Roulette odds and probabilities
The odds are simple to state and easy to misread. The hard part is what they do not tell you.
Short answer
On a single-zero wheel a straight-up number wins 2.70% of the time, a dozen wins 32.43%, and red wins 48.65%. On a double-zero wheel those become 2.63%, 31.58% and 47.37%. Every spin is independent, so none of these probabilities is affected by what came before. Bet one number for 37 straight spins on a single-zero wheel and you have a 63.71% chance of hitting it at least once, which also means a 36.29% chance of never hitting it at all.
Win probability of every bet
Computed directly from the pocket counts.Exact
| Bet | Numbers | Single zero (37) | Double zero (38) |
|---|---|---|---|
| Straight up | 1 | 2.70% | 2.63% |
| Split | 2 | 5.41% | 5.26% |
| Street | 3 | 8.11% | 7.89% |
| Corner | 4 | 10.81% | 10.53% |
| Top line | 5 | Not offered | 13.16% |
| Six line | 6 | 16.22% | 15.79% |
| Dozen or column | 12 | 32.43% | 31.58% |
| Red, black, odd, even, high, low | 18 | 48.65% | 47.37% |
Note what is missing from the even-money row: it is not 50%. It is 48.65% on a single-zero wheel and 47.37% on a double-zero one. Those missing points are the green pockets, and they are the whole game.
How often will you actually see it?
Single-spin probabilities are not what a session feels like. These are the numbers that matter at the table.Exact
| Question | Single zero | Double zero |
|---|---|---|
| Your number hits at least once in 37 spins | 63.71% | 62.72% |
| Your number hits at least once in 100 spins | 93.54% | 93.05% |
| Your dozen hits at least once in 10 spins | 98.02% | 97.75% |
| An even-money bet loses 5 spins in a row | 3.57% | 4.04% |
| An even-money bet loses 8 spins in a row | 0.48% | 0.59% |
The last two rows are the ones that end sessions. A five-loss run on red happens about once every 28 attempts, which at 60 spins an hour is not rare at all. It is why doubling-up systems break: the run that beats you is not unlikely, it is scheduled.
Why 37 spins does not guarantee your number
A number that wins 1 time in 37 sounds like it should appear once in 37 spins. It does, on average. But the average is made of sessions where it appears twice, three times, or not at all. The chance of it never appearing across 37 spins is (36/37) multiplied by itself 37 times, which comes to 36.29%. More than a third of the time, a full cycle of the wheel skips your number entirely. Nothing has gone wrong when that happens.
The wheel has no memory
After six reds in a row, black is not due. The next spin is drawn from the same 37 pockets as every other spin, and black still wins 18 times in 37. Believing otherwise is the gambler's fallacy, and roulette is where it does the most damage, because the scoreboard above the table displays the recent history in a way that invites you to find a pattern in it.
The reverse error, betting with a streak because the wheel is "hot", is the same mistake wearing a different coat. Both assume the last spin tells you something about the next one. It does not.
Odds are not the same as price
A straight-up bet wins 2.70% of the time and red wins 48.65% of the time, and both cost you exactly the same 2.70% of every unit you wager. The odds tell you how the money will move. The house edge tells you how much of it you keep. Confusing the two is the most common mistake at the table.
Common questions
What are the odds of hitting the same number twice in a row?
On a single-zero wheel, 1 in 37 multiplied by 1 in 37, which is 1 in 1,369, or 0.073%. That is the chance stated in advance. Once the first number has landed, the chance of the next spin repeating it is just 1 in 37 again.
Are the odds better on European roulette?
Yes, on every bet. One fewer green pocket lifts the win chance of every bet and cuts the house edge from 5.26% to 2.70%. If both wheels are available at the same minimum, there is no argument for the double-zero table.
Can tracking the scoreboard help?
No. The displayed history is a record of independent draws. It contains no information about the next one.