Roulette Probability Calculator
Last updated: 26 August 2026
Reviewed by Gavin Meiring, Lead research and primary author · Doctoral Candidate (Corporate Governance) · Research and drafting assisted by AI
| Bet type | Pockets | Probability | Payout | House edge | Expected loss |
|---|---|---|---|---|---|
| Single number (Straight up) | 1/37 | 2.70% | 35:1 | 2.70% | $27.03 |
| Two numbers (Split) | 2/37 | 5.41% | 17:1 | 2.70% | $27.03 |
| Three numbers (Street) | 3/37 | 8.11% | 11:1 | 2.70% | $27.03 |
| Four numbers (Corner) | 4/37 | 10.81% | 8:1 | 2.70% | $27.03 |
| Six numbers (Line) | 6/37 | 16.22% | 5:1 | 2.70% | $27.03 |
| Dozen / Column (12 numbers) | 12/37 | 32.43% | 2:1 | 2.70% | $27.03 |
| Red or Black | 18/37 | 48.65% | 1:1 | 2.70% | $27.03 |
| Odd or Even | 18/37 | 48.65% | 1:1 | 2.70% | $27.03 |
| Low (1-18) or High (19-36) | 18/37 | 48.65% | 1:1 | 2.70% | $27.03 |
This calculator shows long-run mathematical expectation. Each spin is independent. Past results do not affect future spins.
- The numbers on a roulette wheel add up to 666 (the sum of 1 through 36), earning the game its nickname 'the devil's game'.
- European roulette has a single zero and a house edge of 2.70%, while American roulette adds a double zero that nearly doubles the edge to 5.26%.
- Legend credits Blaise Pascal's 17th-century experiments with a wheel — made while trying to build a perpetual motion machine — as a forerunner of roulette.
Roulette Probability Calculator
What are your chances of winning on roulette? On a European wheel (37 pockets: 0 to 36), a single-number bet wins 1 spin in 37, a 2.70% chance. Red or black wins 18 spins in 37, a 48.65% chance. Every bet on a European wheel carries the same house edge of 2.70%. The American wheel (38 pockets, double zero) cuts every chance and doubles the house edge to 5.26%. The calculator on this page shows the probability, payout, expected value and house edge for every bet on either wheel.
Roulette chance calculator
Your chance of winning is the number of pockets your bet covers divided by the total pockets on the wheel. The table below shows each bet on a European wheel (37 pockets):
| Bet | Winning pockets | Chance of winning | Payout |
|---|---|---|---|
| Single number (straight up) | 1 | 1/37 = 2.70% | 35 to 1 |
| Split (two numbers) | 2 | 2/37 = 5.41% | 17 to 1 |
| Street (three numbers) | 3 | 3/37 = 8.11% | 11 to 1 |
| Corner (four numbers) | 4 | 4/37 = 10.81% | 8 to 1 |
| Six line (six numbers) | 6 | 6/37 = 16.22% | 5 to 1 |
| Column or dozen | 12 | 12/37 = 32.43% | 2 to 1 |
| Red or black | 18 | 18/37 = 48.65% | 1 to 1 |
| Odd or even | 18 | 18/37 = 48.65% | 1 to 1 |
| Low (1-18) or high (19-36) | 18 | 18/37 = 48.65% | 1 to 1 |
On the American wheel (38 pockets) every chance drops by the same one pocket: a single number wins 1/38 = 2.63% of spins, red or black wins 18/38 = 47.37%, and a dozen wins 12/38 = 31.58%.
Roulette probability calculator
The probability of any roulette bet is one division:
Probability of winning = winning pockets / total pockets
Expected value (EV) per unit staked = (probability of winning x payout) - (probability of losing x 1)
The payout is what the casino pays on a win, written as a ratio (35 to 1 for a single number). House edge is the EV expressed as a percentage of your stake.
Worked Example
Worked example, straight-up bet on a European wheel:
- Winning pockets: 1
- Total pockets: 37
- Probability of winning: 1/37 = 2.70%
- Payout: 35 to 1
- EV = (1/37 x 35) - (36/37 x 1) = 35/37 - 36/37 = -1/37 = -0.027
For every £1 you stake, you expect to lose 2.7p in the long run. Over 100 spins at £1 each, the expected loss is £2.70.
Roulette odds calculator
Odds and probability describe the same event in two ways. Probability is the share of spins you win. Odds are the ratio of losing outcomes to winning outcomes. A red/black bet wins 18 of 37 spins, so the odds against it are 19 to 18 (about 1.06 to 1). The casino pays 1 to 1, and that gap between true odds and payout is exactly where the house edge lives.
| Bet | True odds against (European) | Casino payout | House edge |
|---|---|---|---|
| Single number | 36 to 1 | 35 to 1 | 2.70% |
| Split | 17.5 to 1 | 17 to 1 | 2.70% |
| Street | 11.33 to 1 | 11 to 1 | 2.70% |
| Corner | 8.25 to 1 | 8 to 1 | 2.70% |
| Six line | 5.17 to 1 | 5 to 1 | 2.70% |
| Column or dozen | 2.08 to 1 | 2 to 1 | 2.70% |
| Red or black | 1.06 to 1 | 1 to 1 | 2.70% |
The house edge is 2.70% on every European bet because the single zero pocket is the casino's cut. The American wheel adds a second zero, taking the edge to 5.26% on most bets, and 7.89% on the five-number bet (the only bet with a different edge). French roulette with the "la partage" rule returns half your stake on even-money bets when zero lands, cutting the edge on those bets to 1.35%.
How to use the calculator
- Select the wheel: European (37 pockets) or American (38 pockets, double zero).
- Choose a bet type: straight up, split, street, corner, six line, dozen, column, red/black, odd/even or low/high.
- Set your stake per spin and the number of spins.
- Read the table: probability of winning, payout, house edge and expected loss for every bet type at once.
- Check the summary box for your expected outcome over the total number of spins.
Each spin is independent. Past results do not change future spins, and the calculator shows long-run expectation, not what happens in any particular session.
Why the house edge is the same on every bet
The zero is the mechanism. Remove it and red/black would be exactly 50/50 and the casino would break even. With one zero on a European wheel, every bet pays out as if the zero were not there, so every bet loses 1/37 of the stake on average. That uniform 2.70% is why no bet type is mathematically better than another, and why no betting system can beat the wheel. The Martingale, Fibonacci and Labouchere systems change the size and timing of wins and losses; they do not change the long-run average, which stays at minus 2.70% per unit staked. A losing streak under Martingale grows bets exponentially until the table limit or your bankroll stops the run.
Variance: what the house edge does not tell you
The house edge tells you the average result, not the range of results. Two bets with the same 2.70% edge behave very differently spin to spin.
A straight-up bet pays 35 to 1, so the swings are large. Measured in units staked, its standard deviation per spin is about 5.84. Over 100 spins at one unit each, the typical swing is around 58 units either side of the expected loss. You can be well ahead after a lucky hour and still be losing on average.
An even-money bet such as red or black has a standard deviation of about 1.00 per spin. Over 100 spins the typical swing is around 10 units. The losses accumulate smoothly, the wins come steadily, and the curve stays close to the expected minus 2.70 units per hundred.
The practical difference: straight-up bets produce dramatic short-term wins and equally dramatic losses. Even-money bets grind. Neither changes your expected long-run result, which is the same minus 2.70% per unit on every European bet.
Frequently Asked Questions
Which roulette variant gives the best odds for the player?
European roulette (single zero, 2.70% house edge) beats American roulette (double zero, 5.26%). French roulette with "la partage" is best of all for even-money bets, cutting the edge to 1.35%.
Does it matter which bet I choose?
For your expected return, no. Every bet on a European wheel has the same 2.70% edge, so the long-run average loss is identical. The difference is variance: a straight-up bet wins rarely and pays 35 to 1, red/black wins almost half the time and pays even money. Bigger swings, same average.
Can any bet or system have a positive expected value?
Under standard casino rules, no. All bets carry a negative expected value. A biased wheel could in theory create a positive edge, but modern casinos monitor and replace wheels when wear shows up. Dealer signature is claimed and largely unproven.
What is the Martingale system?
You double your bet after every loss so the first win recovers everything plus one unit. It produces many small wins and one large loss: a long losing streak needs exponentially bigger bets and ends at the table maximum or your bankroll. The expected value per spin does not change.
What is the five-number bet?
On the American wheel, the five-number bet covers 0, 00, 1, 2 and 3. It pays 6 to 1, and it is the only American bet whose edge differs from the standard 5.26%: it carries 7.89%. The maths: (5/38 x 6) - (33/38 x 1) = -3/38 = -7.89%. It is widely described as the worst bet in roulette for that reason.
How much can I expect to lose in an hour?
At a typical 60 spins per hour on a European wheel, a £1 even-money bet loses 60 x 1/37 = £1.62 on average. A £10 stake raises that to £16.20 per hour. That is the long-run average; any single hour can be far better or worse because of variance.
Why is the edge 2.70% and not 1/37 of something else?
Because the casino pays as if the zero did not exist. On red/black, a win pays 1 to 1, which is fair for an 18-out-of-36 game. The real game is 18 out of 37, so the missing pocket is pure profit for the house on every bet. One pocket in 37 is 2.70%.
Is roulette a game of skill?
No. Every spin is independent and every bet has fixed probability. There is no decision that improves your expected result, unlike blackjack where card counting shifts the odds. The only choices that matter are which wheel to play (European over American) and how much variance you can tolerate.
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