Roulette Odds Calculator (Win Chance, Payout and House Edge)

How it works

Win chance p = numbers covered ÷ pockets (37 single-zero, 38 double-zero) · house edge = −(p × payout − (1 − p)) = 1/37 = 2.70% (European), 2/38 = 5.26% (American; 7.89% on the 0-00-1-2-3 basket) · la partage halves even-money losses on zero: 1.35% · expected loss = stake × house edge × spins · P(at least one win in n spins) = 1 − (1 − p)ⁿ

Every roulette bet pays as if the zero (and double zero) did not exist: a single number pays 35 to 1 although the true odds are 36 to 1 on a European wheel and 37 to 1 on an American one. That gap is the house edge — 2.70% on every bet on a single-zero wheel and 5.26% on a double-zero wheel, with the five-number basket worse at 7.89%. French tables with la partage return half of an even-money bet when zero comes up, halving that edge to 1.35%. No betting system changes these numbers; the expected loss grows in proportion to the total amount wagered.

Worked example

European wheel, $10 on red for 100 spins: red covers 18 of 37 pockets, so the chance of winning a spin is 18 ÷ 37 = 48.65%. It pays 1 to 1 while the true odds are 1.06 to 1, a house edge of 1/37 = 2.70%. The expected loss is $0.27 per spin and $27.03 over 100 spins; you expect about 48.6 wins and are virtually certain (> 99.99%) to win at least once.

Sources: Wizard of Odds — Roulette · Encyclopaedia Britannica — Roulette

Frequently asked questions