The math of roulette

Roulette wheel numbers and layout

The wheel order is different from the numbered betting grid. Use the single-zero diagram to identify pockets, colors and neighboring wheel positions.

European roulette wheel with 37 pockets and one zero.

Read the single-zero wheel

The supplied diagram follows the standard clockwise single-zero order beginning with 0, 32, 15, 19 and 4. Every label appears once. Eighteen pockets are red, eighteen are black and zero is green.

Wheel neighbors are not grid neighbors

Numbers next to each other around the wheel are not necessarily adjacent on the table layout. Inside split and corner bets follow the table positions. Named neighbor bets use a specified collection of component tickets.

37, 38 or 39 pockets

A European wheel has one zero. American double zero adds 00. Triple-zero games add a third zero or equivalent house symbol. The decorative photography on this site is not a layout reference; use the precise diagram.

Equal pockets in the mathematical model

The calculator assigns the same probability to each pocket and assumes independent spins. It does not analyze a physical wheel for bias and cannot predict the next result.

European roulette wheel number order

Clockwise from zero, the single-zero wheel reads:

0, 32, 15, 19, 4, 21, 2, 25, 17, 34, 6, 27, 13, 36, 11, 30, 8, 23, 10, 5, 24, 16, 33, 1, 20, 14, 31, 9, 22, 18, 29, 7, 28, 12, 35, 3, 26.

Red and black alternate around the wheel, and the low and high numbers are spread out rather than grouped.

Red and black numbers on the wheel

Red
1, 3, 5, 7, 9, 12, 14, 16, 18, 19, 21, 23, 25, 27, 30, 32, 34, 36
Black
2, 4, 6, 8, 10, 11, 13, 15, 17, 20, 22, 24, 26, 28, 29, 31, 33, 35
Green
0 (plus 00 on American and 000 on triple-zero wheels)

See the red and black roulette odds for the chance of each color.

Roulette wheel odds by pocket count

Chance of any one pocket by wheel type
WheelPocketsOne pocketAny green
European372.70%2.70%
American382.63%5.26%
Triple zero392.56%7.69%