The math of roulette

European roulette odds

A single-zero wheel has 37 pockets. Standard bets have a 2.70% house edge when zero loses the full stake and the usual payouts apply.

2.70%

Standard house edge

37 pockets • RTP 97.30%

One zero, 37 possible outcomes

European roulette includes 1 through 36 and a single 0. There are 18 red and 18 black numbers. A number bet wins on 1/37 of outcomes; a dozen wins on 12/37; a color wins on 18/37.

The standard house edge

For the standard bets whose coverage times total-return multiplier equals 36, expected return is 36/37. House edge is 1/37, or 2.70%. The corresponding theoretical return to player is 97.30%.

European versus American

The standard payouts remain the same when a double-zero pocket is added, but the number of losing outcomes increases. Compare 18/37 for red with 18/38. Use the same stake and payout convention when comparing results.

Check zero settlement separately

Single zero does not by itself promise La Partage. That rule changes eligible even-money bets when zero lands. Confirm the written rule rather than inferring it from a French or European label.

European roulette odds table

Standard bets on a 37-pocket European wheel
BetPocketsPayoutChanceTrue odds
Straight-up135:12.70%36:1
Split217:15.41%35:2
Street311:18.11%34:3
Corner48:110.81%33:4
Six-line65:116.22%31:6
Dozen / column122:132.43%25:12
Red / black181:148.65%19:18
Odd / even181:148.65%19:18
Low / high181:148.65%19:18

European vs American roulette odds compared

Chance of winning on single-zero and double-zero wheels
BetEuropeanAmericanDifference
Straight-up2.70%2.63%0.07 points
Split5.41%5.26%0.14 points
Street8.11%7.89%0.21 points
Corner10.81%10.53%0.28 points
Six-line16.22%15.79%0.43 points
Dozen / column32.43%31.58%0.85 points
Red / black48.65%47.37%1.28 points
Odd / even48.65%47.37%1.28 points
Low / high48.65%47.37%1.28 points

Over $1,000 in total wagers, the expected loss is about $27.03 on a European wheel and $52.63 on an American wheel. The European wheel has better odds on every standard bet.