How it works
One chip on one number. If it hits you are paid 35:1; there are 36 other pockets on a European wheel and 37 on an American one.
That gap is the entire house edge. A fair payout would be 36:1 on a European wheel and 37:1 on an American one. The casino pays 35:1 on both, which is why the American wheel costs nearly twice as much for an identical-looking bet.
The same bet on each wheel
| Wheel | Pockets | Payout | Win chance | House edge |
|---|---|---|---|---|
| European (single zero) | 37 | 35:1 | 2.70% | 2.70% |
| American (double zero) | 38 | 35:1 | 2.63% | 5.26% |
The payout is identical on both wheels. The American wheel simply has one more losing pocket, and that single extra pocket takes the cost from 2.70% to 5.26%, nearly double, for a table that looks the same from three feet away.
How long before it hits
A single number is the bumpiest bet on the layout, and the question people actually ask is not the edge but the wait. The chance of at least one hit in a run of spins is one minus (36/37) raised to the length of the run on a European wheel, and the same with 37/38 on an American one.
| Spins on one number | At least one hit, European | At least one hit, American |
|---|---|---|
| 10 | 23.97% | 23.41% |
| 25 | 49.59% | 48.66% |
| 37 | 63.71% | 62.72% |
| 50 | 74.59% | 73.64% |
| 100 | 93.54% | 93.05% |
Thirty-seven spins is one full cycle of a European wheel, and the number still fails to appear in more than a third of them. The arithmetic of the edge fits in one sentence: stake one chip on the same number for 37 spins, it hits once on average, and you get 36 chips back for the 37 you put in. One chip gone in 37 is 2.70%. On an American wheel it is 38 spins, one hit, 36 chips back: two gone in 38, 5.26%.
Note what does not help. La partage and en prison return half an even-money stake when the zero lands; they do nothing for a straight-up bet, which is why the cheapest seat at a French table is on red or black at 1.35%, not on a number.
Why the edge never changes between bets
Every payout on a roulette layout is calculated the same way: the casino pays as though the zero did not exist. Cover 1 number and you are paid as if there were 36 pockets rather than 37 or 38.
The practical conclusion is unusual among casino games: on a given wheel there is no such thing as a better roulette bet. What varies is variance, not expectation. A straight-up bet and a red bet cost identically per unit staked; one just gets there in a far bumpier line.
The choices that genuinely change your cost are the wheel (European against American) and the zero rule (la partage or en prison). Both are worth more than any bet selection.
Frequently Asked Questions
- What is the house edge on a straight up bet?
- 2.70% on a European single-zero wheel and 5.26% on an American double-zero wheel.
- Does the straight up bet have better odds than other bets?
- No. Every bet on a given roulette wheel carries the same house edge. It differs only in variance.
- What does it pay?
- 35:1. A fair payout would be 36:1 on a European wheel, and that difference is the house edge.
- How often does a straight up number hit?
- Once in 37 spins on average on a European wheel and once in 38 on an American one. Over 37 spins the chance of at least one hit is 63.71%, so a number misses a full cycle more than a third of the time.
- Does la partage reduce the cost of a straight up bet?
- No. La partage and en prison apply only to even-money bets. A straight-up bet costs the full 2.70% on a single-zero wheel whatever the zero rule.
- Can betting systems beat it?
- No. Each spin is independent and every bet has the same negative expectation, so no combination or progression of them can produce a positive one.
House edges on this page are computed from the pocket count and the payout in exact rational arithmetic, then checked against published references before publication. Payouts are standard, but the wheel and the zero rule vary between casinos and between tables in the same casino, so confirm both before you sit down.