Home › Casino Games Explained
The roulette house edge is pure arithmetic: 2.70% on the single-zero wheel, 5.26% on double-zero. Here are the derivations, pocket by pocket.
By Anja Wiedenhöft · August 9, 2026 · 6 min read
Roulette's house edge is pure arithmetic. A straight-up bet pays 35 to 1, but a fair payout would be 36 to 1, so the single green zero creates a 1/37 = 2.70% edge on the European wheel. The American double-zero wheel raises it to 2/38 = 5.26%.
Roulette is the clearest game in the casino for seeing exactly where the house edge comes from, because you can derive it with nothing more than counting. There is no strategy layer, no dealer decision, no skill component — just a wheel, a set of pockets, and a pay table. That transparency makes roulette the perfect place to learn what “house edge” really means and why it is a fixed arithmetic fact rather than something a betting pattern can erase.
There are two standard roulette wheels, and the difference between them is the single most important thing a player can know.
The pay tables are identical on both wheels. The extra pocket on the American wheel changes nothing about what you win — only how often you win it. That one extra green pocket is where the American wheel’s larger edge is manufactured, and the arithmetic below shows exactly how.
Consider the simplest bet: a straight-up bet on a single number. On a European wheel there are 37 pockets, so your chance of winning is 1 in 37. A straight-up bet pays 35 to 1 .
Here is the fair-payout test. If the game were perfectly fair — zero edge — a bet with a 1-in-37 chance would pay 36 to 1, because there are 36 ways to lose for every 1 way to win. It pays only 35 to 1. That missing unit is the house edge, and the green zero is what causes the mismatch.
Now the exact calculation. Stake 1 unit on a single number and imagine playing all 37 equally likely outcomes once:
Net across 37 spins: 35 − 36 = −1 unit. Spread that one-unit loss over 37 units staked:
House edge = 1 / 37 = 0.0270 = 2.70%
That is the European figure. Remarkably, it does not depend on which bet you choose. A red/black bet pays 1 to 1 but wins on only 18 of 37 pockets; a dozen pays 2 to 1 but wins on only 12 of 37. Run the same arithmetic on any of them and you land on the same 2.70%, because the single green zero applies the same proportional bite to every bet on the layout.
Repeat the exercise on the American wheel, where there are 38 pockets. A straight-up bet still pays only 35 to 1 — the pay table has not changed — but now your chance of winning is 1 in 38.
Play all 38 equally likely outcomes once with a 1-unit stake:
Net across 38 spins: 35 − 37 = −2 units. Spread that two-unit loss over 38 units staked:
House edge = 2 / 38 = 0.0526 = 5.26%
The pay table is unchanged, yet the edge has almost doubled. The extra green pocket added one more way to lose while the payout stayed frozen at 35 to 1. That is the entire mechanism: 2.70% versus 5.26% , decided by one pocket.
It is worth proving to yourself that the 2.70% figure really does apply to every bet on the European layout, because that universality is what makes roulette so clean to analyse. Take an even-money outside bet such as red. On a European wheel there are 18 red pockets, 18 black, and 1 green zero. Your chance of winning is 18/37; the bet pays 1 to 1.
Play all 37 outcomes once with a 1-unit stake: on the 18 red outcomes you gain 1 unit each (+18), and on the 19 non-red outcomes (18 black plus the zero) you lose 1 unit each (−19). Net: 18 − 19 = −1 unit over 37 units staked, which is again 1/37 = 2.70%. Try a dozen bet (12 winning pockets, pays 2 to 1): 12 × 2 = +24 on wins, −25 on the 25 losing pockets, net −1 over 37 — 2.70% once more. The green zero levies the identical proportional tax on every bet, which is why no combination of inside and outside bets can dodge it.
There is a single exception on the American wheel worth flagging. The “five-number” or basket bet (0, 00, 1, 2, 3) pays 6 to 1 but covers 5 of 38 pockets. Run the arithmetic: 6 × 5 = 30 on wins, −33 on the 33 losing pockets, net −3 over 38 units staked = 7.89%. It is the worst bet on the table and exists only on the double-zero wheel — a good reason to avoid it and, more broadly, to prefer the single-zero wheel entirely.
House edge is the average fraction of each bet the casino keeps over the long run. On a European wheel, for every 100 units you stake, the maths expects to return roughly 97.30 units, keeping 2.70. On an American wheel it keeps 5.26. Nearly double the cost, for an identical-looking game. If you have the choice, the single-zero wheel is always the cheaper place to play.
Some European tables sweeten single-zero further with La Partage or En Prison rules, which return half your even-money stake when the ball lands on zero. Where those rules apply, the effective edge on even-money bets falls to about 1.35%. That is a genuine rules-based improvement, disclosed at the table — not a trick and not a system.
The edge is a property of each individual spin, and every spin is independent: the wheel has no memory. This is where the popular myths break down, and naming them is the only way to dismantle them.
The ball’s landing pocket on a fair, certified wheel is random and independent of every prior result. No pattern of past numbers tells you where it will land next. A run of reds does not make black more likely; each spin restarts the same fixed probabilities.
A number that has not appeared for fifty spins is not due . Its probability on the next spin is exactly 1 in 37 (or 1 in 38), identical to every other number, exactly as it was fifty spins ago. Believing otherwise is the gambler’s fallacy — mistaking independent events for a self-correcting sequence.
Doubling after a loss, raising after a win, or any other staking progression changes the size and timing of your bets, never their odds. Each bet still carries the same 2.70% or 5.26% edge, so the average of many bets carries it too. Rearranging the stakes cannot turn a negative average into a positive one.
Roulette’s house edge is pure arithmetic: 1/37 = 2.70% on the European wheel, 2/38 = 5.26% on the American wheel, driven entirely by green pockets that pay nothing while the payout table stays fixed at 35 to 1. Choosing single-zero roughly halves your cost, and La Partage lowers it further on even-money bets. But nothing you do at the table — no pattern, no progression, no reading of past numbers — changes the edge on the next spin, because the wheel does not remember and cannot be predicted.
Roulette is entertainment with a guaranteed long-run cost to the player, not a way to make money. Decide what you can afford to lose before you play, and stop when you reach it. If it stops being fun, our responsible gambling resources can help.
On a European (single-zero) wheel the house edge is 1/37 = 2.70%. On an American (double-zero) wheel it is 2/38 = 5.26%. Both figures are arithmetic, derived directly from the pocket count and the pay table.
The pay tables are identical, but the American wheel has an extra green 00 pocket, giving 38 pockets instead of 37. That extra way to lose, with payouts unchanged, nearly doubles the house edge from 2.70% to 5.26%.
A straight-up bet pays 35 to 1 but wins on only 1 of 37 pockets. Across 37 spins of 1 unit you gain 35 on one win and lose 36 on the rest, a net of minus 1 over 37 staked. 1/37 = 2.70%. Every bet on the layout yields the same figure.
No. On a European wheel every bet, from a single number to red or black to a dozen, carries the same 2.70% edge, because the green zero taxes them all proportionally. The one exception is the American five-number bet, which is worse at 7.89%.
No. A certified wheel is random and every spin is independent, so the wheel has no memory. Past results, streaks, and hot patterns tell you nothing about the next spin, and no number is ever due. Believing otherwise is the gambler's fallacy.
No. Doubling after a loss or any other staking progression changes only the size and timing of your bets, never the odds. Each bet still carries the 2.70% or 5.26% edge, so the average over many bets stays negative.