Roulette Strategy Probability
Probability is the foundation of every roulette decision. Knowing the hit rate for a specific bet immediately tells you the win frequency, the variance and the long-run cost.
This page collects the probabilities for every common bet and explains how strategy choices change your overall exposure.
Single-bet probabilities
| Bet type | Numbers | European | American |
|---|---|---|---|
| Single number | 1 | 2.703% | 2.632% |
| Split | 2 | 5.405% | 5.263% |
| Street | 3 | 8.108% | 7.895% |
| Corner | 4 | 10.811% | 10.526% |
| Six line | 6 | 16.216% | 15.789% |
| Dozen / Column | 12 | 32.432% | 31.579% |
| Even-money (red, etc.) | 18 | 48.649% | 47.368% |
Why even-money is not 50/50
Red has 18 numbers. So does black. Zero (and 00 on American) is neither. So in 37 spins of European you average 18 reds, 18 blacks, 1 zero. Red probability is 18/37 = 48.65%, not 50%.
That 1.35% gap (European) or 2.63% gap (American) is exactly the house edge expressed differently. Every 'even-money' bet pays even money on a wheel that does not have even-money odds.
Compound bet probabilities
Strategies that place multiple bets per spin have a different overall hit probability. Examples:
| Strategy | Numbers covered | European hit % | American hit % |
|---|---|---|---|
| Two Dozens | 24 | 64.86% | 63.16% |
| Two Columns | 24 | 64.86% | 63.16% |
| James Bond | 25 | 67.57% | 65.79% |
| Voisins du Zero | 17 | 45.95% | n/a |
| Single column + opposite dozen | 16-20 | varies | varies |
Higher coverage means higher hit frequency but smaller net win per hit. The net expected value still equals total stake times house edge.
Probability of streaks
For a bet with loss probability q, the probability of n consecutive losses is qn. On European red, q = 19/37 = 51.35%.
| Streak length | Probability | Approx. once per N spins |
|---|---|---|
| 2 | 26.4% | ~4 |
| 4 | 6.95% | ~14 |
| 6 | 1.83% | ~55 |
| 8 | 0.48% | ~207 |
| 10 | 0.127% | ~787 |
| 15 | 0.00467% | ~21,400 |
Probability of hitting a specific number in N spins
For a single number on European (p = 1/37), the probability of not hitting in n spins is (36/37)n.
| Spins | P(at least one hit) | P(no hit) |
|---|---|---|
| 10 | 23.8% | 76.2% |
| 37 (one cycle) | 63.7% | 36.3% |
| 100 | 93.4% | 6.6% |
| 200 | 99.56% | 0.44% |
This is why 'this number is overdue' is a fallacy. Each spin is independent. The probability does not change based on history. See Common mistakes.
How strategies change exposure
A strategy can change your variance and your hit rate, but it cannot change the long-run expected value. Martingale raises hit-rate-per-cycle but enormously amplifies loss when streaks hit. James Bond raises hit-rate-per-spin but adds catastrophic losses on 1-12.
Both have the same expected value per dollar wagered as flat betting. Strategy choice is risk-shape selection, not edge improvement.