The math of roulette
Roulette bets and table layout
Learn what each standard bet covers, where it sits on the layout and how its payout works. Inside bets cover fewer numbers; outside bets cover larger groups.
Inside bets
A straight-up covers one number and a split covers two adjacent positions. A street covers a row of three. A corner covers four touching positions, and a six-line covers two neighboring streets. Their standard net payouts are 35:1, 17:1, 11:1, 8:1 and 5:1 respectively.
Outside bets
A dozen or column covers 12 numbers and pays 2:1. Red, black, odd, even, 1–18 and 19–36 each cover 18 and pay 1:1. Zero is not part of any of those groups. On an American wheel, double zero is excluded too.
A street bet example
The street 1, 2, 3 has three winning pockets. Its probability is 3/37, or 8.11%, on a European wheel. A $5 winning street bet earns $55 net profit and returns $60 including the stake.
Separate bets can overlap
Black and odd are not the same event. A number can satisfy both, one or neither. Use the multiple-bet calculator to settle every ticket on each possible outcome instead of adding percentages as if bets were independent. For a single outcome that must be both black and odd, the intersection contains eight numbers, giving 8/37 on a European wheel. Low and red intersects on nine numbers, giving 9/37. An intersection event is different from buying two separate tickets.
Called bets and named groups
Named wheel-neighbor bets are combinations of tickets, not a new universal payout. Write down the exact component bets and stake on each. Table adjacency and wheel adjacency are different, so a split cannot be inferred from two nearby wheel numbers.
Every standard roulette bet and its odds
| Bet | Covers | Payout | European | American | Triple zero |
|---|---|---|---|---|---|
| Straight-up | 1 number | 35:1 | 2.70% | 2.63% | 2.56% |
| Split | 2 adjacent numbers | 17:1 | 5.41% | 5.26% | 5.13% |
| Street | 3 numbers in a row | 11:1 | 8.11% | 7.89% | 7.69% |
| Corner | 4 numbers in a square | 8:1 | 10.81% | 10.53% | 10.26% |
| Six-line (double street) | 6 numbers, two rows | 5:1 | 16.22% | 15.79% | 15.38% |
| Dozen (1st, 2nd or 3rd 12) | 12 numbers | 2:1 | 32.43% | 31.58% | 30.77% |
| Column | 12 numbers | 2:1 | 32.43% | 31.58% | 30.77% |
| Red or black | 18 numbers | 1:1 | 48.65% | 47.37% | 46.15% |
| Odd or even | 18 numbers | 1:1 | 48.65% | 47.37% | 46.15% |
| Low (1–18) or high (19–36) | 18 numbers | 1:1 | 48.65% | 47.37% | 46.15% |
The house edge is the same for all of these bets on one wheel: 2.70% on European, 5.26% on American and 7.69% on triple zero. Only the American first-five basket differs. See the full roulette payouts and odds chart.
Dozens, columns, 1–18 and 19–36
The 1st 12 covers 1–12, the 2nd 12 covers 13–24 and the 3rd 12 covers 25–36. Each column covers the 12 numbers in one long row of the layout. Both pay 2:1 and win with probability 12/37 on a single-zero wheel. The low (1–18) and high (19–36) bets each cover 18 numbers and pay 1:1, with the same 18/37 chance as a color.
Zero never belongs to a dozen, a column or a low/high group, which is why these bets fall short of exactly one third or one half.
Split, corner and six-line examples
- A split on 17 and 20 covers two pockets: 2/37 = 5.41% on European roulette, paying 17:1.
- A corner on 1, 2, 4 and 5 covers four pockets: 4/37 = 10.81%, paying 8:1.
- A six-line on 1 to 6 covers two streets: 6/37 = 16.22%, paying 5:1.
A split must join two numbers that touch on the table layout. Two numbers that sit next to each other on the roulette wheel usually cannot be combined in one split.
Called bets on French and European tables
Some single-zero tables accept named bets that cover a section of the wheel with several chips. Voisins du zéro covers 17 pockets around zero, Tiers du cylindre covers the 12 pockets opposite, Orphelins covers the remaining 8 and Jeu zéro covers the 7 pockets closest to zero. Each chip is an ordinary split, street, corner or straight-up bet, so the house edge stays 2.70% on a standard single-zero wheel.