Computing expected value across uncertain outcomes
Expected value is the sum of all possible outcomes, each weighted by its probability. If option A has a 70 percent chance of gaining 100 and a 30 percent chance of losing 50, its expected value is (0.7 x 100) + (0.3 x -50) = 70 - 15 = 55. If option B has a 50 percent chance of gaining 80, its expected value is 40. On paper, option A is better.
This framework prevents gut feelings from overweighting unlikely but vivid outcomes. It disciplines you to estimate both probability and magnitude separately. Many people reject option A because the 30 percent loss feels too risky, even though the expected return is much higher. The decision tree makes that tradeoff visible.
Practical limits and decision-making shortcuts
Expected value works best for decisions you face repeatedly, where the averages eventually converge to your forecast. For one-off, high-stakes decisions, it can fail: a 10 percent chance of bankruptcy is not the same as losing 10 percent of your wealth, even if the dollar expected values match. You care about ruin risk in ways the formula cannot capture.
In practice, expected value serves as a discipline for thinking clearly about uncertainty rather than a calculation that replaces judgment. It prevents you from ignoring the low-probability tail risks and from overweighting unlikely catastrophes. Use it to structure the decision, then apply additional considerations like regret, reversibility, and personal values to make the final call.