Game Math
Volatility and Session Length
Same house edge, very different sessions: exact roulette calculations of the chance of finishing ahead or going broke, by bet type and bankroll.
An almanac of casino mathematics
The math behind casino games
House edge, RTP and probability for every game, worked out in the open — so you can see exactly what a bet costs before you place it.
Table IHouse edge at a glance
| Game and bet | House edge | Average return per 100 staked |
|---|---|---|
| Baccarat — banker (5% commission) | 1.06% | 98.94 |
| Baccarat — player | 1.24% | 98.76 |
| Craps — pass line | 1.41% | 98.59 |
| Roulette — single zero (European) | 2.70% | 97.30 |
| Roulette — double zero (American) | 5.26% | 94.74 |
| Roulette — five-number bet (American) | 7.89% | 92.11 |
| Baccarat — tie (pays 8 to 1) | 14.36% | 85.64 |
Long-run averages under standard rules (baccarat: eight decks). Sources: Wizard of Odds on baccarat, craps and roulette. The average return is not what any one session will pay.
Latest entries
Myths
The Gambler's Fallacy: Monte Carlo, 1913
The night black came up 26 times in a row at Monte Carlo, the exact odds of that streak, and why past spins never make the next one more likely.
House Edge
House Edge of Every Casino Game, Ranked
The house edge of common casino bets, from the craps odds bet to keno, worked out or sourced bet by bet, with the rules each number assumes.
Game Math
Craps Odds Explained
The exact probabilities behind craps: the 36 dice combinations, why the pass line wins 49.29% of the time, the zero-edge odds bet and the bets to avoid.
Myths
Casino Math Glossary
House edge, RTP, expected value, variance, true odds and gambler's ruin: the terms of casino mathematics explained briefly, with links.
Game Math
Blackjack Basic Strategy and House Edge
What basic strategy is, why it gives blackjack one of the lowest house edges in the casino, and how rules such as 6:5 payouts and soft 17 change the numbers.
The first entries are being worked out.
Chapters
IRTP DatabasePublished return-to-player figures, game by game, each with its source.
IIHouse EdgeWhat every bet costs on average, and why.
IIIGame MathProbabilities worked out step by step.
IVMythsSystems and beliefs the numbers do not support.
18+ only. Every casino game has a house edge: over time, the casino wins. See our Responsible Gambling page.