A game of chance with a built-in edge
Roulette is a game of chance. Every bet carries a built-in house edge, no strategy or timing changes the odds in the player’s favor over time, and most players lose money over time. This guide explains the arithmetic, not a way to beat it. Nobody should gamble money they cannot afford to lose, and anyone struggling with gambling can contact a local support service.
Counting the pockets
A roulette wheel has numbered pockets, and the ball lands in exactly one of them on each spin. Each pocket is equally likely on a fair, properly maintained wheel. The two common layouts differ only in the zeros:
- Single-zero wheel: pockets 1 through 36 plus one zero, so 37 pockets in total.
- Double-zero wheel: pockets 1 through 36 plus a zero and a double zero, so 38 pockets in total.
Some venues offer other layouts, but these two are the standard textbook cases.
Because every pocket is equally likely, a single number has a 1 in 37 chance on a single-zero wheel (about 2.70%) and a 1 in 38 chance on a double-zero wheel (about 2.63%). Every spin is also one of the independent events that probability textbooks describe: the wheel has no memory of earlier results.
Fair odds versus paid odds
Suppose a player bets on one number. There are 36 other pockets, so on a single-zero wheel the fair odds against that number would be 36 to 1: for every one way to win, there are 36 ways to lose. A game that paid 36 to 1 would be break-even over time. Roulette instead pays 35 to 1 on a single number. That one-unit gap is where the casino’s margin comes from.
The same logic applies to every bet type, because the payout is set as if the zeros were not there. The 36 numbered pockets are used to calculate the payout, but the wheel has 37 or 38 pockets in which the ball can land.
The main bet types
Bets fall into two families, covered in more detail in the explanation of inside bets and outside bets. The common ones, with their standard payouts, are:
| Bet | Numbers covered | Standard payout |
|---|---|---|
| Straight up | 1 | 35 to 1 |
| Split | 2 | 17 to 1 |
| Street | 3 | 11 to 1 |
| Corner | 4 | 8 to 1 |
| Dozen or column | 12 | 2 to 1 |
| Red/black, odd/even, high/low | 18 | 1 to 1 |
Notice the pattern. A bet covering n numbers pays roughly 36/n minus 1 to 1, which is the fair payout for 36 pockets, ignoring the zeros. A split covering two numbers pays 36/2 - 1 = 17. A dozen pays 36/12 - 1 = 2. Each payout is built from the same 36-number logic, so the bets look different but are priced alike.
How the zero creates the edge
Expected value is the average result per unit wagered over a very large number of identical bets. For a $1 straight-up bet on a single-zero wheel, the arithmetic is:
- Win with probability 1/37 and gain $35.
- Lose with probability 36/37 and lose $1.
- Expected value = (35 × 1/37) - (1 × 36/37) = (35 - 36)/37 = -1/37, about -$0.027.
That is an average loss of about 2.70 cents per dollar bet. The figure is a long-run average, not a prediction for any one session.
On a double-zero wheel the same payout applies, but the probabilities change:
- Expected value = (35 × 1/38) - (1 × 37/38) = (35 - 37)/38 = -2/38 = -1/19, about -$0.053.
The average loss is about 5.26 cents per dollar, roughly double the single-zero figure. This is why the effect of the extra zero is such a common comparison between the two wheels.
Checking other bets
The same method works for any bet. For a $1 red bet on a single-zero wheel, 18 pockets win and 19 lose (the 18 black pockets plus the zero):
- Expected value = (18 - 19)/37 = -1/37, about -2.70 cents.
On a double-zero wheel, 18 pockets win and 20 lose:
- Expected value = (18 - 20)/38 = -2/38, about -5.26 cents.
For a dozen bet paying 2 to 1 on a single-zero wheel, 12 pockets win and 25 lose:
- Expected value = (12 × 2 - 25)/37 = -1/37 again.
Standard bets on the same wheel all come out to the same percentage, which is a point explored under why every bet shares the same house edge. Even-money bets look like near coin flips, but the zeros make them slightly worse than that. A red bet wins about 48.65% of the time on a single-zero wheel (18/37) and about 47.37% on a double-zero wheel (18/38).
Some wheels and tables differ in details, such as special rules that return part of an even-money stake when the ball lands on zero. Those rules change the edge on those bets, and they vary by venue, so always check the posted rules.
What the percentage does and does not mean
A house edge of 2.70% does not mean a player loses 2.70% of their money in a session. It describes the average loss as a share of the total amount wagered across a large number of bets. Because each spin is wagered again and again, the total amount wagered can be much larger than the amount a player started with.
Short-term results vary widely around that average. A player can win several spins in a row, or leave ahead after an hour, and it says nothing about the odds changing. The law of large numbers describes why the average result moves toward the expected value as the number of spins grows, and why the casino’s position is far more predictable than any individual player’s. Small samples mislead in both directions.
Why past spins do not matter
If red has come up five times in a row, the next spin still has the same probability of red as it did before. The wheel does not balance things out. Believing otherwise is the gambler’s fallacy, and it can lead players to raise bets after losses. Past results are not a reason to bet more, and chasing losses tends to make things worse.
Summary of the key numbers
- Single-zero wheel: 37 pockets, average loss about 2.70% of each wager.
- Double-zero wheel: 38 pockets, average loss about 5.26% of each wager.
- Straight-up payouts are 35 to 1, while the fair price based on the pockets would be 36 to 1 (single zero) or 37 to 1 (double zero).
The math is simple, and it is the same each time: the payouts are calculated as though the zeros did not exist, while the ball can land on them. Treat roulette as paid entertainment with a known cost, set a limit that is truly spare money, and stop when it is reached.