Casino Calculator
Roulette Odds & Expected Value Calculator
Pick a wheel and a bet to see the chance of winning, the payout, the expected value of a $100 bet and how often it wins on average. Add a number of spins to see the chance of at least one win and of a losing streak.
How to Use the Calculator
- 1Choose the wheel: European (single zero, 37 pockets) or American (double zero, 38 pockets).
- 2Choose the bet, from a single number to red/black. The calculator shows the win probability, payout, expected value per $100 and the average number of spins per win.
- 3Optionally enter a number of spins to see the chance of winning at least once, the chance of losing every spin, and the expected loss at $100 a spin.
The formulas
- Win probability = numbers covered ÷ pockets (37 or 38)
- EV per $100 = 100 × (win probability × (payout + 1) − 1)
- At least one win in n spins = 1 − (1 − win probability)^n
A European wheel has 37 pockets (0 to 36) and an American wheel has 38 (0, 00 and 1 to 36). The calculator treats every pocket as equally likely.
Every standard bet pays as if the zero (or zeros) did not exist: a bet covering n numbers pays 36 ÷ n − 1 to 1. That is why every bet on the same wheel has the same expected value, −2.70% on a European wheel and −5.26% on an American wheel. The one exception is the American top line bet (0-00-1-2-3), which pays 6 to 1 and has a −7.89% expected value.
French roulette rules such as La Partage and En Prison return half of an even-money bet when zero hits, halving the edge on those bets to about 1.35%. This calculator covers standard European and American payouts.
Worked Examples
Red at a European wheel
Red wins 18 times in 37, or 48.65%, and pays 1 to 1. A $100 bet returns $200 when it wins, so its expected value is 100 × (18/37 × 2 − 1) = −$2.70.
A single number for 37 spins
A straight-up bet wins once every 37 spins on average, but that is not a promise. Betting one number for 37 spins on a European wheel produces at least one win 63.7% of the time; the other 36.3% of the time all 37 spins lose.
Ten reds in a row
The chance of losing ten even-money bets in a row at a European wheel is (19/37)^10, about 0.13%, or roughly once in 784 attempts. After nine losses, the tenth spin is still 48.65% to win: the wheel has no memory.
Reference Tables
| Bet (payout) | European | American |
|---|---|---|
| Straight up (1 number) · 35 to 1 | 2.70% | 2.63% |
| Split (2 numbers) · 17 to 1 | 5.41% | 5.26% |
| Street (3 numbers) · 11 to 1 | 8.11% | 7.89% |
| Corner (4 numbers) · 8 to 1 | 10.81% | 10.53% |
| Top line (0-00-1-2-3) · 6 to 1 | — | 13.16% |
| Six line (6 numbers) · 5 to 1 | 16.22% | 15.79% |
| Dozen or column (12 numbers) · 2 to 1 | 32.43% | 31.58% |
| Red/black, odd/even, high/low · 1 to 1 | 48.65% | 47.37% |
Win probability = numbers covered ÷ pockets (37 on a European wheel, 38 on an American wheel). The top line bet (0-00-1-2-3) exists only on the American layout.
| Bet | European | American |
|---|---|---|
| Straight up (1 number) | −$2.70 | −$5.26 |
| Split (2 numbers) | −$2.70 | −$5.26 |
| Street (3 numbers) | −$2.70 | −$5.26 |
| Corner (4 numbers) | −$2.70 | −$5.26 |
| Top line (0-00-1-2-3) | — | −$7.89 |
| Six line (6 numbers) | −$2.70 | −$5.26 |
| Dozen or column (12 numbers) | −$2.70 | −$5.26 |
| Red/black, odd/even, high/low | −$2.70 | −$5.26 |
EV = 100 × (win probability × (payout + 1) − 1). On a given wheel every bet has the same EV, except the American top line bet.
| Bet | European | American |
|---|---|---|
| Straight up (1 number) | 37.00 | 38.00 |
| Split (2 numbers) | 18.50 | 19.00 |
| Street (3 numbers) | 12.33 | 12.67 |
| Corner (4 numbers) | 9.25 | 9.50 |
| Top line (0-00-1-2-3) | — | 7.60 |
| Six line (6 numbers) | 6.17 | 6.33 |
| Dozen or column (12 numbers) | 3.08 | 3.17 |
| Red/black, odd/even, high/low | 2.06 | 2.11 |
Pockets ÷ numbers covered: the long-run average gap between wins. A win is never due within that many spins.
What the Calculator Does Not Cover
- —It assumes a fair wheel where each pocket is equally likely. It does not model wheel bias or any other defect.
- —Expected values are long-run averages. Short sessions vary widely around them.
- —It does not cover French La Partage or En Prison rules, side bets, or electronic games with different payouts.
- —No combination of bets changes the expected value: combining bets only changes how results are spread.
Frequently Asked Questions
What are the odds of hitting red or black in roulette?
18/37, about 48.65%, on a European wheel and 18/38, about 47.37%, on an American wheel. Zero (and double zero) make both red and black lose, so the chance is a little under 50%.
Which roulette bet has the best odds?
On the same wheel, every bet has the same expected value: −$2.70 per $100 on a European wheel and −$5.26 on an American wheel. The exception is the American top line bet at −$7.89. Choosing a single-zero wheel matters far more than choosing a bet.
If I bet on one number 37 times, will I win once?
Not necessarily. On a European wheel, 37 straight-up bets win at least once 63.7% of the time and all lose 36.3% of the time. “Once in 37 spins” is a long-run average, not a guarantee.
How much worse is American roulette than European?
The house edge is 2/38, about 5.26%, against 1/37, about 2.70%, nearly double. Betting $100 a spin for 100 spins has an expected loss of about $526 on an American wheel and $270 on a European wheel.
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