Expected Value Calculator
When each choice could turn out several ways, list the outcomes with how likely they are and what they're worth. See the average payoff, and how risky each choice is.
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How to calculate expected value
- Add each choice with + Choice.
- For each, list the possible outcomes, their probability and what each is worth; probabilities should add up to 100%.
- Compare each choice’s expected value, spread, chance of a loss and worst case.
About this tool
Expected value is the probability-weighted average of the outcomes: if you could make the same choice many times, it's what you'd average per go. It's the standard way to compare options whose results are uncertain, from business bets to insurance to which job offer to take.
But you usually only make a decision once, so the average isn't the whole story. The table also shows the spread (standard deviation: how far results typically land from the average), the chance of a loss (the total probability of outcomes below zero) and the worst case. A choice with a slightly lower expected value but no chance of disaster is often the wiser one, especially if you can't afford the worst case.
Probabilities for each choice should add up to 100%. If they don't, the tool warns you and can scale them for you. Everything is saved on this device, and "Copy link" shares your setup.
Questions about expected value
What is expected value?
The probability-weighted average outcome: what you’d average per go if you made the same choice many times. A 50% chance of £100 and 50% of nothing is worth £50.
Should I always pick the highest expected value?
Not always. If you only decide once, a choice with a slightly lower average but no chance of disaster is often wiser.
What does the spread mean?
The standard deviation: how far results typically land from the average. Bigger spread means more risk.
What if my probabilities don’t add up to 100%?
The tool warns you, because the result would be misleading.