Corner bet in roulette: odds and payout on four numbers
A corner covers a block of four numbers and pays 8 to 1. It wins 10.81% of spins on a European wheel (1 in 9.3) and 10.53% on American, so the house keeps 2.70% and 5.26% of every stake.
Where the chip goes
Distinct placements: 22: every block of four where two neighbouring rows meet two neighbouring columns. The 0–1–2–3 first-four bet is priced like a corner.
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 | 4 of 37 | 4 of 38 |
| Win chance | 10.81% | 10.53% |
| As odds | 1 in 9.3 | 1 in 9.5 |
| Pays | 8 to 1 | 8 to 1 |
| True odds | 8.25 to 1 | 8.50 to 1 |
| House edge | 2.70% | 5.26% |
| Expected result, $10 bet | −$0.27 | −$0.53 |
| Std. deviation per $1 | $2.795 | $2.762 |
| Edge outweighs luck after | 10,692 spins | 2,754 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 9.3 spins on a European wheel. Half of all players see a hit within 7 spins, nine in ten within 21, and 99 in 100 within 41.
| Within | European | American |
|---|---|---|
| 1 spin | 10.81% | 10.53% |
| 5 spins | 43.56% | 42.66% |
| 10 spins | 68.15% | 67.12% |
| 25 spins | 94.27% | 93.80% |
| 37 spins | 98.55% | 98.37% |
| 50 spins | 99.67% | 99.62% |
| 100 spins | >99.99% | >99.99% |
| 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 |
|---|---|---|
| 19 | 11.374% | >99.99% |
| 28 | 4.062% | 99.30% |
| 46 | 0.518% | 42.52% |
| 74 | 0.021% | 2.11% |
| 111 | <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 × 9 − 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 | 10.81% | 10.53% | -$0.27 |
| 10 | 29.54% | 28.43% | -$2.70 |
| 37 | 37.09% | 34.92% | -$10 |
| 100 | 39.67% | 36.11% | -$27.03 |
| 500 | 41.05% | 33.22% | -$135.14 |
| 1,000 | 36.05% | 25.77% | -$270.27 |
| 10,000 | 16.36% | 2.83% | -$2,702.70 |
First four
On a single-zero layout the chip at the corner of 0, 1, 2 and 3 is the first four, priced exactly like a corner: 8 to 1 on four numbers, 2.70%. The double-zero layout has no equivalent; its zero bet is the five-number top line, which is worse.
Corners as gap fillers
Systems that cover most of the layout use corners to plug holes. The Romanosky puts three units on each of two dozens and one on each of two corners in the third, covering 32 of 37 numbers. It wins most spins and still returns the edge on every unit staked.
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 |
|---|---|---|
| Romanosky | −$2.70 | two dozens at three units each plus two corners at one unit, covering 32 numbers. |
Questions
What does a corner pay in roulette?
8 to 1. A winning $10 corner bet pays $80 and the $10 stake comes back too. For the bet to be fair on a European wheel it would have to pay 8.25 to 1; the difference is the house edge.
How often does a corner win?
10.81% of spins on a European wheel, or 1 in 9.3 (10.53% on an American wheel). On average it hits once every 9.3 spins, and there is a better-than-even chance of at least one hit within 7 spins.
Is a corner 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 $2.79 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