Expected Value Calculator

How to Use This Calculator

1. Enter probability % and value for each outcome (probabilities should sum to 100%).
2. EV = Σ(p × v) is computed instantly.
3. Use the 5 Outcomes tab for more complex distributions.
4. Use Compare 2 Scenarios to find the higher-EV option.
5. Use Professional for variance, risk-adjusted EV, and decision theory metrics.

Formula

Example

Frequently Asked Questions

• What is expected value? ▼
  Expected value (EV) = Σ(probability × value) for all outcomes. It is the long-run average outcome if you repeated the same random event many times. EV > 0 means favorable; EV < 0 means unfavorable.
• How do I calculate EV with 3 outcomes? ▼
  EV = P1×V1 + P2×V2 + P3×V3, where probabilities must sum to 1 (100%). Example: 50% chance of +$100, 30% of $0, 20% of −$50: EV = 0.5(100) + 0.3(0) + 0.2(−50) = 50 − 10 = $40.
• What is variance in expected value? ▼
  Variance = Σ[p × (v − EV)²]. It measures how spread out outcomes are around the expected value. High variance means outcomes vary widely even if EV is positive. Standard deviation = √Variance.
• What is risk-adjusted EV? ▼
  Risk-adjusted EV = EV − λ×σ, where λ is a risk-aversion factor and σ is standard deviation. A risk-neutral investor uses λ=0; a risk-averse person uses λ=0.5–1.0, penalizing high-variance choices.
• What is the gambler's fallacy? ▼
  The gambler's fallacy is the false belief that past independent outcomes affect future ones. If a fair coin lands heads 10 times, the next flip is still 50/50. Each trial is independent; past results don't change probabilities.

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