Expected American Roulette Odds

Published on 7 August 2013

An American roulette wheel contains 38 equally sized spaces and when the ball spins it will only land in one of these spaces. Two spaces are green with numbers 0 and 00. The others are numbered from 1 to 36. Half of these 36 slots are red and half are black. You can wager differently on where you think the ball will land. The most common type of bet is the color bet, in which you can wager in red with 18 chances of winning.

Because the slots in the American roulette wheel are all in the same size, it involves a uniform probability distribution. To calculate the expected value read above:

There are 38 slots on the wheel, and so the probability that a ball lands on one particular space is 1/38.
There are 18 red spaces on the roulette wheel, and so the probability that red occurs is 18/38.
There are 20 black and green spaces, and so the probability that red does not occur is 20/38.

The amount of winning on a roulette bet can be randomly variable. If you bet $1 on red and the ball lands on red, you will win one dollar and another dollar. So the results in net winnings is 1. If you bet $1 on red and green or black occurs, then you lose your bet. The results in net winnings is -1.

The presence of 0 and 00 on the amriacn roulette wheel made the house advantage slightly higher than the players. However, this avantage is so small that one cannot even find out but in the end the house always wins.