Weighted Averages of Outcomes

Expected value (EV) is the average outcome you would get if you played the same game thousands of times. Flip a coin: win $10 on heads, lose $6 on tails. EV = 0.5 × $10 + 0.5 × (-$6) = $2 per flip. Over many flips, you gain roughly $2 each time.

EV does not predict any single outcome — you either win $10 or lose $6, never $2. It predicts the long-run average. Any business that handles repeated financial decisions, from casinos to insurers, uses expected value as its compass.