Part III: Business & Regulation · Gambling Mathematics & Probability

14. Independent Events

Foundational Probability

Two events are independent if the outcome of one event has no effect on the probability of the other event occurring. In casino games, roulette spins, dice rolls, and slot machine spins are all independent events — the result of one trial does not influence the next. This mathematical property is crucial because it means no betting system can overcome the house edge through pattern-based wagering. Many players erroneously believe in “hot” or “cold” streaks, but for independent events, the probability remains constant regardless of previous outcomes. Games like blackjack involve dependent events because removing cards from the deck changes the probabilities for subsequent hands.

In practice

Testing for game randomness and independence is a core function of gaming laboratories like GLI and eCOGRA. Slot machine RNGs are specifically designed to produce independent outcomes on each spin.

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.