Roulette Probability Calculator

Roulette Wheel Layout The European roulette wheel (invented in France in the 1790s) has 37 slots: numbers 1-36 alternating red and black, plus one green 0. The American roulette wheel adds a second green slot (00), making 38 total. This extra slot nearly doubles the house edge.

How Probability Works in Roulette Probability = (favorable outcomes) / (total outcomes). For a straight-up bet on a single number on a European wheel: P = 1/37 = 2.70%. On an American wheel: P = 1/38 = 2.63%. The payout is 35:1 for both wheels, but the true odds differ.

House Edge The house edge is the difference between the true odds and the payout odds. European wheel: (37-36)/37 = 2.70% house edge. American wheel: (38-36)/38 = 5.26% house edge. This means for every $100 bet over time, you can expect to lose $2.70 (European) or $5.26 (American).

Common Bet Types Straight Up: 1 number, pays 35:1. Split: 2 numbers, pays 17:1. Street: 3 numbers, pays 11:1. Corner: 4 numbers, pays 8:1. Six Line: 6 numbers, pays 5:1. Dozen/Column: 12 numbers, pays 2:1. Red/Black, Odd/Even, High/Low: 18 numbers, pays 1:1.

Every bet on a wheel costs the same, with one exception Straight up, split, corner or red: on a European wheel every one of them carries a 2.70% edge, and on an American wheel every one carries 5.26%. The payouts are set so that covering more numbers pays proportionally less. Choosing between bets is a choice about how wild the ride is, not about how much it costs you.

The exception is the American five-number basket bet on 0, 00, 1, 2 and 3. It pays 6:1 where the true odds are 6.6:1, giving a 7.89% edge. It is the worst bet on the table and the only one that breaks the rule.

La Partage and En Prison Some European casinos apply La Partage: if the ball lands on zero and you had an even-money bet down, half your stake comes back instead of all of it going away. That halves the edge on those bets to 1.35%, which is better than the craps pass line and beaten only by well-played blackjack.

En Prison is the same idea arranged differently. Your bet is locked for one more spin instead of being split, and if it wins that spin you get the stake back with no profit. Over many spins it comes to the same expected cost, which is why the calculator treats the two identically.

Both apply only to even-money bets, only on single-zero wheels, and only in casinos that offer them. Use the zero-rule selector above to see what it does to your figures.

The Gambler’s Fallacy, and why the board exists Each spin is independent. After ten reds in a row, red is still exactly as likely as it was on the first spin. The wheel has no memory and no obligation to even out.

Casinos know this perfectly well, which is why they pay to install the electronic board displaying the last twenty results. That board is not a service. It is the single cheapest piece of marketing on the floor.