Calculate the long-term average outcome of a random variable.
Outcomes & Probabilities
Enter outcome/probability pairs separated by space or comma.
Expectation Analysis
Expected Value E[X]25Long-term profit
Total Probability Σp1.000Valid Probability Space
Outcome Count2
Weighted Breakdown
100P = 0.5
50Contribution
-50P = 0.5
-25Contribution
About this calculator
Overview
The Expected Value is the weighted average of all possible outcomes of a random variable. It represents the value you would expect to see 'on average' if the experiment were repeated an infinite number of times.
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Pro Tips
Probabilities should sum to exactly 1.0; if they don't, the result is technically a weighted average, not a true expectation.
For financial bets, an EV > 0 means the bet is profitable in the long run.
Expected value doesn't tell you what will happen in a single trial, but what happens over many trials.
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Mathematical Formula
The expected value is the sum of each outcome multiplied by its probability:
