Casino mathematics uses a small set of ideas again and again. This glossary defines them in plain language, with a worked number where it helps, and links to the entries where we cover them in depth.
Core quantities
| Term | Definition |
|---|---|
| House edge | The average share of each bet the casino keeps over the long run. Single-zero roulette: 2.70%. See House Edge of Every Casino Game, Ranked. |
| RTP (return to player) | The share of stakes a game pays back on average: 100% minus the house edge. |
| Expected value (EV) | The average result of a bet if repeated many times. Negative for every standard casino bet. |
| Expected loss | Total amount bet × house edge. 1,000 units bet at 2.70% means an expected loss of 27 units. |
| True odds | The ratio of losing to winning outcomes. A single number in single-zero roulette: 36 to 1. |
| Payout odds | What the casino actually pays. A single number: 35 to 1. The gap between true and payout odds creates the edge. |
Variation and risk
| Term | Definition |
|---|---|
| Variance / volatility | How widely results spread around the average. See Volatility and Session Length. |
| Standard deviation | A measure of that spread, in the same units as the bet. |
| Hit frequency | How often a bet or game pays anything at all, regardless of size. |
| Gambler's ruin | The near-certainty that a player with a finite bankroll eventually loses it against a game with a house edge, if play continues long enough. |
| Bankroll | The money set aside for gambling. |
Probability ideas
| Term | Definition |
|---|---|
| Independence | One outcome does not affect the next. Roulette spins and dice rolls are independent. |
| Gambler's fallacy | Believing a result is "due" after a streak. See The Gambler's Fallacy. |
| Law of large numbers | Over many trials, the average result approaches the expected value. |
| Combinations | The number of ways an outcome can happen; two dice have 36. See Craps Odds Explained. |
Game-specific terms
| Term | Definition |
|---|---|
| Basic strategy | The best play for every blackjack hand. See Blackjack Basic Strategy and House Edge. |
| Commission | The share of banker wins taken in baccarat, usually 5%. See Baccarat: The Math of Banker vs Player. |
| La partage / en prison | Roulette rules that return half of an even-money bet when zero comes up, halving its edge. |
| Martingale | Doubling the stake after each loss. See Why the Martingale System Fails. |
| RNG | Random number generator, used by digital games to decide outcomes. |
Worked example: Putting several terms together. A single-number roulette bet has true odds of 36 to 1 and payout odds of 35 to 1. Its expected value per unit is (1/37 × 35) − (36/37 × 1) = −1/37, a house edge of 2.70% and an RTP of 97.30%.
Key point: Almost every casino question reduces to two numbers: the house edge, which sets the average cost, and the volatility, which sets how far a session can stray from it.
Watch out: Understanding casino maths does not create an advantage. It shows the cost. Play only with money you can afford to lose, and set limits before you start.
Try the numbers on any roulette bet with the roulette odds and house edge calculator.
- House edge, RTP and expected loss describe the average cost.
- Volatility, standard deviation and hit frequency describe how results spread.
- True odds versus payout odds is where every house edge comes from.
Sources
- Gambling mathematics — Wikipedia
- Law of large numbers — Wikipedia
18+ only. No betting system changes the house edge. See our Responsible Gambling page.
RTP Data explains the mathematics of casino games, with every figure sourced or worked out in the text.