Part III: Business & Regulation · Gambling Mathematics & Probability

8. Variance

Foundational Probability

Variance measures the statistical dispersion of outcomes around the expected value, quantifying how far actual results deviate from the theoretical average. In casino games, high variance means results fluctuate wildly — players may experience long losing streaks punctuated by large wins. Slot machines typically have higher variance than table games because they feature rare but large jackpot payouts among many small losses. Casino operators must understand variance because it affects cash flow, player psychology, and the time required for games to converge to their theoretical house edge. Surveillance analysts use variance calculations to determine whether observed results are within normal statistical ranges.

In practice

Formula for variance of a bet: Var = (P(win) x (Win Amount - EV) + P(lose) x (Loss Amount - EV)). Variance increases with the square of bet size. High-variance games require larger bankrolls for both players and casinos.

One entry from the Casino Industry Glossary — 1,157 terms written for surveillance, compliance and operations professionals rather than for players. Definitions describe industry usage; where a term carries a regulatory meaning, verify against the instrument that governs your jurisdiction.