The math of roulette

French roulette odds and La Partage

La Partage returns half an eligible even-money stake when zero lands on a single-zero wheel. With that rule, the house edge on those bets is 1.35%.

1.35%

Eligible even-money bets only

Single zero with La Partage

What La Partage changes

Red/black, odd/even and low/high bets are the eligible even-money groups in this model. A normal win pays 1:1. An opposite result loses the stake. Zero loses half rather than all of it.

The 1.35% calculation

For a $10 red bet: 18 outcomes earn $10, 18 lose $10 and zero loses $5. Expected net is −$5/37, or about −$0.1351. Dividing by $10 gives 1/74, or 1.351351%, house edge.

Other bets keep their normal treatment

The half-loss rule does not automatically apply to straight-up bets, dozens or columns. A standard single-number wager still has its usual 2.70% edge on the 37-pocket wheel.

En Prison needs its own rules

En Prison can hold an eligible stake over to a later spin instead of immediately returning half. The treatment of another zero must be specified. This package does not model that deferred settlement in the calculator.

House edge with and without La Partage

Single-zero house edge by bet and zero rule
BetStandard ruleWith La Partage
Red/black, odd/even, low/high2.70%1.35%
Dozen or column2.70%2.70%
Straight-up and other inside bets2.70%2.70%

French roulette table terms

Rouge / Noir
Red / black
Pair / Impair
Even / odd
Manque / Passe
Low 1–18 / high 19–36
Douzaine / Colonne
Dozen / column
Plein
Straight-up on one number
Cheval
Split
Transversale pleine
Street
Carré
Corner
Sixain
Six-line

A French layout uses the same 37-pocket wheel as European roulette. The European roulette odds apply unless a written rule such as La Partage changes settlement.