Split bet in roulette: odds, payout and how it works
A split covers two neighbouring numbers and pays 17 to 1. It wins 5.41% of spins on a European wheel (1 in 19) and 5.26% on American, so the house keeps 2.70% and 5.26% of every stake.
Where the chip goes
Distinct placements: 57 between the numbers 1 to 36: 24 across a row of three and 33 between neighbouring rows. Tables also accept splits with zero.
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 | 2 of 37 | 2 of 38 |
| Win chance | 5.41% | 5.26% |
| As odds | 1 in 19 | 1 in 19 |
| Pays | 17 to 1 | 17 to 1 |
| True odds | 17.50 to 1 | 18 to 1 |
| House edge | 2.70% | 5.26% |
| Expected result, $10 bet | −$0.27 | −$0.53 |
| Std. deviation per $1 | $4.070 | $4.019 |
| Edge outweighs luck after | 22,680 spins | 5,832 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 18.5 spins on a European wheel. Half of all players see a hit within 13 spins, nine in ten within 42, and 99 in 100 within 83.
| Within | European | American |
|---|---|---|
| 1 spin | 5.41% | 5.26% |
| 5 spins | 24.26% | 23.69% |
| 10 spins | 42.63% | 41.76% |
| 25 spins | 75.07% | 74.12% |
| 37 spins | 87.20% | 86.47% |
| 50 spins | 93.79% | 93.30% |
| 100 spins | 99.61% | 99.55% |
| 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 |
|---|---|---|
| 37 | 12.795% | >99.99% |
| 56 | 4.452% | 93.30% |
| 93 | 0.570% | 25.41% |
| 148 | 0.027% | 1.26% |
| 222 | <0.001% | 0.02% |
Chance of being ahead after n spins
Flat stakes, the same bet every spin. After n spins with w wins the net is w × 18 − 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 | 5.41% | 5.26% | -$0.27 |
| 10 | 42.63% | 41.76% | -$2.70 |
| 37 | 32.33% | 30.86% | -$10 |
| 100 | 45.67% | 43.13% | -$27.03 |
| 500 | 45.12% | 39.54% | -$135.14 |
| 1,000 | 41.21% | 33.59% | -$270.27 |
| 10,000 | 25.29% | 9.64% | -$2,702.70 |
A split is two straight-ups
$2 on a split and $1 straight-up on each of its two numbers pay the same: either number returns $36 ($17 × 2 + $2). The split exists to save a chip, not to change the odds.
Where splits do the work
The French call bets are mostly splits. Voisins du Zéro covers the 17 pockets around zero with five splits, a corner and the 0–2–3 trio; Tiers du Cylindre covers the 12 opposite with six splits; Orphelins mixes splits and one straight-up. They cover a slice of the wheel rather than a block of the layout, and they carry the same 2.70%. The simulator’s racetrack places all three in Advanced mode.
Questions
What does a split pay in roulette?
17 to 1. A winning $10 split bet pays $170 and the $10 stake comes back too. For the bet to be fair on a European wheel it would have to pay 17.50 to 1; the difference is the house edge.
How often does a split win?
5.41% of spins on a European wheel, or 1 in 19 (5.26% on an American wheel). On average it hits once every 18.5 spins, and there is a better-than-even chance of at least one hit within 13 spins.
Is a split 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 $4.07 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?
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- 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
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