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Roulette Math Tool

Roulette House Edge Calculator

Compare house advantages between variations including La Partage and En Prison rules.

Educational mathematical tool — evaluate wheel variants and special rule benefits.

Research & Editorial

Prince Chattri

Technical SEO & iGaming Research · Adzvelo

Last reviewed: October 7, 2026

Method: Probability, payout & published-rule analysis

European Roulette (Single Zero — 37 pockets)
₹
%
House Edge
2.70%
Theoretical RTP
97.30%
Total Wagered
₹10,000.00
Expected Loss
₹270.00
Expected Return
₹9,730.00
Theoretical Return (97.30%) House Edge (2.70%)
RETURN

*Visual representation of the theoretical long-run expectation across selected roulette rules.

Comparing Roulette House Advantages

The house edge in roulette is primarily dictated by the ratio of winning pockets to total pockets relative to payout odds, as well as specific table rules like La Partage and En Prison.

Roulette Variant Wheel Layout Standard House Edge Even-Money Edge
French Roulette (La Partage/En Prison) 37 pockets (Single Zero '0') 2.70% 1.35%
European Roulette 37 pockets (Single Zero '0') 2.70% 2.70%
American Roulette 38 pockets ('0' and '00') 5.26% 5.26%
Triple Zero Roulette 39 pockets ('0', '00', '000') 7.69% 7.69%

La Partage Rule

Under La Partage (French for "the sharing"), if you place an even-money wager (Red/Black, High/Low, Even/Odd) and the ball lands on zero (0), you do not lose your entire wager. Instead, half of your bet is immediately refunded, reducing the house edge from 2.70% to 1.35% on those specific wagers.

Formula: Edge = (1/37) × 0.5 = 1.3513%

En Prison Rule

Under En Prison ("in prison"), when the ball lands on zero, your even-money bet is "imprisoned" for the next spin rather than half being returned. If your bet wins on the subsequent spin, it is returned in full without additional winnings. Mathematically, this yields the same 1.35% house advantage as La Partage.

Formula: Expected Loss = 50% on Zero Outcome

Roulette Expectation Example

Comparing the theoretical impact over 200 spins with ₹500 bets per spin (Total Wager: ₹100,000):

  • French Roulette (La Partage): ₹1,350 Expected Loss (1.35%)
  • European Roulette: ₹2,700 Expected Loss (2.70%)
  • American Roulette: ₹5,260 Expected Loss (5.26%)

Frequently Asked Questions

The house edge is calculated using the formula: Edge = (Total Pockets - Winning Pockets - (Winning Pockets × Payout)) / Total Pockets. For a single zero wheel (37 pockets) on a straight-up bet paying 35 to 1: (37 - 1 - (1 × 35)) / 37 = 1/37 = 2.70%.
American roulette adds a double zero ('00') pocket, increasing total pockets to 38 without increasing the payout odds (which remain 35-to-1 for straight bets and 1-to-1 for even money bets). This nearly doubles the house edge from 2.70% to 5.26%.

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