🎯Expected Value Calculator

About this tool

List each possible outcome with its value (negative for a loss) and its probability as a percentage, a decimal or a raw weight. The tool gives the expected value, standard deviation, variance and the total over 100 plays, and warns if probabilities don't add to 100%.

What expected value tells you

The expected value (EV) is the probability-weighted average of all possible outcomes, EV = Σ x × p: what you'd average per try if you repeated a situation many times. It's how insurers price policies, how casinos guarantee an edge and how analysts compare decisions. In the example, a game that costs 5, with a 1% chance of winning 100 and a 10% chance of winning 10, has an EV of 100 × 0.01 + 10 × 0.10 − 5 × 0.89 = −2.45 per play. Expected value alone hides risk, so the tool also gives the standard deviation, √Σ p(x − EV)², which shows how widely individual results swing. Two options with the same EV can feel very different when one has a far bigger spread. Use weights if you have counts rather than probabilities, such as how often each result happened in past data, and the tool normalises them. Honest limits: a positive EV doesn't guarantee a profit over a few tries, and people reasonably weigh some outcomes, like ruin, more heavily than their face value. Not financial or gambling advice. The probability calculator and the Poisson distribution calculator are related.

Frequently asked questions