Roulette spins produce equally likely outcomes, so the probability of a bet winning equals the count of covered pockets divided by the total pockets. For a European wheel , while an American wheel includes a double zero, giving . The win probability is therefore where is the number of pockets your wager covers.
Expected value combines the win probability with the payout ratio. Casinos pay a straight bet 35:1, a split 17:1, a street 11:1, a corner 8:1, a six line 5:1, dozens and columns 2:1, and even-money wagers 1:1. The expected return for a one-unit stake is where is the payout ratio. Because roulette payouts assume the zero pocket is ignored, the formula yields a negative EV equal to the house edge.
The table summarizes coverage, payout, probability, and house edge for the most popular wagers. Use it to compare volatility and expected loss across the two wheel formats.
| Bet | Numbers covered | Payout | Prob. win (EU) | Prob. win (US) | House edge |
|---|---|---|---|---|---|
| Straight | 1 | 35:1 | 1/37 | 1/38 | ≈2.70% / 5.26% |
| Split | 2 | 17:1 | 2/37 | 2/38 | ≈2.70% / 5.26% |
| Street | 3 | 11:1 | 3/37 | 3/38 | ≈2.70% / 5.26% |
| Corner | 4 | 8:1 | 4/37 | 4/38 | ≈2.70% / 5.26% |
| Six line | 6 | 5:1 | 6/37 | 6/38 | ≈2.70% / 5.26% |
| Dozen/Column | 12 | 2:1 | 12/37 | 12/38 | ≈2.70% / 5.26% |
| Red/Black, Even/Odd, High/Low | 18 | 1:1 | 18/37 | 18/38 | ≈2.70% / 5.26% |
Although the house edge remains constant for a given wheel, volatility differs among bets. Straight wagers win rarely but deliver high payouts. Even-money bets hit nearly half the time, smoothing bankroll swings but not changing long-term expectation. Combine this calculator with the roulette bias detection sample size calculator or the gambling odds calculator to explore broader gambling scenarios.
Always gamble responsibly. Set limits, take breaks, and remember that a negative expected value means the casino has the advantage over many spins.
