Street bet in roulette: odds and payout on a row of three
A street covers one row of three numbers and pays 11 to 1. It wins 8.11% of spins on a European wheel (1 in 12) and 7.89% on American, so the house keeps 2.70% and 5.26% of every stake.
Where the chip goes
Distinct placements: 12, one for each row of three from 1–2–3 to 34–35–36. Single-zero tables also take the 0–1–2 and 0–2–3 trios at the same 11 to 1.
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 | 3 of 37 | 3 of 38 |
| Win chance | 8.11% | 7.89% |
| As odds | 1 in 12 | 1 in 13 |
| Pays | 11 to 1 | 11 to 1 |
| True odds | 11.33 to 1 | 11.67 to 1 |
| House edge | 2.70% | 5.26% |
| Expected result, $10 bet | −$0.27 | −$0.53 |
| Std. deviation per $1 | $3.276 | $3.236 |
| Edge outweighs luck after | 14,688 spins | 3,780 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 12.3 spins on a European wheel. Half of all players see a hit within 9 spins, nine in ten within 28, and 99 in 100 within 55.
| Within | European | American |
|---|---|---|
| 1 spin | 8.11% | 7.89% |
| 5 spins | 34.48% | 33.71% |
| 10 spins | 57.07% | 56.06% |
| 25 spins | 87.92% | 87.20% |
| 37 spins | 95.62% | 95.23% |
| 50 spins | 98.54% | 98.36% |
| 100 spins | 99.98% | 99.97% |
| 200 spins | >99.99% | >99.99% |
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 |
|---|---|---|
| 25 | 12.076% | >99.99% |
| 37 | 4.378% | 98.23% |
| 62 | 0.529% | 34.19% |
| 99 | 0.023% | 1.70% |
| 148 | <0.001% | 0.03% |
Chance of being ahead after n spins
Flat stakes, the same bet every spin. After n spins with w wins the net is w × 12 − 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 | 8.11% | 7.89% | -$0.27 |
| 10 | 57.07% | 56.06% | -$2.70 |
| 37 | 35.26% | 33.42% | -$10 |
| 100 | 42.31% | 39.21% | -$27.03 |
| 500 | 42.88% | 36.07% | -$135.14 |
| 1,000 | 38.40% | 29.27% | -$270.27 |
| 10,000 | 20.25% | 5.22% | -$2,702.70 |
Trios with zero
On a single-zero layout a chip on the corner where 0 meets 1 and 2 (or 2 and 3) makes a trio: three numbers including zero, paid 11 to 1 like any street. It is the only way to cover zero with a three-number bet, and it appears inside Voisins du Zéro. Same odds, same edge.
Two streets make a six line
Two neighbouring streets at $1 each and a six line at $2 pay the same on every spin. Four streets make a dozen-sized bet that doesn’t follow the dozen boundaries.
Questions
What does a street pay in roulette?
11 to 1. A winning $10 street bet pays $110 and the $10 stake comes back too. For the bet to be fair on a European wheel it would have to pay 11.33 to 1; the difference is the house edge.
How often does a street win?
8.11% of spins on a European wheel, or 1 in 12 (7.89% on an American wheel). On average it hits once every 12.3 spins, and there is a better-than-even chance of at least one hit within 9 spins.
Is a street 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 $3.28 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
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