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Let's look a little into the not so complicated mathematics of roulette, and talk about the expected outcome for the bets you like to place. To begin with let's look at the classic equation that defines the house edge for American roulette. The house edge for all bets except the five number bet on American roulette is 5.26%.
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]
Which 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) = -0.0526 = -5.26%
The negative simply shows you that you are expected to walk away down, as expectation is calculated as 'player expectation'. Reversing this to a positive gives you the 'casino expectation' or house edge. So now you can see where the house edge in American roulette comes from, and how it weighs in at 5.26%. You'll find that the roulette odds behind every single bet on the table work out to the same incontrovertible house edge, with the exception of the five number bet, which doesn't pay it's odds back as well as the other bets on the table, and works out to an even worse house edge of 7.89%.
The sad thing about American roulette is that this house edge is unalterable. Each and every bet, and every combination of bets, and every way you can think to hedge your bets, all work out to a 5.26% house edge. That's why your strategy should include a host of ways to play games that are a slightly altered form of American roulette, and seek out rules that are beneficial. Roulette odds, as unalterable as they are, provide a sense of stability to the game. Hey, at least we know the casino isn't ripping us off with some trickery we don't understand!
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