Expected Value Calculator
Find the average result of a bet or decision with up to three outcomes.
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Expected Value Calculator by TheCalcTools
How the Expected Value Calculator works
Enter each possible outcome and its probability. The probabilities must sum to 100%.
The expected value is the probability-weighted average of the outcomes.
Variance and standard deviation show how widely the outcomes are spread.
The formula
Worked example
Using the default values shown in the calculator:
| Outcome 1 value | $100 |
|---|---|
| Probability 1 (%) | 10 |
| Outcome 2 value | $20 |
| Probability 2 (%) | 30 |
| Outcome 3 value | $-10 |
| Probability 3 (%) | 60 |
- E[X] = 0.10 × 100 + 0.30 × 20 + 0.60 × (−10).
- = 10 + 6 − 6 = $10.00.
- The standard deviation is 32.86.
Result:
| Expected value | $10.00 |
|---|---|
| Variance | 1,080.00 |
| Standard deviation | 32.86 |
Frequently asked questions
Does a positive expected value guarantee a profit?
Not on any single attempt. It describes the long-run average over many repetitions.
Is a bet with negative expected value always bad?
Financially it loses money on average. People may still accept it for entertainment or to insure against a larger loss.
Sources and further reading
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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.