The roulette house edge
You cannot play roulette better. You can only pay less for it, and the discount is entirely in which table you sit at.
Short answer
The roulette house edge is 2.70% on a single-zero wheel, 5.26% on a double-zero wheel, and 7.69% on a triple-zero wheel. It is the same on every standard bet on a given wheel, so the bet you choose does not change the price. Two things do change it: a single-zero table offering la partage or en prison drops the cost of an even-money bet to 1.35%, and the American five-number top line raises it to 7.89%.
The edge by wheel
The edge is simply the green pockets divided by the total pockets. Nothing else in the game contributes to it.Exact
| Wheel | Pockets | Green | House edge |
|---|---|---|---|
| Single zero (European) | 37 | 0 | 2.70% |
| Double zero (American) | 38 | 0 and 00 | 5.26% |
| Triple zero | 39 | 0, 00 and 000 | 7.69% |
| Single zero with la partage or en prison, even-money bets only | 37 | 0 | 1.35% |
| Double zero, top line (0, 00, 1, 2, 3) | 38 | 0 and 00 | 7.89% |
Adding one green pocket to a European wheel does not raise the cost by a little. It raises it by 95%, from 2.70% to 5.26%. The second zero is the single most expensive object in the casino.
Where the number comes from
Every payout in roulette is calculated as though the wheel had 36 pockets. A bet covering n numbers pays (36 minus n) to n. That formula would be exactly fair on a 36-pocket wheel, returning every unit staked over the long run. The green pockets are not in the formula, so they are pure retention. One green pocket out of 37 is 1/37, which is 2.70%. Two out of 38 is 2/38, which is 5.26%. That is the whole derivation, and it is why the edge is identical on a straight-up number and on red.
La partage and en prison
Some single-zero tables, mostly French-rules ones, apply a special rule to even-money bets when zero lands.
- La partage. You lose half your even-money bet instead of all of it. The zero now costs you 0.5 units instead of 1, so the edge halves to 1.35%.
- En prison. Your bet is held on the layout for the next spin. If it wins, you get the stake back with no profit. If it loses, it is gone. Solving that as a recurrence, including the case where zero lands again and the bet stays imprisoned, gives the imprisoned stake a value of exactly minus one half. The edge is 1.35%, identical to la partage.
At 1.35%, an even-money bet under these rules is one of the cheapest bets on any casino floor. It applies only to even-money bets. Your straight-up numbers on the same table still cost 2.70%.
What it costs per hour
A roulette table runs roughly 60 spins an hour. Flat-betting 10 units per spin, the expected loss is your total wagered multiplied by the edge.Exact
| Table | Loss per 100 units wagered | Expected cost per hour, 10 units flat |
|---|---|---|
| Single zero with la partage, even money | 1.35 | 8.11 units |
| Single zero | 2.70 | 16.22 units |
| Double zero | 5.26 | 31.58 units |
| Triple zero | 7.69 | 46.15 units |
Same game, same chips, same hour. Choosing the single-zero table cuts the bill in half, and a la partage table cuts it in half again. That is the only decision in roulette that is worth anything.
Why systems do not move the number
The Martingale, the Fibonacci, the d'Alembert and every other progression share one property: they change how much you bet, never what each bet is worth. Every individual wager still returns 97.30 units per 100 on a single-zero wheel. The expected loss of a session is the total amount wagered multiplied by the edge, and a progression that raises your bets after losses only increases the amount wagered. It cannot create an advantage out of bets that all have the same negative one.
What a progression does do is trade many small wins for one large loss. On a single-zero wheel, an even-money bet loses five spins in a row 3.57% of the time and eight in a row 0.48% of the time. A Martingale doubling from 10 units needs 320 units on the sixth bet and 1,280 on the eighth, which is where the table maximum, or your bankroll, ends the experiment. See odds for the full run figures.
How roulette prices against the floor
At 5.26%, an American wheel is one of the more expensive games on the floor. At 2.70%, a European wheel is mid-table. At 1.35% with la partage, an even-money roulette bet is competitive with the best table games available. It is the same game each time. Compare it against every other game in the house edge comparison.
Common questions
Does betting more numbers reduce the house edge?
No. Every standard bet on a given wheel carries the same edge, because every payout is computed on 36 pockets while the wheel has 37 or 38. Covering more numbers changes your win frequency and your swing, not your price.
Is 2.70% good or bad?
It is worse than blackjack played with correct basic strategy and better than most side bets and long-shot wagers. The point is that it is fixed. Roulette gives you no way to improve it through play, unlike the strategy games on this site.
Can a betting system beat the edge?
No system can. Every bet carries a negative expectation, and no arrangement of negative-expectation bets produces a positive one. Systems redistribute your results, making small wins common and large losses rare but severe. The expected cost stays exactly the edge multiplied by everything you wager.
What is the edge on a triple-zero wheel's zero basket?
TODO. The zero basket on a triple-zero wheel is not paid consistently across casinos, so no figure is published here until a specific pay table is supplied and run through the engine. The baseline 7.69% for every standard bet on that wheel is exact.