Expected value is the most powerful concept in decision-making. It tells you what an outcome is worth on average, accounting for all possibilities and their probabilities. Every smart bet, investment, and business decision implicitly uses expected value analysis.
Step 1: Basic Probability
P(event) = Favorable Outcomes / Total Possible Outcomes Probability ranges from 0 (impossible) to 1 (certain). Often expressed as a percentage.
Step 2: Expected Value
EV = Σ(Outcome_i × Probability_i) Multiply each outcome by its probability and sum. Positive EV means profitable on average.
Example: A coin flip game pays $10 on heads and costs $6 on tails. EV = (0.5 × $10) + (0.5 × -$6) = $5 - $3 = +$2. On average, you gain $2 per flip. Calculate with the Expected Value Calculator.
Step 3: Real-World Applications
| Decision | EV Calculation | Result |
|---|---|---|
| Insurance ($1,200/yr, 2% claim probability, $50,000 payout) | (0.02 × 50,000) + (0.98 × 0) - 1,200 | EV = -$200/yr |
| Job offer (80% chance of $90K, 20% chance of $120K startup) | (0.8 × 90K) + (0.2 × 120K) | EV = $96K |
Insurance has negative EV but positive value for catastrophic risk protection — expected value is a starting point, not the complete answer.
Calculate expected value for any set of outcomes and probabilities
Try the Expected Value Calculator →Key Takeaways
- EV = Σ(outcome × probability) for all possible outcomes.
- Positive EV decisions are profitable on average over many repetitions.
- Insurance is negative EV but valuable for catastrophic risk — EV is not the only factor.
- Combine EV with risk tolerance for complete decision-making.