Roulette probability: pockets, odds and payouts

For a fair roulette wheel, one wager's win probability equals its number of covered pockets divided by the total pockets. A standard European wheel has 37; a standard American wheel has 38. The payout printed on a table is a separate quantity.

Count winning outcomes

Percentages round the exact fractions. Zero and double zero are separate outcomes, excluded from all selections above except a straight-up wager explicitly placed on one of them.

True odds differ from payout odds

A European straight-up wager has 36 losing outcomes for one winning outcome: true odds against it are 36 to 1. Its ordinary profit payout is 35 to 1. A one-chip winner returns 36 chips including its stake, while the average total return is only 36/37 chip per chip wagered.

For red, true odds against are 19 to 18. The table pays 1 to 1 in profit. The difference becomes the house edge.

Choose the right operation

For mutually exclusive outcomes on one spin, add probabilities. First dozen or second dozen covers 24 unique pockets, so its chance is 24/37. Red plus odd is different: some red pockets are odd, so adding 18/37 twice counts shared outcomes twice. Count the union once instead. Our overlapping-bets guide separates coverage and money returned.

For independent events on successive spins, multiply. Red twice in a specified two-spin sequence has probability (18/37)^2. That calculation does not describe a run of two reds anywhere in a 100-spin session; read streak probability for the longer-window question.

The calculator shows the probability and payout for one standard wager. A larger winning set gives a higher hit rate, but comparing expected returns still requires all payments and losses.