What are your chances of winning at roulette after n spins?
It depends on how long you play and what you bet. Flat-betting red on a European wheel, the exact chance of being ahead is 48.6% after one spin, 35.5% after 100, and 18.8% after 1,000. The edge is small per spin and certain over many.
Being ahead, by bet and session length
Same bet, same stake, every spin. After n spins with w wins, the net is w × (payout + 1) − n stakes, and w is binomial. The tables sum the exact binomial probabilities of every winning count that leaves you strictly ahead. Finishing exactly even counts as not ahead.
| Spins (European) | Red / black | Dozen | Single number | Expected, $10 bets |
|---|---|---|---|---|
| 1 | 48.65% | 32.43% | 2.70% | -$0.27 |
| 10 | 34.42% | 41.61% | 23.97% | -$2.70 |
| 37 | 43.43% | 42.26% | 26.42% | -$10 |
| 100 | 35.53% | 40.53% | 50.94% | -$27.03 |
| 500 | 25.80% | 33.76% | 48.40% | -$135.14 |
| 1,000 | 18.76% | 26.69% | 45.11% | -$270.27 |
| 5,000 | 2.71% | 8.78% | 37.98% | -$1,351.35 |
| 10,000 | 0.33% | 2.71% | 32.51% | -$2,702.70 |
| Spins (American) | Red / black | Dozen | Single number | Expected, $10 bets |
|---|---|---|---|---|
| 1 | 47.37% | 31.58% | 2.63% | -$0.53 |
| 10 | 31.41% | 39.29% | 23.41% | -$5.26 |
| 37 | 37.35% | 37.90% | 25.44% | -$19.47 |
| 100 | 26.50% | 33.58% | 49.16% | -$52.63 |
| 500 | 11.07% | 20.33% | 44.45% | -$263.16 |
| 1,000 | 4.48% | 11.45% | 39.61% | -$526.32 |
| 5,000 | <0.01% | 0.40% | 26.76% | -$2,631.58 |
| 10,000 | <0.01% | <0.01% | 18.46% | -$5,263.16 |
Why the single number looks better for longer
A single number wins rarely and pays big, so one hit can carry a short session. At 37 spins the straight-up bettor is ahead 26.4% of the time: two hits or more in 37 spins puts them up. Red at 37 spins is ahead 43.4%. Both lose the same $2.70 per $100 on average. The single number just spreads the outcomes wider, so a bigger share of sessions lands on the lucky side for longer. Eventually the edge catches every bet; the crossover table shows when.
The sawtooth in the single-number column is real, not a rounding error. Being ahead requires 36 × wins > spins, so the number of wins needed jumps by one every 36 spins. Just after a jump, the chance drops.
What “winning” can’t mean here
A higher chance of being ahead is not a better bet. A Martingale finishes ahead in most sessions and still loses the edge on every dollar, because the sessions it loses are large. The only levers that move expected value are the wheel and its rules (2.70% versus 5.26%, 1.35% with la partage) and avoiding the American top line. No staking pattern does.
Calculator
Any bet, up to 20,000 spins, either wheel. Exact binomial sums, computed in your browser.
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