List the possible outcomes of a decision, each with a probability and a value. The tool computes the probability-weighted average — the expected value.

01What it is

Expected value is the single most useful number for comparing uncertain choices. It weights each possible outcome by how likely it is, so a large but improbable payoff and a modest but likely one can be judged on the same scale. Over many similar decisions, choosing the higher expected value is how the arithmetic works in your favour.

Each outcome contributes its value multiplied by its probability. Values can be positive or negative — gains and losses — and the probabilities should describe a complete set of what could happen, summing to one hundred percent.

02How to use it

Add a row for each outcome with a short name, its probability as a percentage, and its value in whatever unit matters — money, time, points. The expected value updates as you type, and the tool warns you if your probabilities don't add up to one hundred percent.

Keep the outcomes genuinely distinct and collectively exhaustive: every plausible result should be represented once, so the probabilities form a real distribution rather than a handful of cherry-picked scenarios.

03Reading the output

A positive expected value means the bet tilts in your favour on average; a negative one means it works against you over repetition. But expected value says nothing about a single try — a positive-EV bet can still lose, and if a bad outcome would ruin you, a good average is no comfort. Read it alongside the worst case, not instead of it.

04When to use it

Use it whenever a choice involves real uncertainty and you can estimate rough odds — taking a risk on a project, weighing an insurance decision, sizing a bet, or comparing a safe option against a volatile one.

05Worked example

Example run

A project has a 60% chance of returning $1,000 and a 40% chance of losing $500. The expected value is 0.6 × 1,000 plus 0.4 × (−500), or +$400 — positive, so worth taking if you can survive the downside and repeat similar bets. If that $500 loss would sink you, the positive average is irrelevant.

06Common pitfalls

Probabilities that don't sum to 100%. If they don't, you've either missed an outcome or double-counted one.
Ignoring ruin. A positive expected value is worthless if a single bad outcome ends the game; consider the worst case separately.
Overconfident odds. The result is only as good as your probability estimates; vague guesses produce a precise-looking but hollow number.
Applying it to one-off, unrepeatable decisions as if the average were guaranteed.

Underlying idea: Base Rates ›