House edge is expected loss divided by the amount staked. To calculate it, multiply each possible net result by its probability and add those weighted results. A negative expected profit gives a positive house edge. RTP describes expected total return, including returned winning stakes.
Derive the ordinary European edge
One chip on red wins one on 18 pockets and loses one on 19. Expected profit is:
18/37 × 1 + 19/37 × (−1) = −1/37.
Expected loss is about 2.70% of that chip. A straight-up wager wins 35 on one pocket and loses one on the other 36: (35 − 36)/37 gives the same −1/37 result.
The red wager returns two chips on a win, including the stake. Its expected total return is 18/37 × 2 = 36/37, or about 97.30% RTP. The two measures describe the same payout model from different directions.
Compare exact assumptions
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| Wager and rules | House edge |
|---|---|
| Ordinary European red, full loss on zero | 1/37, about 2.70% |
| Ordinary American red, full loss on 0 and 00 | 2/38, about 5.26% |
| American first five at 6 to 1 | 3/38, about 7.89% |
| Eligible single-zero even-money bet with la partage | 1/74, about 1.35% |
Special payouts and zero rules must be included explicitly. A game title alone does not establish the applicable row. See la partage and en prison and bets and payouts.
Apply the percentage to turnover
If 1,000 chips are staked in total on ordinary European wagers, expected loss is about 27.03 chips. That does not mean a 1,000-chip starting wallet loses that amount in a particular sitting. Returned chips can be wagered again, so cumulative turnover and starting balance are different quantities.
With changing stakes, add each actual wager to turnover. More chips exposed to the same edge produce a larger expected loss. A stop rule changes session length and possible endings, without changing the next fair spin's paytable. Variance explains how a negative mean can coexist with winning sessions; bankroll limits explains why a finite session can end before a progression recovers.
Sources and scope
- Rules of Play for Table Games, Roulette. British Columbia Lottery Corporation. Double-zero standard payout table and placement. European pocket count is independently verified from native Wheel.
Publication date: not stated. Checked 2026-11-07.
- Roulette probability derivation. Amenti Labs LLC. Fair independent pockets, fixed payouts, full outside loss on zero. Formula and all supported bets regression tested.
Publication date: 2026-11-07. Checked 2026-11-07.
- European Roulette: rules of the game. Monte-Carlo Société des Bains de Mer. Published venue European roulette rules:37 pockets, wager names/payouts including firstfour, evenmoney zero division/barredstake choices and prohibition on spokenbets. Does not establish universal French game rules or a repeatedzero policy. Reducededge figures are separately scoped mathematical derivations.
Publication date: not stated. Checked 2026-11-08.