Part III: Business & Regulation · Gambling Mathematics & Probability

3. True Odds

Foundational Probability

True odds are the mathematically accurate payout ratio that would make a bet fair — that is, with zero expected value for both the player and the house. True odds are calculated directly from the probability of winning. For example, in European roulette, a single-number bet has a 1 in 37 chance of winning, so the true odds would be 36 to 1. However, the casino only pays 35 to 1, with the difference between true odds (36:1) and payout odds (35:1) creating the house edge of 2.70%. In craps, the Free Odds bet is unique because it pays at true odds with no house advantage, making it the only commonly available casino bet without a built-in edge.

In practice

No casino game offers true odds on standard bets — the gap between true odds and payout odds is precisely how casinos generate profit. True odds are sometimes called “fair odds” in mathematical literature.

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.