- Probability = numbers covered ÷ pockets.
- Every European bet has the same 2.70% edge; every American bet 5.26%, except the basket at 7.89%.
- Spins are independent. Streaks do not change the next result.
- Variance, not edge, decides how a single session feels.
Roulette probability is arithmetic, not mystery. Every bet's chance of winning is the number of pockets it covers divided by the number of pockets on the wheel, and every payout is the same on both wheels. Once you see those two facts side by side, the house edge falls out on its own.
Probability on the European wheel
37 pockets. A straight-up bet wins 1/37 of the time — 2.70%. Red wins 18/37 — 48.65%. A dozen wins 12/37 — 32.43%.
| Bet | Numbers | Probability | True odds | Payout |
|---|---|---|---|---|
| Straight | 1 | 2.70% | 36:1 | 35:1 |
| Split | 2 | 5.41% | 17.5:1 | 17:1 |
| Street | 3 | 8.11% | 11.33:1 | 11:1 |
| Corner | 4 | 10.81% | 8.25:1 | 8:1 |
| Six line | 6 | 16.22% | 5.17:1 | 5:1 |
| Dozen / column | 12 | 32.43% | 2.08:1 | 2:1 |
| Even-money | 18 | 48.65% | 1.056:1 | 1:1 |
Every payout is what it would be on a 36-pocket wheel. The 37th pocket is the casino's.
Probability on the American wheel
38 pockets, same payouts. Straight-up drops to 1/38 = 2.63%; red to 18/38 = 47.37%. Because the payouts do not move, the edge nearly doubles to 5.26%. The five-number basket bet pays 6:1 on a 7.6:1 shot for an edge of 7.89% — the single worst bet in the game.
Expected value
Expected value (EV) is what a bet is worth on average. For a CA$10 red bet on a European wheel:
EV = (18/37 × CA$10) − (19/37 × CA$10) = CA$4.865 − CA$5.135 = −CA$0.27
That −27 cents is 2.70% of CA$10. Run the same sum for any European bet and you get −2.70% every time. On the American wheel you get −5.26% every time (except the basket). This is why "which bet is best" has no answer on a given wheel: they are all priced identically.
Streaks and the gambler's fallacy
Each spin is independent. After ten reds in a row, black is still 18/37. The probability of ten reds in a row before you start is (18/37)10 ≈ 0.07%, but after nine have happened the tenth is just another spin. Our wheel simulator shows how often long runs actually appear — in 10,000 spins you will routinely see runs of ten or more.
Probability of hitting at least once in N spins
The chance of a straight-up number hitting at least once in 37 spins is not 100% — it is 1 − (36/37)37 ≈ 63.6%. In 100 spins it is 93.5%. Use the odds calculator for any bet, and the payout calculator for streak odds.
Variance: why sessions feel nothing like the edge
A 2.70% edge is invisible over 50 spins. The standard deviation of an even-money bet is almost exactly one bet per spin, so over 50 spins of CA$10 you should expect a result anywhere between about −CA$85 and +CA$60 two-thirds of the time, with an average of −CA$13.50. Straight-up bets have far more variance: the same 50 spins will most often show a loss of CA$500 (no hits) or a profit of CA$360 (one hit). The edge is the same; the ride is completely different. Our bankroll calculator simulates this for you.
Try it yourself
Every number in this guide can be checked on the site: spin the European and American demos side by side, run bets through the odds calculator, or test any system in the strategy simulator.
