Jan 20th 2007
We will present you the mathematics behind the roulette, a thing not so complicated as you may think. The expected outcome of your favorite bets will be presented. First of all the equation that defines the American roulette's house edge will be described. The house edge found at an American roulette is of 5.26%. This doesn't apply in the case of a five number bet.
Imagine that a 1$ bet is placed on an individual number. You will have a 37 to 1 or 1 in 38, probability of hitting the number. In reality you will get paid only 35 to 1, the casino keeping their size as well. In this case you will lose 2$ at every 38 spins. These two dollars represent 5.26% of the total of 38$ you bet.
The mathematical formula is this:
The expectancy: [the winning outcome probability X the amount of money you would probably win] + [the losing outcome probability X the amount of money you would probably lose]
This means that your bet's winning expectancies combined with your bet's losing expectancies would determine your expected outcome.
Here is the formula mentioned above presented in numbers :
E = [1/38 x 35] + [37/38 x (-1)]
= 0.921 + (-0.97368)
The result is with a negative result in front of it as it represents the player's expectation. The result would be positive if it would represent the house's expectation (the house edge). No matter what bet you would play, the house's edge remains the same changing only in the case of the five number bet. The house edge is increased to 7.89% in this.
In the American Roulette game no matter what combinations of bets you would try the edge remains the same: 5.26%. This is a disadvantage and you should try playing some versions that change the rules a little bit in your convenience. The consolation is that you won't get cheated while playing static house edge roulette.