The two common wheels
A European wheel has 37 pockets: numbers 1 to 36 plus a single zero. An American wheel has 38, adding a double zero. Every pocket is intended to be equally likely on every spin, so the chance of any one number is 1 in 37 on the first wheel and 1 in 38 on the second. The extra pocket is the reason the American game costs players more.
The payouts are set as if there were 36 pockets. The zero pockets belong to no ordinary bet, and that gap is where the casino’s advantage comes from.
Chances and payouts by bet type
For a European wheel, the probability and payout for each bet are:
| Bet | Pockets covered | Chance of winning | Payout |
|---|---|---|---|
| Straight (one number) | 1 | 2.70% | 35 to 1 |
| Split (two numbers) | 2 | 5.41% | 17 to 1 |
| Street (three numbers) | 3 | 8.11% | 11 to 1 |
| Corner (four numbers) | 4 | 10.81% | 8 to 1 |
| Six line | 6 | 16.22% | 5 to 1 |
| Dozen or column | 12 | 32.43% | 2 to 1 |
| Red/black, odd/even, high/low | 18 | 48.65% | 1 to 1 |
On an American wheel the same bets have one extra losing pocket, so a straight bet wins 1 time in 38 (2.63 percent) and an even-money bet wins 18 times in 38 (47.37 percent), at the same payouts.
The edge is the same for almost every bet
Take a 1-unit straight bet on the European wheel. It wins 35 units with probability 1/37 and loses 1 unit with probability 36/37. The expected value is 35/37 minus 36/37 = minus 1/37, about minus 2.70 percent.
A split gives 17 x 2/37 minus 35/37 = 34/37 minus 35/37 = minus 1/37. The same result appears for every row in the table, because the payouts are all calibrated to the same 36-pocket arithmetic. The even-money bet gives 18/37 minus 19/37 = minus 1/37 as well.
On a double-zero wheel the edge doubles in size: 2/38, about 5.26 percent. One American layout also offers a five-number bet (0, 00, 1, 2, 3) that pays 6 to 1, which works out at minus 3/38, about 7.89 percent, and is the most expensive standard bet on the table.
Some European tables return half of an even-money stake when the ball lands on zero, which roughly halves the edge on those bets, to about 1.35 percent. Whether this applies depends entirely on the table’s rules.
Probabilities that mislead
Because the single-number chance is small, many people expect that spinning for a number “enough times” must bring it. The chance of hitting a particular number at least once in 37 spins is easiest to find by complement counting: work out the chance of missing every time, (36/37) to the power 37, which is about 36.3 percent, and subtract it from 1. That leaves about 63.7 percent. So even after a full 37 spins, a hit is far from certain, and the 35 to 1 payout on a hit does not make up for the roughly 37 stakes spent on average.
The wheel has no memory. If a European wheel produces ten reds in a row, the next spin still has an 18/37 chance of red. Believing black is “due” is the mirror image of the hot hand belief, which expects the streak to continue, and the mathematics supports neither. Spins are independent, so past results carry no information about the next one.
Why betting systems do not change the maths
A betting system is a rule for changing the stake from spin to spin. The best-known is the Martingale: bet 1, and after each loss double the stake until a win recovers everything plus a profit of 1 unit.
It looks safe because, in the short run, it usually works. Its problem is the rare run of losses. On a European wheel, the chance of losing an even-money spin is 19/37. Six losses in a row has probability (19/37) to the power 6, about 0.018 or roughly 1 in 55. After six losses the player has staked 1 + 2 + 4 + 8 + 16 + 32 = 63 units, and the next bet required is 64. Table limits and a finite bankroll cap how far doubling can go, and the final loss is far larger than the many small wins that preceded it.
The deeper point is that every spin remains a bet with a negative expectation. The expected value of a series of bets is the sum of the expected values of the individual bets, so no pattern of stakes can turn a set of losing bets into a winning one on average. Systems only change the shape of the results, mostly many small wins and occasional large losses, and not the average. The Fibonacci, D’Alembert and Labouchere systems follow the same logic. They are different ways of sizing stakes, and none of them changes the odds.
Increasing the stake after losses is also the pattern behind chasing losses, which raises the risk of ruin, because a longer losing run needs a larger bankroll just to continue.
What this means
Roulette is a game of chance with a fixed cost built into every bet. Over many spins, the average outcome per unit staked approaches that cost, as the law of large numbers describes, even though a single session can finish ahead or behind. Nothing in the layout of the wheel, the history of recent numbers or the size of the stake alters that.
Gambling can be harmful, and any outcome is uncertain. If you play, treat the money as the price of entertainment, not as a way of earning, and set a firm limit beforehand. If gambling is a concern for you or someone close to you, a local support service can help.