Roulette OddsOn this page I am going to outline and detail how the casino comes up with the roulette odds. This is not a complicated process and if you have ever played or even looked at the table before, you can roughly figure out what your odds and what your payout will be.
For simplicity reasons I will be referring only to the American style of roulette as the European style is done the same way, but with one less number. If you have read some of the other pages on the site you will already know that the house holds a 5.26% edge and if you didn't, now you do.
In order for me to explain how the math is done here, I will use an example of how it was explained to me. Picture a $1 bet on an individual number. The probability of hitting that particular number is 1 in 38, or 37 to 1. Of course the casinos only pay you 35 to 1, robbing you a bit of what's rightfully yours. With this shortfall, you know that in 38 spins you will lose $2. Two dollars just happens to be 5.26% of the $38 you put into those spins.
The mathematical formula for expectation reads as follows:
Expectancy = [probability of a winning outcome X the amount you would win] + [probability of a losing outcome X the amount you would lose]
This kind of makes sense. What you would expect to win on the bet, combined with what you would expect to lose, should tell you what you're expected outcome is. For the single dollar bet in roulette mentioned above:
E = [1/38 x 35] + [37/38 x (-1)]
= 0.921 + (-0.97368)
The negative indicates that in the players eyes they will lose 5.26% of there money, but it is usually referred to as a positive number because it is the casinos edge, not the players demise. So if you were to make any bet on the table, no matter what numbers you play or how many you play the house will always have the edge of 5.26%. The only bet that doesn't hold the same edge is the "five number bet" and it has an even bigger edge for the casino at 7%.
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