Expected Value
Probability-weighted average outcome of a decision.
Formula
Variables
Example
50% win $100, 50% lose $40: EV = $30
How it works
Expected value tells you the long-run average result of a random choice if you could repeat it many times under the same conditions. It works by multiplying each possible outcome by how likely it is, then adding those contributions together, so unlikely outcomes count less than common ones. This gives a single number that summarizes the average payoff or cost of a risky decision.
When to use it
Use expected value when comparing games, bets, business decisions, or any situation with uncertain outcomes and known probabilities. It is especially useful for deciding whether an option is favorable on average, even if individual results can vary.
Worked example, step by step
A game pays $20 with probability 0.3, $5 with probability 0.5, and $0 with probability 0.2. EV = (0.3)(20) + (0.5)(5) + (0.2)(0) EV = 6 + 2.5 + 0 EV = 8.5 Expected value = $8.50 per play
Common mistakes to avoid
- Forgetting to include every possible outcome in the sum
- Using percentages as if they were whole numbers instead of decimals or fractions
- Adding the payoffs without weighting them by their probabilities
Did You Know?
Rational players choose the option with the highest expected value — the foundation of decision theory.
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