Variance

Detailed Explanation

Variance (and its square root, standard deviation) quantifies the volatility of gambling outcomes around the expected value. A game with low variance produces results that cluster closely around the theoretical long-run average; high variance produces a wider range of outcomes, with more frequent large wins and large losses.

For a single even-money bet (50/50 odds), the standard deviation over 100 bets is 10 units. For roulette, blackjack, and baccarat, standard deviations per 100 units of action range from 10–11 units. For slots with bonus features or high-multiplier payouts, standard deviation can exceed 50+ units per 100 spins, indicating extreme volatility.

Variance is the primary reason why short-term results are not predictive of skill. A skilful blackjack player using basic strategy may lose over 10 sessions in a row purely due to negative variance. Over thousands of sessions, results converge toward their mathematical expectation.