A European roulette wheel has 37 outcomes.
Our model draws uniformly from 0 to 36. A single number has probability 1/37, approximately 2.70%. A dozen covers twelve numbers, so its next-spin probability is 12/37, approximately 32.43%. Red, black, odd, even, low and high each cover eighteen numbers. Their probability is 18/37, approximately 48.65%, because zero belongs to neither half.
The model uses full loss on zero for outside bets. It does not include La Partage, En Prison, a double zero or multiplier bonuses. These distinctions matter when comparing a roulette strategy across different rules.
Roulette odds chart: the layouts in this library.
| Layout | Coverage | Hit probability | Base outlay | Net on a covered result |
|---|---|---|---|---|
| Red | 18/37 | 48.65% | 10 u | +10 u |
| Dozen 1 | 12/37 | 32.43% | 10 u | +20 u |
| Column 1 | 12/37 | 32.43% | 10 u | +20 u |
| Tiers | 12/37 | 32.43% | 12 u | +24 u |
| Voisins | 17/37 | 45.95% | 18 u | +18 u or +30 u |
| Orphelins | 8/37 | 21.62% | 10 u | +26 u or +62 u |
| Spiel | 7/37 | 18.92% | 8 u | +28 u or +64 u |
Net figures subtract the entire base layout cost. Sector payouts differ by number; the table is not a single uniform payout per sector.
How to calculate a roulette payout.
A winning component covering n numbers returns 36/n times that component’s stake, including the stake itself. A 10 u dozen returns 30 u gross, which is +20 u net. A 2 u split returns 36 u gross. If that split is one part of the 12 u Tiers layout, the whole layout’s net result is +24 u.
Voisins uses nine chips across seven combinations. Its two-chip trio and two-chip corner must be paid at their own rates. Orphelins includes overlapping splits: 17 wins both 14/17 and 17/20. Treating either sector as a dozen would produce incorrect results. See the exact layouts in the Voisins strategy and the Orphelins strategy.
Roulette streak probability and rare patterns.
For a chosen group covering c pockets, the probability of k consecutive misses from a fixed starting point is ((37 − c)/37)k. That calculation describes a specified run. It is not the probability of seeing at least one such run while monitoring many tables and overlapping windows.
After those misses, the next independent spin still has hit probability c/37. Historical rarity and next-spin probability answer different questions. Winnary helps organise the historical observation; it does not alter the wheel model.
What Martingale changes.
A Martingale roulette strategy increases stakes after losses. In our bounded versions, a cap of N doublings permits N+1 stakes. Starting at b units, the full losing ladder costs b × (2N+1 − 1). With b = 10 u and N = 5, the stakes are 10, 20, 40, 80, 160 and 320 u: a maximum loss of 630 u.
Doubling changes the distribution of episode results and the amount exposed. Under this model, each unit staked retains an expected loss of 1/37, approximately 2.70%. A capped progression does not reverse that expectation. The original first-dozen example shows the full ladder, including the seven entries that reached its limit in the saved sample.
Is there a best roulette strategy?
“Best roulette strategy” needs a criterion. A one-attempt fixed stake has a smaller loss ceiling than six doubled stakes; a broader layout covers more pockets but has its own cost and payout. None of those comparisons demonstrates a positive expectation on an independent fair wheel with these payouts. Compare the rules and exposure, then examine the entire result, rather than selecting the biggest positive total.
Use the roulette simulator to inspect the saved paths, the Rare strategies for short windows, and the Record Breaker strategies for strict monthly record entries.
Combination cross-checks: Casino di Venezia roulette rules and Casinos Austria roulette layouts. Probabilities and examples are calculated from the model stated above.