European vs American roulette

European roulette has 37 pockets with a single zero; American roulette has 38, adding a double zero. The payouts are identical, so the extra pocket is pure house edge: 2.70% on a European wheel, 5.26% on an American one and 7.69% on the newer triple-zero wheels. Given the choice, play single zero — as at our tables.

Every bet pays as if there were 36 numbers. On a European wheel the 37th pocket, zero, is the house’s share: 1/37 = 2.70%. The American wheel has two such pockets, 0 and 00: 2/38 = 5.26%. A triple-zero wheel has three: 3/39 = 7.69%.

Nothing else changes. A number still pays 35 to 1 and red still pays 1 to 1; you just hit them less often.

A round in the Rotunda of Shai takes about 33 seconds, so an hour is roughly 108 spins. Bet 1,000 a spin for an hour and the expected loss is about 2,900 debens on a European wheel, 5,700 on an American one and 8,300 with three zeros. Same evening, same bets — and the worst wheel costs nearly three times as much.

Short sessions hide it: over 20 spins luck swamps the difference. Over hundreds of spins the edge decides almost everything.

An edge of a few percent sounds small until you watch it work. Here is 1,000 on red every spin, computed exactly for each wheel:

After 1,000 spins — about nine hours at our table — roughly one player in five is still ahead on a European wheel. On an American wheel it is one in 22, and with three zeros one in 150.

The American layout has one bet a European layout cannot have: the top line, or basket, on 0, 00, 1, 2 and 3. It pays 6 to 1. Five numbers × 7 chips returned = 35 out of 38 pockets, so the house keeps 3/38 = 7.89% — the worst bet on the American table. Its European cousin, the first four 0–1–2–3, pays 8 to 1 with the usual 2.70%.

The order of the numbers differs too. On the European wheel red and black alternate all the way round, zero sits between 26 and 32, no two consecutive numbers are neighbours, and low and high numbers alternate almost everywhere — 10 next to 5 is the only pair from the same half. Clockwise from zero it runs 0, 32, 15, 19, 4, 21, 2, 25, 17, 34, 6, 27…

The American wheel is built on pairs: directly across from every number sits its neighbour on the layout — 1 opposite 2, 27 opposite 28 — and 0 opposite 00. For your bets it makes no difference: every pocket on either wheel is equally likely.

Count the green pockets. One zero means a European or French wheel; 0 and 00 mean American; a third green pocket marked 000 means triple zero. The layout gives it away as well: on an American table 0 and 00 share the head of the grid, and a French table often labels the outside bets in French — Rouge and Noir, Pair and Impair, Manque (1–18) and Passe (19–36) — and usually plays La Partage.

In Anubis City there is only one wheel: a single green zero between 26 and 32.

Some single-zero tables go further. Under La Partage half of an even-money bet comes back when zero hits, cutting the edge on red/black, odd/even and the halves to 1.35%. En Prison holds the bet for one more spin instead, with almost the same effect. A few American casinos offer something similar called surrender on 0 and 00: half back, and an edge of 2.63% on even chances.

We describe these rules so that you recognise them elsewhere. In the Rotunda of Shai things are simpler: one zero, no half-back rules and 2.70% on every bet.