Expected Value
Calculator
Results
- Expected value
- 80
Statistical results
| Expected value | 80 |
formula-map diagram
- Expected value
- 80
Statistical relationship
Formula
EV = p × gain − (1 − p) × loss= 80
Note
This is a simplified model: it applies the displayed standard formula to the summary values you entered and assumes their underlying conditions (independence, normality, correct sampling) hold. It does not analyse a real data set. Check the assumptions before relying on the result.
More in Statistics and probability
See all →Frequently asked questions
What is expected value and what does it represent?+
Expected value is the long-run average outcome of a random process if it were repeated many times, calculated by summing each possible outcome multiplied by its probability. It doesn't predict any single event, only the average over many repetitions.
Why can expected value be a number that never actually occurs?+
Because it's a probability-weighted average, expected value can land between the actual possible outcomes, like an expected value of 3.5 for a single die roll even though you can never actually roll a 3.5. That's normal and expected for this kind of average.
How is expected value used to evaluate a bet or investment?+
A bet with a positive expected value is, on average, profitable over many repetitions, while a negative expected value means you'd lose money on average over time. Most casino games and lottery tickets have a negative expected value for the player by design.
Does a positive expected value guarantee a win in any single instance?+
No. Expected value describes averages over many trials, not guarantees for a single event; you can have a positive expected value bet and still lose on any given attempt, especially if the probability of the good outcome is low, even if the payoff is large.
How does variance relate to expected value?+
Two options can have the same expected value but very different risk profiles, one with outcomes clustered tightly around the average and another with wide swings. Expected value alone doesn't capture that risk, which is why it's often considered alongside variance or standard deviation.