Straight-up bet in roulette: odds, payout and how often one number hits
A straight-up bet covers one number and pays 35 to 1. It wins 2.70% of spins on a European wheel (1 in 37) and 2.63% on American, so the house keeps 2.70% and 5.26% of every stake.
Where the chip goes
Distinct placements: 37 on a European layout (0 to 36) and 38 on an American one, which adds 00. Every one of them has the same odds.
Odds and payout on both wheels
The win chance is pockets covered over pockets on the wheel. True odds are what the bet would have to pay for the house to make nothing; the gap between true odds and the actual payout is the edge.
| European | American | |
|---|---|---|
| Numbers covered | 1 of 37 | 1 of 38 |
| Win chance | 2.70% | 2.63% |
| As odds | 1 in 37 | 1 in 38 |
| Pays | 35 to 1 | 35 to 1 |
| True odds | 36 to 1 | 37 to 1 |
| House edge | 2.70% | 5.26% |
| Expected result, $10 bet | −$0.27 | −$0.53 |
| Std. deviation per $1 | $5.838 | $5.763 |
| Edge outweighs luck after | 46,656 spins | 11,988 spins |
The last row is where the expected loss grows past one standard deviation of luck; the house edge page derives it and compares every bet.
How often it hits
The chance of at least one hit in n spins is 1 − (1 − p)n. On average the bet comes in once every 37 spins on a European wheel. Half of all players see a hit within 26 spins, nine in ten within 85, and 99 in 100 within 169.
| Within | European | American |
|---|---|---|
| 1 spin | 2.70% | 2.63% |
| 5 spins | 12.80% | 12.48% |
| 10 spins | 23.97% | 23.41% |
| 25 spins | 49.59% | 48.66% |
| 37 spins | 63.71% | 62.72% |
| 50 spins | 74.59% | 73.64% |
| 100 spins | 93.54% | 93.05% |
| 200 spins | 99.58% | 99.52% |
Droughts
A drought is a run of spins without a hit. The chance that the next L spins all miss is (1 − p)L. Seeing a drought that long somewhere in a long session is far more likely, and the last column is computed exactly by dynamic programming over the current run of misses, not by simulation.
| Misses in a row | Next L spins | Somewhere in 1,000 spins |
|---|---|---|
| 74 | 13.166% | 99.32% |
| 111 | 4.777% | 75.42% |
| 185 | 0.629% | 13.85% |
| 296 | 0.030% | 0.60% |
| 444 | <0.001% | <0.01% |
Chance of being ahead after n spins
Flat stakes, the same bet every spin. After n spins with w wins the net is w × 36 − n stakes, and w is binomial, so these are exact sums. Breaking even counts as not ahead. The chances of winning page compares bets side by side and has a calculator for any session length.
| Spins | European | American | Expected, $10 bets |
|---|---|---|---|
| 1 | 2.70% | 2.63% | -$0.27 |
| 10 | 23.97% | 23.41% | -$2.70 |
| 37 | 26.42% | 25.44% | -$10 |
| 100 | 50.94% | 49.16% | -$27.03 |
| 500 | 48.40% | 44.45% | -$135.14 |
| 1,000 | 45.11% | 39.61% | -$270.27 |
| 10,000 | 32.51% | 18.46% | -$2,702.70 |
Which number?
It makes no difference. Every pocket is the same size in the simulator and, on a fair wheel, in a casino. A number that has not come up for a while is not due, and one that keeps hitting is not hot; the sleeping numbers page has the exact odds of both patterns appearing by chance.
The layout is one bet in different sizes
Twelve $1 straight-up bets cover twelve numbers. One wins 12/37 of the time and returns $36, net +$24 on $12 staked: 2 to 1. That is a dozen bet, exactly. Two numbers at $1 each are a split at $2; three are a street. Every inside and outside bet is a bundle of straight-ups priced at 35 to 1, which is why every one of them carries the same 2.70% on a single-zero wheel.
Systems built on this bet
Each runs over the same seeded sessions as every other system on the site. The figure is the result per $100 wagered on a European wheel.
| System | Per $100 wagered | In short |
|---|---|---|
| Single number | −$2.74 | one unit straight-up on 17, every spin. |
| Hot number (Andrucci-style) | −$2.73 | watch 37 spins, then bet straight-up on whichever number has hit most. |
| James Bond | −$2.66 | spread 20 units across high (19–36), the 13–18 six-line, and zero. |
Questions
What does a straight-up bet pay in roulette?
35 to 1. A winning $10 straight up bet pays $350 and the $10 stake comes back too. For the bet to be fair on a European wheel it would have to pay 36 to 1; the difference is the house edge.
How often does a straight-up bet win?
2.70% of spins on a European wheel, or 1 in 37 (2.63% on an American wheel). On average it hits once every 37 spins, and there is a better-than-even chance of at least one hit within 26 spins.
Is a straight-up bet a good bet?
It is no better and no worse than the rest of the layout: 2.70% house edge on a European wheel, 5.26% on American, the same as every other bet there except the American top line. Only the swing differs: about $5.84 of standard deviation per $1 staked, per spin.
Related
- Roulette house edge: where 2.70% and 5.26% come from
- What are the odds of red 10 times in a row in roulette?
- What are your chances of winning at roulette after n spins?
- How many spins until every roulette number comes up?
- Every bet’s odds and payout, both wheels
- Does any betting system work? 20 systems on the same seeds
- Study: European versus American roulette, the risk distribution
Every bet on the layout
Straight upSplitStreetCornerSix lineDozen & columnRed / blackTop line