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.