What is going on?
Expected value is a probability-weighted average. Multiply each result by its chance, then add the products. The average can be a value that never occurs in an individual attempt. Negative values represent losses or costs; all outcomes must use the same unit.
Work through it
- List mutually exclusive outcomes that cover every possibility.
- Assign probabilities that total 100%. This two-outcome tool calculates the second probability automatically.
- Multiply each value by its probability and add the contributions.
Put numbers to the idea
A game has a 25% chance of a net gain of 100 units and a 75% chance of a net loss of 20 units. Its expected value is 0.25 × 100 + 0.75 × (−20) = 10 units per play. A single play still produces either 100 or −20, never 10.
A little more clarity
Does positive expected value guarantee a gain?
No. It describes an average under the specified probabilities. Any individual attempt can still lose, and repeated attempts can also have a losing run.
What if there are more than two outcomes?
The same sum works for any finite number of outcomes. This page deliberately shows two so you can see each contribution clearly.
Why use net values?
If a ticket costs 5 and a winning payout is 50, the winning net value is 45 and the losing net value is −5. Leaving out the ticket cost overstates the expected result.