Expected Value Calculator
Put a single number on an uncertain choice. Enter the outcomes, their odds, and their payoffs to get the probability-weighted average — plus a look at the best and worst cases the average hides.
Expected value
Reading the result
The expected value is the long-run average payoff of the decision if you could repeat it under the same odds. A positive EV means the decision pays off on average; a negative EV means it costs you on average. Comparing the EV of two options is often the cleanest way to choose between them — take the higher one, all else equal.
But the average is only half the story. The best and worst cases show the spread you’re signing up for, and that matters most when the decision is a one-off. A choice with a slightly higher EV but a catastrophic worst case is usually the wrong one when you only get to play once and can’t afford to lose.
Frequently Asked Questions
What is expected value?
Expected value (EV) is the probability-weighted average of every possible outcome: multiply each outcome's payoff by its probability and add them all up. It answers the question, 'If I could face this exact decision many times, what would the average result be?' — which makes it the natural yardstick for repeatable choices under uncertainty.
How do I enter probabilities and payoffs?
List every outcome that could happen, give each a probability as a percentage, and enter its payoff — positive for a gain, negative for a loss. The probabilities should cover all the possibilities and add up to 100%; the calculator shows the running total so you can spot a gap or an overlap.
When is expected value the wrong tool?
EV assumes you can average over many trials, so it's a poor guide for one-shot, high-stakes decisions — especially any that carry a risk of ruin you can't recover from. A bet with a positive expected value is still a bad idea if losing wipes you out. For those, weigh the worst case and how reversible it is, not just the average.
What's the difference between expected value and expected utility?
Expected value treats every dollar (or point) as equal. Expected utility recognises that outcomes don't feel linear — losing your savings hurts far more than gaining the same amount helps, and a guaranteed sum can be worth more than a risky bet with a higher EV. When stakes are large relative to what you can afford, think in utility, not raw value.
A decision aid, not a decision. Expected value depends entirely on the probabilities and payoffs you supply, which are estimates — treat the result as one input among many.