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The Fundamentals of the House Advantage in European Roulette

By: Mark Freedman, Thursday September 18th 2014
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There are a lot of general lessons about gambling that can be found in European roulette. One of those lessons is about the role of the house advantage and player payout percentages regarding the payouts you receive for different types of bets. We want to show you the fundamentals of this advantage in this particular game and show you how it works with different bets that have different levels of risk. Common knowledge tells us that all bets in European roulette have the same payout rate, but is that true? We're going to show you how to find out.

Let's look at a straight-up bet. You can win a 35x payout a total of 1/37 of the time, and you will lose a 1x bet a total of 36/37 of the time. This means that the value of winning is 35 * (1/37) = 0.946 while the value of losing is -1 * (36/37) = -0.973. If we add these values together, we'll get -0.0270 which translates to a loss of 2.7 percent. This is the house advantage of a straight-up bet in European roulette proven with basic statistics and mathematics.

Now let's change the game up a bit. What if we have a corner bet instead? A corner bet wins an 8x payout a total of 4/37 of the time, and it loses a 1x bet a total of 33/37 of the time. Following the same basic format for the equations, we'll do (8 * 4/37) + (-1 * 33/37) = 0.865 - 0.892 = -0.0270 or, again, a loss of 2.7 percent. If you repeat this process with any of the other possible bets, you'll get the same 2.7 percent loss which represents the house advantage no matter how you bet in this game.

One of the really cool things about European roulette is that the house advantage stays stable no matter how you bet, so the risk and reward ratio automatically evens out to give you the same payout rate. So if you bet on one number for a while then change up to betting on three, the payout rate will adjust itself automatically to keep your payout rate the same. This means that you can develop as complex of strategies as you want without having to worry about a negative impact on your overall house advantage.

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