# Expected Loss for American Roulette

#### Shapeshift

Hey everyone! So I'm getting a bit stuck when it comes to calculating expected loss for American Roulette (38 spots: 18 are red (odd numbers between 1 and 35), 18 are black (even numbers between 1 and 36), and 2 spots are green (one is 0 and the other is 00)).

For example, I understand that If I bet on red, my expected loss is (18/38 - 20/38) = -1/19 = -0.0526

However, I am confused when it comes to betting on a colour as well as numbers. For example, if I bet on red and the numbers 1, 2, 3, and 4, how would I go about calculating the expected loss then?

I figure it should be (18/38 - 20/38 + 20/38 - 18/38), but this would give 0, so this seems wrong.

Any help would be very much appreciated!

#### chiro

MHF Helper
Hey Shapeshift.

Can you outline how roulette pays out (for people like me not familiar with the game)?

#### Shapeshift

Hey sorry I forgot to include that!
The payoff for red is 1 to 1, so a $1 bet would have a net gain of$1.
The payoff for the block of four numbers is 8 to 1, so a $1 bet would have a net gain of$8.

So if I place a $1 bet on the red, and a$1 bet on the block of four numbers, I end up getting

18/38 + 8(4/38) - 20/38 - 34/38 = -0.105263 which I believe is right?

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#### chiro

MHF Helper
That looks right.