Roulette Odds: The House Edge on Every Spin

Q: What is the house edge in roulette?

On an American wheel (38 pockets, with 0 and 00) every bet carries a 5.26% house edge. On a European wheel (37 pockets, single zero) the edge drops to 2.70%. The one exception is the American five-number bet on 0-00-1-2-3, which is worse at 7.89%.

Q: Is European roulette better than American roulette?

Yes. The European wheel removes the double zero, leaving 37 pockets, so the straight-up house edge is 1/37 = 2.70% instead of 2/38 = 5.26%, exactly half the damage on every spin. If you have the choice, single-zero is always the better table.

Q: Can a betting system like the Martingale beat roulette?

No. Every spin is independent and carries the same negative expected value, so no staking pattern (Martingale, doubling, chasing a color) can change the average. Systems rearrange when you win and lose, not whether the edge is against you. A cold streak plus a table limit is how the Martingale ends.

By Alex Thornton · author of the MIT-licensed teachersbettextbook library · Last reviewed 24 July 2026

Roulette is the most honest game in the casino: it hides nothing and beats you anyway. No strategy to learn, nothing to count. A wheel, a ball, and a house edge baked into the geometry. Where that edge comes from, and why no system can lift it.

How to read this game

One tool decodes every casino game: expected value. Multiply each outcome’s payoff by its probability, then add. That’s the average result of one spin:

\mathrm{EV} = \sum_i p_i \cdot (\text{payoff}_i)

The house edge is that number, sign flipped, per dollar staked. An EV of $-0.0526$ is a 5.26% edge: the casino keeps about a nickel of every dollar, on average, forever, by paying winners a little less than the true odds. In roulette, the gap between true odds and paid odds is two little green pockets.

The American wheel: 38 pockets, two of them green

An American wheel has 38 pockets: 1 through 36, plus a $0$ and a $00$ . A single number pays 35 to 1; with 38 pockets, break-even is 37 to 1. The house pays you as if the two zeros weren’t on the wheel. They are. That’s the whole trick.^[1]

Worked example: one number, straight up

\mathrm{EV} = \underbrace{\tfrac{1}{38}}_{\text{you win}}(+35) + \underbrace{\tfrac{37}{38}}_{\text{you lose}}(-1)

= \frac{35 - 37}{38} = -\frac{2}{38} = -5.26\%

One pocket pays 35; the other 37 take your dollar. The whole edge is the two green zeros, sitting in the numerator as a

-2

Every bet, the same tax

It doesn’t matter which bet you make. Red or black, a single number, a column, a corner. Almost every bet on the American wheel returns the exact same 5.26% house edge, because every payout is priced as if the zeros weren’t there.^[1]

The safest-feeling bet: red or black, even money. 18 red pockets, 18 black, and two green that belong to neither.

Worked example: red/black (even-money bet)

\mathrm{EV} = \underbrace{\tfrac{18}{38}}_{\text{red hits}}(+1) + \underbrace{\tfrac{20}{38}}_{\text{black or green}}(-1)

= \frac{18 - 20}{38} = -\frac{2}{38} = -5.26\%

Same

-2/38

, same 5.26%. The zeros are neither red nor black, so on an even-money bet they’re pure house. A bet that feels like a coin flip is quietly 47.4%/52.6%.

Change the bet and the arithmetic collapses back to the same two zeros out of 38. The 5.26% is a property of the pockets, not of your wager.

The one bet that’s even worse

One exception, and it’s a warning, not a loophole. The five-number bet covers $0$ , $00$ , 1, 2, and 3 with a single chip and pays 6 to 1. It’s the worst bet on the table.

Worked example: the five-number bet (0-00-1-2-3)

\mathrm{EV} = \underbrace{\tfrac{5}{38}}_{\text{one of five}}(+6) + \underbrace{\tfrac{33}{38}}_{\text{everything else}}(-1)

= \frac{30 - 33}{38} = -\frac{3}{38} = -7.89\%

A fair payout would be 6.6 to 1; the house pays a flat 6. The rounding-down costs an extra

-1/38

, pushing the edge to 7.89%, half again worse than every other bet.

American vs European roulette: the double zero is the difference

If the green pockets are the edge, removing one should halve the damage. It does. The European wheel has a single $0$ , 37 pockets in all, and that missing pocket is the whole story.

Worked example: straight up on a European wheel

\mathrm{EV} = \tfrac{1}{37}(+35) + \tfrac{36}{37}(-1) = \frac{35 - 36}{37} = -\frac{1}{37} = -2.70\%

Same 35-to-1 payout, one fewer losing pocket: the numerator drops from

-2

-1

, and the edge falls from 5.26% to 2.70%, almost exactly half. Same game, one pocket, twice the price on the American side.

Some European tables add la partage or en prison: land on zero and even-money bets get half the stake back (or ride another spin), cutting those bets to about 1.35%. Fewer green pockets, smaller tax.

Why you can’t beat it long-term

Every number above is negative, and no cleverness changes the sign. Three facts settle it:

Every spin is independent. The ball has no memory; pockets don’t rearrange to “balance out.” Believing a color is “due” is the textbook gambler’s fallacy. Researchers have filmed it at a live casino wheel.^[2] Each spin is a fresh 5.26% tax.
No skill, no information. Blackjack has a deck with memory, so a counter can flip the edge. Roulette has 38 identical pockets every time. Nothing to track; the EV is fixed the moment you place the chip.
No betting system moves the edge. The Martingale (double after every loss) rearranges when you win and lose; it cannot touch the average. A sequence of −5.26% bets is still −5.26% no matter how you size them. Doubling into a cold streak just hits the table limit, or an empty bankroll, with a stake too large to recover.

The formal version is short. Expected value is linear: a batch of bets is worth the sum of its parts, in any order, at any size.

\mathrm{EV}\!\left(\sum_i \text{bet}_i\right) = \sum_i \mathrm{EV}(\text{bet}_i) = \sum_i \big(-0.0526 \times \text{stake}_i\big) < 0

A system chooses the stakes. It does not choose the −0.0526. Every strategy ever sold to beat roulette is a different arrangement of losing bets, and a sum of negatives is negative.

The takeaway

American wheel: almost every bet costs 5.26%; the five-number bet costs 7.89%; the European single-zero wheel halves the damage to 2.70%. Every payout is priced as if the zeros didn’t exist. They do, and they never move. Each spin is an independent draw with a fixed, negative expected value, and no system touches it. None of this is advice; it’s the price list.

The same expected-value math runs the sports side, where an edge can actually go positive: the free +EV tool, or how expected value finds an edge. The whole casino floor: the house edge, game by game.

Watch your money disappear

Six players, $25 a spin on a single number, 1,000 spins. A lucky hit spikes a line. Then the −5.26% grinds every one to nothing. Replay it; the ending doesn’t change.

Want more math?the Nerd Corner

Nerd Corner

Advanced material. Nothing above depends on it.

Where these numbers come from

The 5.26%, 2.70%, and 7.89% aren’t estimates. They fall straight out of counting pockets, worked in full in the standard reference.^[1] The one empirical claim, that players bet as if the wheel had a memory, is on camera.^[2]

Ethier, S. N. (2010). The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer. A full roulette chapter: the game’s exact probabilities and house advantages, worked from first principles.
Croson, R. & Sundali, J. (2005). “The Gambler’s Fallacy and the Hot Hand: Empirical Data from Casinos.” Journal of Risk and Uncertainty 30(3), 195–209. 18 hours of casino security footage: real bettors chase “due” outcomes, exactly as the fallacy predicts.

Frequently asked questions

What is the house edge in roulette?

American wheel (38 pockets, with 0 and 00): 5.26% on every bet. European wheel (37 pockets, single zero): 2.70%. The one exception is the American five-number bet on 0-00-1-2-3, worse at 7.89%.

Why do all American roulette bets have the same house edge?

Every payout is set as if the two green zeros did not exist. A straight-up number pays 35 to 1 against true odds of 37 to 1; red or black pays even money against 20 to 18. The gap is always the same two zeros out of 38 pockets.

Is European roulette better than American roulette?

Yes. Removing the double zero leaves 37 pockets, so the straight-up edge is 1/37 = 2.70% instead of 2/38 = 5.26%, exactly half the damage on every spin.

Can a betting system like the Martingale beat roulette?

No. Every spin is independent with the same negative expected value, so no staking pattern changes the average. Systems rearrange when you win and lose, not whether the edge is against you. A cold streak plus a table limit is how the Martingale ends.