How to Calculate Expected Value
What is Expected Value?
Expected Value (EV), also called mathematical expectation, is the probability-weighted average of all possible outcomes of a random variable. It represents the long-run average result if an experiment is repeated many times. EV is the cornerstone of decision theory, financial modelling, insurance, and gambling strategy.
Formula
- E
- Σ xᵢ × P(xᵢ) for all outcomes i — Σ xᵢ × P(xᵢ) for all outcomes i
- X
- Σ xᵢ × P(xᵢ) for all outcomes i — Σ xᵢ × P(xᵢ) for all outcomes i
- P
- P value — Variable used in the calculation
Step-by-Step Guide
- 1E(X) = Σ xᵢ × P(xᵢ) for all outcomes i
- 2All probabilities must sum to 1
- 3Variance σ² = Σ P(xᵢ) × (xᵢ − E(X))²
- 4Standard deviation σ = √Variance — measures spread around the mean
- 5A positive EV game is profitable in the long run; negative EV is a loss
Worked Examples
Frequently Asked Questions
What is Expected Value?
Expected Value (EV), also called mathematical expectation, is the probability-weighted average of all possible outcomes of a random variable. It represents the long-run average result if an experiment is repeated many times
How accurate is the Expected Value calculator?
The calculator uses the standard published formula for expected value. Results are accurate to the precision of the inputs you provide. For financial, medical, or legal decisions, always verify with a qualified professional.
What units does the Expected Value calculator use?
This calculator works with inches. You can enter values in the units shown — the calculator handles all conversions internally.
What formula does the Expected Value calculator use?
The core formula is: E(X) = Σ xᵢ × P(xᵢ) for all outcomes i. Each step in the calculation is shown so you can verify the result manually.
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