Part III: Business & Regulation · Gambling Mathematics & Probability

2. Odds

Foundational Probability

Odds represent the ratio of the probability of an event occurring to the probability of it not occurring. In casino terminology, odds are commonly expressed as the payout ratio offered to a winning player — for example, “35 to 1” on a single-number roulette bet means a player wins $35 for every $1 wagered. It is critical to distinguish between true odds (the mathematically correct payout based on actual probability) and payout odds (the amount the casino actually pays, which is always lower than true odds to create the house edge). Surveillance staff should understand that odds are not the same as probability: odds of 35:1 correspond to a probability of 1/36.

In practice

Odds can be expressed “to one” (profit only) or “for one” (including the original wager). European roulette single-number odds are 35:1 (to one), which is equivalent to 36:1 (for one).

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.