House edge is the share of every bet the casino keeps on average over the long run. In roulette it comes from one fact: a single-number bet pays 35 to 1, but there are more than 36 pockets. On a 37-pocket European wheel the expected return on a 1-unit bet is 35 times 1/37 minus 36/37, which is minus 1/37, a house edge of 2.70%. On a 38-pocket American wheel the edge is 2/38, or 5.26%, and on a 39-pocket triple-zero wheel 3/39, or 7.69%. The edge is identical on every bet type of a given wheel, with one exception listed below.
How the house edge is calculated, by wheel type
| Wheel | Pockets | House edge | Expected loss per €100 staked | Changes after a streak? |
|---|---|---|---|---|
| French (single zero, la partage) | 37 | 1.35% on even-money bets, 2.70% on all others | €1.35 / €2.70 | No |
| European (single zero) | 37 | 2.70% | €2.70 | No |
| American (double zero), Atlantic City rules | 38 | 2.63% on even-money bets, 5.26% on all others | €2.63 / €5.26 | No |
| American (double zero) | 38 | 5.26%; five-number bet 0-00-1-2-3: 7.89% | €5.26 (€7.89) | No |
| Triple-zero | 39 | 7.69% | €7.69 | No |
Why 5.26% is not simply double 2.70%: the extra zero adds a losing pocket to the denominator as well, so the edge is $2/38$, not $2 \times 1/37$. Why the five-number bet is worse: it pays 6 to 1 on a 5-in-38 chance, giving $6 \cdot \tfrac{5}{38} - \tfrac{33}{38} = -\tfrac{3}{38} = -7.89\%$.
Expected-loss calculator
Pick a wheel, a bet size and a number of spins. The calculator returns the expected loss (edge × total staked) and the typical range after that many spins for a single even-money bet, so you can see how big the short-term swings are compared with the long-term drift.
Range: for an even-money bet the per-spin standard deviation is $\sqrt{1 - e^2}$ units where $e$ is the edge, so after $n$ spins the total is roughly $-e n \pm 2\sqrt{n}$ units. The last card shows the $n$ at which $e n = 2\sqrt{n}$, i.e. $n = 4/e^2$: beyond it, a loss is the normal outcome rather than a coin flip.
Why betting systems and hot numbers do not change the edge
Expected value is linear. If $b_i$ is the bet on spin $i$ and $X_i$ its per-unit result, then $\mathbb{E}\left[\sum b_i X_i\right] = \mathbb{E}[X] \sum b_i$. Whatever rule chooses $b_i$, Martingale, Fibonacci, d'Alembert, "bet the hot number", "bet against the streak", the expectation is the house edge times the total amount staked. The rule only reshapes the distribution: many small wins and a rare large loss, or the reverse.
This is not only theory. In 18 hours of security video from a Reno casino (139 players, 24,131 bets, 904 spins), after six or more identical even-money outcomes 85% of bets went against the streak, and the wheel showed no bias at all: the most frequent number came up 3.7% of the time, the least frequent 1.7%, against an expected 2.6%. Every one of those "due" bets carried the same 5.26% edge as a bet placed at random.
Sources
- Wizard of Odds. "Roulette for Beginners: Rules, Odds and House Edge." wizardofodds.com/games/roulette/basics/ (accessed 24 October 2026): 2.70%, 5.26%, 7.69%, 7.89%, Atlantic City 2.63%, la partage expected value −0.0135.
- Croson, R. and Sundali, J. (2005). "The Gambler's Fallacy and the Hot Hand: Empirical Data from Casinos." The Journal of Risk and Uncertainty, 30(3), 195–209. doi:10.1007/s11166-005-1153-2
Frequently asked questions
What is the house edge in European roulette?
2.70% on every bet. It comes from the 35-to-1 payout on a 37-pocket wheel: the expected return per unit is 35/37 minus 36/37, which is minus 1/37. Under French la partage rules even-money bets lose only half the stake when zero hits, which lowers the edge on those bets to 1.35%.
What is the house edge in American roulette?
5.26% on every bet except the five-number bet on 0, 00, 1, 2 and 3, which carries 7.89%. Under Atlantic City rules even-money bets drop to 2.63%. The edge is 2/38, not double 1/37, because the second zero also enlarges the denominator.
Does the house edge change after a long streak of red or black?
No. Every spin is independent, so the probability of red is 18/37 on a European wheel regardless of history. Betting against a streak, or with it, carries exactly the same edge. The 1913 Monte Carlo run of 26 blacks and a 2005 casino study of 24,131 bets both illustrate this.
Can a betting system such as Martingale reduce the house edge?
No. Expected value is linear in the bet size, so the expected loss of any sequence of bets equals the edge times the total amount staked. Systems change the shape of outcomes, not their average, and table limits plus a finite bankroll make the rare large loss certain over time.
How many spins before the house edge beats luck?
For an even-money bet the expected loss grows with the number of spins while the random swing grows with its square root. They are equal at about 4 divided by the edge squared: around 5,500 spins on a European wheel and 1,450 on an American wheel. Beyond that, finishing behind is the normal result, not a toss-up.