questions
What does a positive or negative expected value mean?
A positive expected value means the weighted average outcome favors you over many repetitions; a negative expected value means it works against you on average, even though any single instance could go either way.
Do the probabilities have to add up to exactly 1?
For the expected value to correctly represent all possible outcomes, yes — if your probabilities sum to less than 1, you're missing at least one possible outcome from your calculation.
Is expected value the same as the most likely outcome?
No — expected value is a weighted average, which may not match any single actual outcome at all. For example, an expected value of 39 might arise from outcomes of 100, 50, and -20, none of which is 39 itself.