Roulette Odds Calculator
Every roulette bet has an exact, fixed win probability and a fixed house edge that depends only on the wheel. Enter how many pockets your bet covers, the payout to one for a win, and the total number of pockets on the wheel (37 for European single-zero, 38 for American double-zero). The calculator returns your win probability, the expected value per unit staked, and the house edge as a percentage. These figures are pure combinatorics: there is no estimation, only the geometry of the wheel and the casino's payout schedule.
Roulette odds formulas
Win probability p = pockets covered / total pockets
Lose probability = 1 - p
Expected value = p * payout - (1 - p) * 1
House edge percent = -Expected value * 100
The payout to one is the net win per unit staked, so a single-number bet that pays 35 to 1 returns 35 plus your 1 unit on a win. The expected value, multiplied by minus 100, is the house edge as a percentage.
Standard wheel figures
- Single number on a 37-pocket wheel: probability 1/37, payout 35 to 1, edge 2.70 percent.
- Red or black on a 37-pocket wheel: probability 18/37, payout 1 to 1, edge 2.70 percent.
- Single number on a 38-pocket wheel: probability 1/38, payout 35 to 1, edge 5.26 percent.
- A dozen bet covers 12 pockets and pays 2 to 1.
- All standard bets on a given wheel share the same house edge.
Roulette odds: frequently asked questions
How does the roulette house edge arise?
Payouts are set as if the wheel had only the numbers you can bet on, but the wheel also has a 0 (and a 00 on American wheels). Those extra pockets are not covered by inside or even-money bets, so over many spins the casino keeps a fixed fraction of every wager. The difference between the fair payout and the actual payout is the edge.
What is the house edge on each wheel?
On a single-zero (European) wheel with 37 pockets the house edge on most bets is 1/37, about 2.70 percent. On a double-zero (American) wheel with 38 pockets it is 2/38, about 5.26 percent. This calculator computes the exact edge for the bet and wheel you choose.
What inputs does this calculator use?
Enter the number of pockets your bet covers (for example 18 for red, 1 for a single number, 12 for a dozen), the payout to one (the net amount won per unit staked), and the total pockets on the wheel (37 or 38). All three determine the probability, expected value and edge.
What is expected value per unit staked?
Expected value is the win probability times the payout, minus the lose probability times 1. It is the average net result per unit wagered. A negative expected value equals the house edge as a fraction, which is why every standard roulette bet has the same expected loss on a given wheel.
Why do different bets share the same house edge?
On a single-zero wheel every standard bet, whether a single number paying 35 to 1 or red paying 1 to 1, has the same 2.70 percent edge, because the payouts are all scaled from a 36-number fair wheel while the real wheel has 37 pockets. The edge depends on the wheel, not the bet type.
Official sources
- Nevada Gaming Control Board: Gaming regulations and approved game rules.
- NIST/SEMATECH e-Handbook of Statistical Methods: Probability and expected value.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.