Every roulette bet with its true probability, payout and cost per unit staked. Single-zero versus double-zero wheel, and why no betting system changes it.
Roulette pays every bet as if the zero were not on the wheel. The gap between the true odds and the posted payout is the entire house edge, and it is the same on every bet on the layout — which is why no combination of them is cheaper than any other.
| Bet | Covers | Pays | Chance | Odds | Cost per unit |
|---|---|---|---|---|---|
| Straight up | 1 | 35:1 | 2.70% | 1 in 37.0 | 2.70% |
| Split | 2 | 17:1 | 5.41% | 1 in 18.5 | 2.70% |
| Street | 3 | 11:1 | 8.11% | 1 in 12.3 | 2.70% |
| Corner | 4 | 8:1 | 10.81% | 1 in 9.3 | 2.70% |
| Six line | 6 | 5:1 | 16.22% | 1 in 6.2 | 2.70% |
| Column | 12 | 2:1 | 32.43% | 1 in 3.1 | 2.70% |
| Dozen | 12 | 2:1 | 32.43% | 1 in 3.1 | 2.70% |
| Red / Black | 18 | 1:1 | 48.65% | 1 in 2.06 | 2.70% |
| Odd / Even | 18 | 1:1 | 48.65% | 1 in 2.06 | 2.70% |
| Low / High | 18 | 1:1 | 48.65% | 1 in 2.06 | 2.70% |
| Bet | Covers | Pays | Chance | Odds | Cost per unit |
|---|---|---|---|---|---|
| Straight up | 1 | 35:1 | 2.63% | 1 in 38.0 | 5.26% |
| Split | 2 | 17:1 | 5.26% | 1 in 19.0 | 5.26% |
| Street | 3 | 11:1 | 7.89% | 1 in 12.7 | 5.26% |
| Corner | 4 | 8:1 | 10.53% | 1 in 9.5 | 5.26% |
| Six line | 6 | 5:1 | 15.79% | 1 in 6.3 | 5.26% |
| Column | 12 | 2:1 | 31.58% | 1 in 3.2 | 5.26% |
| Dozen | 12 | 2:1 | 31.58% | 1 in 3.2 | 5.26% |
| Red / Black | 18 | 1:1 | 47.37% | 1 in 2.11 | 5.26% |
| Odd / Even | 18 | 1:1 | 47.37% | 1 in 2.11 | 5.26% |
| Low / High | 18 | 1:1 | 47.37% | 1 in 2.11 | 5.26% |
| Basket (top line) | 5 | 6:1 | 13.16% | 1 in 7.6 | 7.89% |
On French tables with la partage or en prison an even-money bet loses only half its stake to zero, which brings those bets down to 1.35%. It does not apply to any other bet on the table.
Roulette is the most transparent game on a casino floor, and the reason is arithmetic rather than honesty. A straight-up number wins once in thirty-seven spins on a single-zero wheel and pays thirty-five to one. Pay it thirty-six to one and the game would be even; the missing unit is the entire house edge, and it works out to 2.70% of everything staked.
The same subtraction runs through every bet on the layout. Red pays even money on a chance that is not quite even, a dozen pays two to one on a chance that is not quite one in three. That is why the cost column in the table above is the same figure over and over — spreading chips across the felt changes how often you win and how much, and leaves the price untouched.
A double-zero wheel has thirty-eight pockets and pays exactly what the thirty-seven-pocket wheel pays. That extra pocket takes the edge from 2.70% to 5.26% — the same bet costs you very nearly twice as much. Sitting at the right wheel is worth more than every betting decision you will make in a session combined.
French tables go the other way. Under la partage or en prison, an even-money bet loses only half its stake when the ball lands in zero, which brings the edge on those bets down to 1.35%. It applies to red, black, odd, even, high and low only — a straight-up number still costs 2.70%.
The Martingale doubles after each loss so that one win recovers everything. It works until the run of losses outlasts either your bankroll or the table maximum, and both are finite. What the system really does is trade a large number of small wins for a rare, very large loss; the average stays exactly where the wheel put it.
The same is true of the d’Alembert, the Fibonacci, the Labouchère and every progression yet invented. Each spin is independent, so no sequence of past results changes the next one, and no staking pattern can turn a negative expectation into a positive one. Systems change the shape of the distribution — how often you win and how badly you lose — never its mean.
This is not a caution about discipline. It is a statement about arithmetic that holds however carefully the system is followed.
Three things, in order of size. The wheel: single zero over double zero, and French rules over both if the table offers them. The bet size relative to bankroll, which does not change expected cost but decides how long a session survives normal variance. And time at the table, because the edge is charged per spin — the expected loss is the edge multiplied by everything staked, not by what you sat down with.
One in thirty-seven on a European wheel (2.70%) and one in thirty-eight on an American one (2.63%). Both pay thirty-five to one, which is where the house edge comes from.
2.70% on a single-zero wheel and 5.26% on a double-zero wheel. On French tables with la partage or en prison, even-money bets cost 1.35%.
None of them has a better price. Red, black, odd, even, high and low win most often, but every bet on the layout carries the same expected cost per unit staked — the only exception is the American basket bet, which is worse at 7.89%.
No. It converts many small wins into one rare catastrophic loss, bounded by your bankroll and the table maximum. The average outcome is unchanged, because each spin is independent of the last.
European, without qualification. Same bets, same payouts, one fewer pocket — the edge is 2.70% instead of 5.26%.
On provably fair implementations you can verify each spin yourself from the seed pair. Elsewhere you are relying on RNG certification, which is an audit rather than a proof.