The math of roulette
European roulette odds
A single-zero wheel has 37 pockets. Standard bets have a 2.70% house edge when zero loses the full stake and the usual payouts apply.
2.70%
Standard house edge
37 pockets • RTP 97.30%
One zero, 37 possible outcomes
European roulette includes 1 through 36 and a single 0. There are 18 red and 18 black numbers. A number bet wins on 1/37 of outcomes; a dozen wins on 12/37; a color wins on 18/37.
The standard house edge
For the standard bets whose coverage times total-return multiplier equals 36, expected return is 36/37. House edge is 1/37, or 2.70%. The corresponding theoretical return to player is 97.30%.
European versus American
The standard payouts remain the same when a double-zero pocket is added, but the number of losing outcomes increases. Compare 18/37 for red with 18/38. Use the same stake and payout convention when comparing results.
Check zero settlement separately
Single zero does not by itself promise La Partage. That rule changes eligible even-money bets when zero lands. Confirm the written rule rather than inferring it from a French or European label.
European roulette odds table
| Bet | Pockets | Payout | Chance | True odds |
|---|---|---|---|---|
| Straight-up | 1 | 35:1 | 2.70% | 36:1 |
| Split | 2 | 17:1 | 5.41% | 35:2 |
| Street | 3 | 11:1 | 8.11% | 34:3 |
| Corner | 4 | 8:1 | 10.81% | 33:4 |
| Six-line | 6 | 5:1 | 16.22% | 31:6 |
| Dozen / column | 12 | 2:1 | 32.43% | 25:12 |
| Red / black | 18 | 1:1 | 48.65% | 19:18 |
| Odd / even | 18 | 1:1 | 48.65% | 19:18 |
| Low / high | 18 | 1:1 | 48.65% | 19:18 |
European vs American roulette odds compared
| Bet | European | American | Difference |
|---|---|---|---|
| Straight-up | 2.70% | 2.63% | 0.07 points |
| Split | 5.41% | 5.26% | 0.14 points |
| Street | 8.11% | 7.89% | 0.21 points |
| Corner | 10.81% | 10.53% | 0.28 points |
| Six-line | 16.22% | 15.79% | 0.43 points |
| Dozen / column | 32.43% | 31.58% | 0.85 points |
| Red / black | 48.65% | 47.37% | 1.28 points |
| Odd / even | 48.65% | 47.37% | 1.28 points |
| Low / high | 48.65% | 47.37% | 1.28 points |
Over $1,000 in total wagers, the expected loss is about $27.03 on a European wheel and $52.63 on an American wheel. The European wheel has better odds on every standard bet.