Red or black odds in roulette: every even-money bet, both wheels
Red, black, odd, even, 1–18 and 19–36 each cover eighteen numbers and pay 1 to 1. Zero belongs to none of them. Each wins 48.65% of spins on a European wheel (1 in 2.1) and 47.37% on American, so the house keeps 2.70% and 5.26% of every stake.
Where the chip goes
Even-money bets: 6, in three pairs: red or black, odd or even, low (1–18) or high (19–36). Each covers 18 numbers. Zero, and 00, lose them all.
Odds and payout on both wheels
The win chance is pockets covered over pockets on the wheel. True odds are what the bet would have to pay for the house to make nothing; the gap between true odds and the actual payout is the edge.
| European | American | |
|---|---|---|
| Numbers covered | 18 of 37 | 18 of 38 |
| Win chance | 48.65% | 47.37% |
| As odds | 1 in 2.1 | 1 in 2.1 |
| Pays | 1 to 1 | 1 to 1 |
| True odds | 1.06 to 1 | 1.11 to 1 |
| House edge | 2.70% | 5.26% |
| Expected result, $10 bet | −$0.27 | −$0.53 |
| Std. deviation per $1 | $1.000 | $0.999 |
| Edge outweighs luck after | 1,368 spins | 360 spins |
The last row is where the expected loss grows past one standard deviation of luck; the house edge page derives it and compares every bet.
How often it hits
The chance of at least one hit in n spins is 1 − (1 − p)n. On average the bet comes in once every 2.1 spins on a European wheel. Half of all players see a hit within 2 spins, nine in ten within 4, and 99 in 100 within 7.
| Within | European | American |
|---|---|---|
| 1 spin | 48.65% | 47.37% |
| 5 spins | 96.43% | 95.96% |
| 10 spins | 99.87% | 99.84% |
| 25 spins | >99.99% | >99.99% |
| 37 spins | >99.99% | >99.99% |
| 50 spins | >99.99% | >99.99% |
| 100 spins | 100.00% | 100.00% |
| 200 spins | 100.00% | 100.00% |
Droughts
A drought is a run of spins without a hit. The chance that the next L spins all miss is (1 − p)L. Seeing a drought that long somewhere in a long session is far more likely, and the last column is computed exactly by dynamic programming over the current run of misses, not by simulation.
| Misses in a row | Next L spins | Somewhere in 1,000 spins |
|---|---|---|
| 4 | 6.954% | >99.99% |
| 6 | 1.834% | >99.99% |
| 10 | 0.128% | 46.17% |
| 16 | 0.002% | 1.12% |
| 25 | <0.001% | <0.01% |
Chance of being ahead after n spins
Flat stakes, the same bet every spin. After n spins with w wins the net is w × 2 − n stakes, and w is binomial, so these are exact sums. Breaking even counts as not ahead. The chances of winning page compares bets side by side and has a calculator for any session length.
| Spins | European | American | Expected, $10 bets |
|---|---|---|---|
| 1 | 48.65% | 47.37% | -$0.27 |
| 10 | 34.42% | 31.41% | -$2.70 |
| 37 | 43.43% | 37.35% | -$10 |
| 100 | 35.53% | 26.50% | -$27.03 |
| 500 | 25.80% | 11.07% | -$135.14 |
| 1,000 | 18.76% | 4.48% | -$270.27 |
| 10,000 | 0.33% | <0.01% | -$2,702.70 |
Six bets, one probability
Red or black, odd or even, 1–18 or 19–36: each side has 18 numbers and zero sits on none of them, so all six share the same 48.65% on a European wheel. Zero is neither odd nor even for betting purposes. That single pocket is the whole edge.
Rules that halve the edge
Some single-zero tables use la partage: when zero comes up, even-money bets lose only half their stake. A few use en prison, which holds the stake for one more spin instead. Both bring the even-money edge down to about 1.35%, the lowest of any roulette bet. The simulator plays standard European and American rules, so it does not model either.
The bet the progressions use
Almost every staking system is built on an even-money bet, because it wins often enough to keep a progression alive. That is also why long losing runs matter so much: the red-in-a-row page has the exact odds of a streak, and the systems below show what those streaks do to a bankroll.
Systems built on this bet
Each runs over the same seeded sessions as every other system on the site. The figure is the result per $100 wagered on a European wheel.
| System | Per $100 wagered | In short |
|---|---|---|
| Flat betting | −$2.71 | one unit on red, every spin, no progression. The baseline. |
| Martingale | −$2.52 | double the stake after every loss, return to one unit after a win. |
| Grand Martingale | −$2.66 | double the stake and add one unit after every loss. |
| Reverse Martingale | −$2.70 | double the stake after every win, return to one unit after a loss. |
| Paroli | −$2.69 | double after a win, bank the streak after three wins in a row. |
| Fibonacci | −$2.78 | move one step up the Fibonacci sequence after a loss, two steps back after a win. |
| D’Alembert | −$2.87 | add one unit to the stake after a loss, remove one after a win. |
| Contra D’Alembert | −$2.71 | add one unit after a win, remove one after a loss. |
| Labouchère | −$2.69 | bet the sum of the first and last numbers on a list; cross them off on a win, append the stake on a loss. |
| Reverse Labouchère | −$2.66 | Labouchère inverted: append the stake on a win, cross off two numbers on a loss. |
| Oscar’s Grind | −$2.67 | aim for one unit of profit per series, raising the stake only after a win. |
| 1-3-2-6 | −$2.71 | stake 1, 3, 2, then 6 units across a winning run; reset on any loss. |
| Betting against a streak | −$2.77 | after five reds (or blacks) in a row, bet the other colour. |
| Fixed fraction (2%) | −$2.69 | stake 2% of the current bankroll on red, every spin. |
| James Bond | −$2.66 | spread 20 units across high (19–36), the 13–18 six-line, and zero. |
Questions
What does an even-money bet pay in roulette?
1 to 1. A winning $10 red / black bet pays $10 and the $10 stake comes back too. For the bet to be fair on a European wheel it would have to pay 1.06 to 1; the difference is the house edge.
How often does an even-money bet win?
48.65% of spins on a European wheel, or 1 in 2.1 (47.37% on an American wheel). On average it hits once every 2.1 spins, and there is a better-than-even chance of at least one hit within 2 spins.
Is an even-money bet a good bet?
It is no better and no worse than the rest of the layout: 2.70% house edge on a European wheel, 5.26% on American, the same as every other bet there except the American top line. Only the swing differs: about $1.00 of standard deviation per $1 staked, per spin.
Related
- Roulette house edge: where 2.70% and 5.26% come from
- What are the odds of red 10 times in a row in roulette?
- What are your chances of winning at roulette after n spins?
- How many spins until every roulette number comes up?
- Every bet’s odds and payout, both wheels
- Does any betting system work? 20 systems on the same seeds
- Study: European versus American roulette, the risk distribution
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