American vs European vs French Roulette: Statistical Differences

The three main roulette variants share the same basic structure — a spinning wheel, a ball, numbered pockets — but differ in ways that matter significantly to expected value and pattern analysis. Here is a precise breakdown of the statistical differences.

The Core Difference: Number of Pockets

American Roulette: The Double Zero

American roulette adds a double zero (00) pocket to the standard 0–36 layout, creating 38 total pockets. Single-number bets still pay 35:1 — the same as European — but the true probability of winning is now 1/38, not 1/37. This creates a house edge of:

That is nearly double the European edge. For even-money bets (red/black, odd/even, high/low), the payout is 1:1 but you lose when either 0 or 00 lands — two losing outcomes out of 38. Expected value on a $1 even-money bet: (18/38 × $1) − (20/38 × $1) = −$0.0526. You lose 5.26 cents per dollar wagered on average.

American roulette also features the "five-number bet" (0, 00, 1, 2, 3) with a uniquely bad house edge of 7.89% — the worst bet in standard casino roulette.

European Roulette: The Baseline

European roulette has 37 pockets (0–36). Single-number bets pay 35:1. House edge:

European roulette is the standard variant in Europe, Australia, and most international casinos. It is the benchmark for roulette mathematics and the variant most commonly used in academic analysis of wheel bias.

French Roulette: La Partage and En Prison

French roulette uses the same 37-pocket wheel as European but adds two optional rules that apply to even-money bets when zero lands:

• La Partage — When zero lands, you recover half your even-money bet. The house takes the other half. This halves the house edge on even-money bets from 2.70% to 1.35%.
• En Prison— When zero lands, your even-money bet is "imprisoned" for the next spin. If your bet wins on the next spin, you get your stake back (but no profit). If it loses, the casino keeps it. Mathematically equivalent to La Partage in expected value — the house edge is the same 1.35%.

At 1.35%, French roulette with La Partage has one of the lowest house edges of any standard casino game — lower than most blackjack variants (1.5–2%), baccarat (1.06–1.24% on banker), and craps pass line (1.41%).

Wheel Geometry Differences

The number sequence on the wheel is not the same across variants. European and French wheels use the same physical sequence: 0, 32, 15, 19, 4, 21, 2, 25, 17, 34, 6, 27, 13, 36, 11, 30, 8, 23, 10, 5, 24, 16, 33, 1, 20, 14, 31, 9, 22, 18, 29, 7, 28, 12, 35, 3, 26 — designed to alternate red/black and balance odd/even and high/low across the wheel.

The American wheel uses a different sequence: 0, 28, 9, 26, 30, 11, 7, 20, 32, 17, 5, 22, 34, 15, 3, 24, 36, 13, 1, 00, 27, 10, 25, 29, 12, 8, 19, 31, 18, 6, 21, 33, 16, 4, 23, 35, 14, 2. The 00 is positioned opposite the 0.

This matters for sector bias analysis: a deviation around physical positions 10–15 on a European wheel corresponds to different numbers than the same arc on an American wheel. Roulette Ace applies the correct wheel geometry for each variant when running sector analysis.

Which Variant to Choose

From a pure expected-value perspective: French with La Partage > European > American. There is no mathematical reason to play American roulette over European if both are available.

For pattern analysis purposes, European and French wheels are preferable: the 37-number geometry is better studied, bias detection methods are calibrated for it, and the single-zero layout means sector analysis is more interpretable. American wheels are common in US casinos and Las Vegas where European tables are less available.