The math of roulette
Roulette pays as if the wheel had 36 pockets, but it has 37 or 38. The extra zero pockets are the casino’s edge. No betting system can change that: every bet on the same wheel carries nearly the same expected loss.
Wheel types
- American: 0 and 00, 38 pockets. House edge 5.26% on every bet except the five-number bet (0-00-1-2-3), which is worse at 7.89%.
- European: a single 0, 37 pockets. House edge 2.70%.
- French: a single 0 plus the la partage (or en prison) rule: when the ball lands on zero, even-money bets lose only half. The edge on those bets falls to 1.35%.
Bets and payouts
| Bet | Numbers covered | Payout |
|---|---|---|
| Straight up | 1 | 35 to 1 |
| Split | 2 | 17 to 1 |
| Street | 3 | 11 to 1 |
| Corner | 4 | 8 to 1 |
| Six line | 6 | 5 to 1 |
| Dozen or column | 12 | 2 to 1 |
| Red/black, odd/even, high/low | 18 | 1 to 1 |
The probability of winning is the numbers covered divided by 37 or 38.
Example
$10 on red, 100 spins, American wheel:
- chance of winning each spin: 18 ÷ 38 = 47.4%;
- expected value per spin: 18/38 × 10 − 20/38 × 10 ≈ −$0.53;
- total wagered: $1,000; expected loss about $53.
On a European wheel, the expected loss for the same play would be about $27.
Why systems do not work
Martingale (doubling after each loss) and similar systems change the shape of the results, many small wins and occasional large losses, but not the expected loss. Table limits and finite bankrolls guarantee that a long losing streak eventually wipes out the gains. Each spin is independent: a run of reds does not make black more likely.
Variance
Over a short session, anything can happen; over thousands of spins, results converge toward the house edge. The more you wager in total, the closer your loss gets to the expected value.
Play responsibly
Treat gambling as paid entertainment, set a budget and a time limit in advance, and never chase losses. If gambling is causing problems for you or someone close to you, the National Problem Gambling Helpline at 1-800-GAMBLER offers free, confidential help 24/7.