Expected Value: The Long-Run Average

Expected value is the average you'd get if you could repeat a gamble forever — every outcome weighted by its probability.

A fair die pays its face in dollars: (1+2+3+4+5+6) / 6 = 3.5. You'll never roll a 3.5 — EV isn't a prediction of the next roll. It's the price of admission: if the casino charges $4 a roll, you lose 50 cents per roll on average, no matter how lucky tonight feels.