How it works
The expected value is the probability-weighted average of all possible outcomes: what you would average per trial if you repeated the situation many times. It is the standard way to compare bets, insurance, investments and business decisions under uncertainty.
Enter each outcome on its own line as a value and its probability. A bet that wins $100 with 10% chance, wins $20 with 30% chance and loses $10 with 60% chance has an expected value of 100 × 0.1 + 20 × 0.3 − 10 × 0.6 = $10 per play.
The standard deviation shows how much individual results swing around the expected value; two choices with the same expected value can carry very different risk.
Formula
E[X] = Σ xᵢ pᵢ · Var(X) = Σ pᵢ (xᵢ − E[X])²
Questions people ask
Does a positive expected value mean I will win?
No. It means you would come out ahead on average over many repetitions. Any single trial can still lose, and with high variance a long losing streak is possible.
Can the expected value be a value that never actually occurs?
Yes. The expected roll of a fair die is 3.5, even though no single roll can be 3.5.
What if my probabilities do not add to 1?
Then the list of outcomes is incomplete or the probabilities are off. The calculator checks the total and asks you to fix it.