Roulette Odds, Payouts & House Edge by Wheel
Every payout on a roulette table is calculated from the number 36: divide 36 by the number of pockets your chip
covers and subtract 1. Because the wheel actually holds 37 pockets (European 0),
38 pockets (American 0, 00), or 39 pockets (Triple-Zero
0, 00, 000), the green pockets create a fixed house edge of
2.70%, 5.26%, or 7.69%.
Interactive Bet EV & Volatility Calculator
- Win probability
- 2.63% (1 in 38.0)
- Payout vs. true odds
- 35:1 paid vs. 37.0:1 true
- House edge (RTP)
- 5.26% (94.74% RTP)
- Expected loss over run
- −$131.58 on $2,500 action
- 1σ standard deviation
- ±$1,440.96 (±5.76 bets/spin)
- 95% session range (±1.96σ)
- −$2,955.86 to +$2,692.70
Complete Roulette Odds Table: Single-Zero (0), Double-Zero (00) & Triple-Zero (000)
Every figure below is computed directly from the pocket counts in roulette.ts. Notice that within
any wheel column, the house edge is identical for every bet except two special cases: French
La Partage / En Prison on single-zero even-money bets (1.35%),
and the 5-number Top Line basket on double-zero wheels (7.89%).
| Bet | Pockets (k) | Pays | European (0) Win % / Edge | American (00) Win % / Edge | Triple-Zero (000) Win % / Edge | Std. Dev. (Am.) |
|---|---|---|---|---|---|---|
| Straight Up (1 number) | 1 | 35 : 1 | 2.70% / 2.70% | 2.63% / 5.26% | 2.56% / 7.69% | 5.76× |
| Split (2 numbers) | 2 | 17 : 1 | 5.41% / 2.70% | 5.26% / 5.26% | 5.13% / 7.69% | 4.02× |
| Street / Trio (3 numbers) | 3 | 11 : 1 | 8.11% / 2.70% | 7.89% / 5.26% | 7.69% / 7.69% | 3.24× |
| Corner / Square (4 numbers) | 4 | 8 : 1 | 10.81% / 2.70% | 10.53% / 5.26% | 10.26% / 7.69% | 2.76× |
| Top Line / Basket (0, 00, 1, 2, 3) | 5 | 6 : 1 | N/A | 13.16% / 7.89% | 12.82% / 10.26% | 2.37× |
| Six Line / Double Street (6 numbers) | 6 | 5 : 1 | 16.22% / 2.70% | 15.79% / 5.26% | 15.38% / 7.69% | 2.19× |
| Dozen (1st 12, 2nd 12, 3rd 12) | 12 | 2 : 1 | 32.43% / 2.70% | 31.58% / 5.26% | 30.77% / 7.69% | 1.39× |
| Column (2 to 1) | 12 | 2 : 1 | 32.43% / 2.70% | 31.58% / 5.26% | 30.77% / 7.69% | 1.39× |
| Red / Black (18 numbers) | 18 | 1 : 1 | 48.65% / 2.70% | 47.37% / 5.26% | 46.15% / 7.69% | 1.00× |
| Even / Odd (18 numbers) | 18 | 1 : 1 | 48.65% / 2.70% | 47.37% / 5.26% | 46.15% / 7.69% | 1.00× |
| Low 1–18 / High 19–36 (18 numbers) | 18 | 1 : 1 | 48.65% / 2.70% | 47.37% / 5.26% | 46.15% / 7.69% | 1.00× |
| Even Money + French La Partage (0 returns ½) | 18 | 1 : 1 | 48.65% / 1.35% | N/A | N/A | 0.99× |
Why Roulette Volatility Changes While House Edge Stays Constant
Because a Straight Up bet and a Red/Black bet carry the same 5.26% house edge on an American wheel (or 2.70% on a European wheel), your expected loss over 100 spins at $10 per spin ($1,000 total wagered) is identical: $52.63 on double-zero or $27.03 on single-zero.
What changes dramatically is the standard deviation per unit wagered: σ = (p + 1)√(w(1 − w)), where p is the payout and w = k / N is the win probability:
- Even-Money Bet (Red/Black, 18 numbers, pays 1:1): Standard deviation is 0.999 units per spin. Over 100 spins of $10, 1σ is $10 × √100 × 0.999 ≈ $99.86. It is nearly impossible to win or lose more than $300 in 100 spins of flat $10 even-money betting.
- Straight-Up Bet (1 number, pays 35:1): Standard deviation is 5.763 units per spin on an American wheel (5.835 on European). Over 100 spins of $10, 1σ is $576.26—nearly six times the swing of Red/Black for the exact same expected cost.
French & European Racetrack Sector Bets ("Call Bets")
On a single-zero wheel, the racetrack layout prints four traditional French sector combinations based on the physical clockwise wheel sequence rather than the sequential felt grid:
| Call Bet Name | Chips Required | Wheel Pockets Covered | Win Probability | Chip Placement on Felt |
|---|---|---|---|---|
| Voisins du Zéro (Neighbors of Zero) | 9 chips | 17 of 37 (45.95%) | 17 / 37 | 2 chips on 0-2-3 trio; 2 chips on 25-26-28-29 corner; 1 chip each on splits 4/7, 12/15, 18/21, 19/22, 32/35 |
| Jeu Zéro (Zero Game) | 4 chips | 7 of 37 (18.92%) | 7 / 37 | 1 chip straight on 26; 1 chip each on splits 0/3, 12/15, 32/35 |
| Tiers du Cylindre (Thirds of the Wheel) | 6 chips | 12 of 37 (32.43%) | 12 / 37 | 1 chip each on 6 splits opposite zero: 5/8, 10/11, 13/16, 23/24, 27/30, 33/36 |
| Orphelins (Orphans, en plein / à cheval) | 5 chips | 8 of 37 (21.62%) | 8 / 37 | 1 chip straight on 1; 1 chip each on splits 6/9, 14/17, 17/20 (17 covered twice), 31/34 |
Streak Probabilities: How Often Does Red or Black Hit N Times in a Row?
Because an even-money bet loses on green zeros, the probability of losing k consecutive even-money bets is (19/37)k on a European wheel, (20/38)k on an American wheel, and (21/39)k on a Triple-Zero (000) wheel. The table below shows the exact probability that a chosen even-money bet wins k times in a row:
| Consecutive Wins (k) | European (18/37)k | American (18/38)k | Triple-Zero (18/39)k | 1 in N (American) |
|---|---|---|---|---|
| 1 in a row | 48.649% | 47.368% | 46.154% | 1 in 2 |
| 2 in a row | 23.667% | 22.438% | 21.302% | 1 in 4 |
| 3 in a row | 11.514% | 10.628% | 9.832% | 1 in 9 |
| 4 in a row | 5.601% | 5.034% | 4.538% | 1 in 20 |
| 5 in a row | 2.725% | 2.385% | 2.094% | 1 in 42 |
| 6 in a row | 1.326% | 1.130% | 0.967% | 1 in 89 |
| 7 in a row | 0.645% | 0.535% | 0.446% | 1 in 187 |
| 8 in a row | 0.314% | 0.253% | 0.206% | 1 in 395 |
| 9 in a row | 0.153% | 0.120% | 0.095% | 1 in 833 |
| 10 in a row | 0.074% | 0.057% | 0.044% | 1 in 1,758 |
| 12 in a row | 0.018% | 0.013% | 0.009% | 1 in 7,837 |
| 15 in a row | 0.002% | 0.001% | 0.001% | 1 in 73,734 |
Frequently asked questions
- Why do almost all roulette bets have the exact same house edge on a given wheel?
- Because every payout formula on a roulette table is 36 / k − 1, where k is the number of pockets your bet covers (35:1 for 1 number, 17:1 for 2 numbers, 11:1 for 3, 8:1 for 4, 5:1 for 6, 2:1 for 12, and 1:1 for 18). When you multiply k/N by (36/k − 1) and subtract the losing probability (N − k)/N, the k cancels out completely: EV = (36 − N) / N. That leaves −1/37 (2.70%) on single-zero, −2/38 (5.26%) on double-zero, and −3/39 (7.69%) on triple-zero regardless of whether you bet one number or eighteen.
- Why is the 5-number Top Line bet (0, 00, 1, 2, 3) worse than every other bet?
- Because 36 is not divisible by 5. A fair zero-edge payout for 5 numbers out of 36 would be 36/5 − 1 = 6.2 to 1. Casino chips cannot cleanly pay 6.2 to 1 on unit bets, so the house rounds the payout down to 6 to 1. On a 38-pocket double-zero wheel, that rounding costs you (5 × 7 − 38) / 38 = −3/38, or a 7.89% house edge instead of 5.26%.
- How does La Partage or En Prison cut the European roulette house edge to 1.35%?
- Under French La Partage rules on a single-zero wheel, when the ball lands in 0, any even-money outside bet (Red/Black, Even/Odd, 1–18/19–36) immediately returns half of your wager instead of losing in full. Because 0 lands 1/37 of the time, saving half a bet on 0 recovers 0.5 / 37 of your stake, reducing the house edge from 1/37 (2.70%) to 1/74 (1.35%).
- How does a third green zero (000 or a casino logo pocket) affect roulette odds?
- Some casinos print their own logo in the third green pocket instead of 000. It is still a third zero, and the math is the same: because there are now 39 pockets on the wheel while payouts remain based on 36 numbers, your probability of hitting a straight-up number drops from 1/38 to 1/39 and the house edge rises from 5.26% to 7.69% on every standard inside and outside bet.