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Roulette Odds, Payouts and House Edge Explained
Every roulette bet with its payout, probability and house edge for European, French and American wheels, with the maths shown and a Martingale stress test.
Short answer
Every standard roulette bet has the same house edge on a given wheel: 2.70% on single-zero European roulette, 5.26% on double-zero American roulette and 7.89% on the American five-number bet. French rules such as la partage cut the edge on even-money bets to 1.35%. No betting system changes these numbers.
Roulette looks like a game with dozens of different bets, but mathematically it is one of the simplest games in a casino. Every bet is priced the same way: the casino pays slightly less than the true odds, and the gap is the house edge. This guide shows the payout and probability of every standard bet on European, French and American wheels, works through the maths, and explains why betting systems cannot change the result.
If you only need the short version: choose a single-zero wheel, prefer French rules on even-money bets when they are offered, and avoid the American five-number bet. For the game rules themselves, see our roulette overview.
How roulette odds work
A European wheel has 37 pockets (1 to 36 plus a single zero). An American wheel has 38 pockets (1 to 36 plus 0 and 00). Each spin lands in one pocket, and on a fair wheel every pocket is equally likely.
Payouts are quoted as “x to 1”, which means you receive x units of profit plus your stake back. A straight-up bet on one number pays 35 to 1. If the payout matched the true odds, a single number on a 37-pocket wheel would pay 36 to 1. The casino keeps the difference.
The house edge is the average share of each stake the casino expects to keep. The UK Gambling Commission describes it as the percentage a casino “would expect to keep, on average, from each hand or spin”. You can calculate it for any bet as an expected value:
Expected value per 1 unit staked = (probability of winning × payout) − (probability of losing × 1)
For a straight-up bet on a European wheel: (1/37 × 35) − (36/37 × 1) = −1/37 = −2.70%. On an American wheel: (1/38 × 35) − (37/38 × 1) = −2/38 = −5.26%. A college statistics text uses exactly this method on an American wheel and arrives at the same result of about −5 cents per $1 staked.
Roulette odds table for every bet
The payouts are the same on single-zero and double-zero wheels; only the number of pockets changes. The probabilities below are calculated as numbers covered ÷ 37 (European and French) or ÷ 38 (American).
| Bet | Numbers covered | Payout | Win chance, European | Win chance, American |
|---|---|---|---|---|
| Straight up | 1 | 35 to 1 | 2.70% | 2.63% |
| Split | 2 | 17 to 1 | 5.41% | 5.26% |
| Street | 3 | 11 to 1 | 8.11% | 7.89% |
| Corner | 4 | 8 to 1 | 10.81% | 10.53% |
| Five-number (0, 00, 1, 2, 3) | 5 | 6 to 1 | Not offered | 13.16% |
| Six line | 6 | 5 to 1 | 16.22% | 15.79% |
| Dozen or column | 12 | 2 to 1 | 32.43% | 31.58% |
| Red/black, odd/even, 1–18/19–36 | 18 | 1 to 1 | 48.65% | 47.37% |
Run the expected-value formula on any row and you get the same answer for that wheel. A dozen on a European wheel: (12/37 × 2) − (25/37 × 1) = −1/37. A six line on an American wheel: (6/38 × 5) − (32/38 × 1) = −2/38. The pricing is consistent by design, so on a given wheel no inside or outside bet is “better” than another in the long run, apart from the exceptions below.
House edge by roulette variant
| Variant and bet | House edge | How it is calculated |
|---|---|---|
| European (single zero), all bets | 2.70% | 1/37 |
| French, even-money bets with la partage | 1.35% | 0.5/37 = 1/74 |
| French, even-money bets with en prison | about 1.35% to 1.39% | Depends on the exact prison rule |
| French, all other bets | 2.70% | 1/37 |
| American (double zero), all bets except the five-number bet | 5.26% | 2/38 |
| American five-number bet | 7.89% | 3/38 |
European roulette: 2.70%
With one zero, every bet loses 1/37 of the stake on average. Wizard of Odds lists the single-zero edge as “1/37, or 2.70%, on all bets”.
French roulette: la partage and en prison
French roulette uses the same single-zero wheel, but some tables add a rule for even-money bets when the ball lands on zero.
- La partage: you get half of your even-money stake back when zero comes up. Per unit staked on red: win +1 with probability 18/37, lose −1 with probability 18/37, lose −0.5 with probability 1/37. Expected value = (18 − 18 − 0.5)/37 = −0.5/37 = −1.35%.
- En prison: your stake stays on the table for the next spin instead. Wizard of Odds calculates about 1.39% when a single imprisonment is allowed and about 1.37% when repeated imprisonment is allowed. Where you can choose between losing half and imprisonment, it gives 1.35%.
These rules apply only to even-money bets. A straight-up bet on a French table still carries 2.70%.
American roulette: 5.26% and the five-number bet
The second zero doubles the casino’s share: every bet loses 2/38 on average. The exception is the five-number bet on 0, 00, 1, 2 and 3, which pays 6 to 1. Per unit staked: (5/38 × 6) − (33/38 × 1) = (30 − 33)/38 = −3/38 = −7.89%. It is the worst bet on the roulette table.
Worked example: what the edge costs over many spins
Suppose you bet 10 on red for 100 spins, so 1,000 in total stakes. The expected loss is total stakes × house edge:
| Wheel and rule | Total staked | House edge | Expected loss |
|---|---|---|---|
| French with la partage | 1,000 | 1.35% | 13.51 |
| European | 1,000 | 2.70% | 27.03 |
| American | 1,000 | 5.26% | 52.63 |
This is an average, not a forecast for one session. Over 100 spins your actual result can be well above or below it. Over many thousands of spins the average loss per unit staked moves closer to the house edge. The RTP and house edge calculator runs the same sum for any game.
Why betting systems cannot change the house edge
Betting systems change how much you stake after a win or a loss. They do not change the probability of any outcome or the payout. Each spin is independent, so every unit staked carries the same negative expected value. Wizard of Odds puts it plainly: varying bet size based on recent results “makes no difference in the long run outcome”, and the ratio of loss to amount wagered “will always approach the house edge”.
Martingale: a worked example with a table limit
The Martingale doubles the stake after each loss, so that one win recovers all losses plus the first stake. It usually produces a small win, which is why it feels convincing. The problem is the rare long losing streak combined with the table maximum.
Example: a European table with a minimum bet of 5 and a maximum bet of 500, betting on red.
| Spin | Stake | Total lost if this spin also loses |
|---|---|---|
| 1 | 5 | 5 |
| 2 | 10 | 15 |
| 3 | 20 | 35 |
| 4 | 40 | 75 |
| 5 | 80 | 155 |
| 6 | 160 | 315 |
| 7 | 320 | 635 |
| 8 | 640 (not allowed: above the 500 limit) | The system cannot continue |
Red loses with probability 19/37 on each spin (18 black pockets plus zero). The chance of seven losses in a row is (19/37) to the power of 7 ≈ 0.94%, roughly once in every 106 sequences.
- Chance a sequence ends with a win of 5: about 99.06%.
- Chance a sequence ends with a loss of 635: about 0.94%.
- Expected result per sequence: (0.9906 × 5) − (0.0094 × 635) ≈ 4.95 − 5.98 = −1.03.
- The expected total staked per sequence works out at about 37.97, and −1.03 ÷ 37.97 = −2.70%, exactly the house edge.
So the Martingale turns many small wins and one large loss into the same long-run result as flat betting. Wizard of Odds reaches the same conclusion in its simulations: the Martingale “is neither better nor worse than flat betting”, and it “won’t even dent” the house edge. On an American wheel the same seven-loss streak has a probability of about 1.12%, and the expected result per sequence falls to about −2.16.
Fibonacci and D’Alembert
The Fibonacci system raises stakes along the sequence 1, 1, 2, 3, 5, 8 and so on after losses. D’Alembert adds one unit after a loss and removes one after a win. Both rise more slowly than the Martingale, so they reach the table limit less often but recover losses more slowly. Neither changes the probability of red, the 1 to 1 payout or the zero, so the expected loss is still the house edge multiplied by everything you stake. Systems that make you stake more in total make you lose more on average, not less.
Live roulette vs RNG roulette
RNG (digital) roulette uses a random number generator to pick the pocket. Live roulette uses a physical wheel streamed from a studio. In standard versions the pay table and house edge are identical; what differs is how the outcome is produced and checked.
- RNG roulette: under UK technical standards, results must be “acceptably random” and the probabilities of a simulated device should match those of the real one. Test labs such as eCOGRA review the RNG source code, run statistical tests on its output and check how seeds are generated.
- Live roulette: the UK standards treat physical devices as mechanical RNGs that must meet the same randomness requirement, and players must not be able to interfere with them. eCOGRA’s live dealer testing covers studio security, equipment, procedures for spinning roulette wheels and ongoing monitoring of game sessions.
- Speed: expected loss equals total stakes × house edge. A slower game means fewer spins and less staked per hour at the same bet size, so a lower expected loss per hour. The edge per spin is unchanged.
Some live and digital variants add multipliers or side features and adjust the payouts to pay for them, which changes the house edge. In Great Britain, operators must make the house edge and RTP or win probabilities easily available before you play, so check the game’s help screen. You can compare formats in our live casino section.
Checklist: getting the most from your roulette stake
- Choose a single-zero wheel (European or French) over a double-zero wheel.
- For even-money bets, look for la partage or en prison: 1.35% instead of 2.70%.
- Never place the American five-number bet.
- Read the game rules for the RTP and any changed payouts on multiplier variants.
- Ignore systems and “hot number” displays; past spins do not affect the next one.
- Decide your budget beforehand and set a deposit limit. Our responsible gambling page lists the tools available.
If you want a casino game where your decisions change the edge, see our blackjack basic strategy guide. For how digital games are tested, read how online slots work.
FAQ
What are the odds of hitting a single number in roulette?
On a European or French wheel the chance is 1 in 37, or 2.70%. On an American wheel it is 1 in 38, or 2.63%. The bet pays 35 to 1 on both, which is why the American version has the higher house edge.
Which roulette bet has the lowest house edge?
Even-money bets on a French table with la partage or en prison, at about 1.35%. On a standard European wheel all bets carry 2.70%. On an American wheel all bets carry 5.26%, except the five-number bet at 7.89%.
Is it better to bet on red or on a single number?
On the same wheel both have the same house edge, so the expected loss per unit staked is identical. Red wins far more often with small payouts; a single number wins rarely with large payouts. The difference is variance, not value.
Does the Martingale system work in online roulette?
No. It produces frequent small wins and occasional large losses, and table limits stop the doubling. In our example with a 5 to 500 table, the expected loss is still 2.70% of everything staked on a European wheel.
Is live roulette fairer than RNG roulette?
Neither is inherently fairer. Regulated versions of both must produce random outcomes, and the standard house edge is the same. Live games are slower, which lowers the expected loss per hour at the same stake.
Sources
- Wizard of Odds: Roulette basics, payouts and house edge
- Wizard of Odds: Betting systems
- Wizard of Odds: The Martingale
- LibreTexts Mathematics (Lake Tahoe Community College): Expected value
- UK Gambling Commission: Return to player and house edge
- UK Gambling Commission: RTS 3, rules and likelihood of winning
- UK Gambling Commission: RTS 7, generation of random outcomes
- eCOGRA: Live dealer testing
- eCOGRA: RNG certification
Last updated October 25, 2026 by the Gambling Hero editorial team.