In roulette, the numbers from 1 to 36 are evenly distributed between red and bla

Question

In roulette, the numbers from 1 to 36 are evenly distributed between red and black. A player who bets $1 on black wins $1 (and gets the $1 bet back) if the ball comes to rest on black; otherwise (if the ball lands on red, 0, or 00), the $1 bet is lost. One option in a roulette game is to bet

$ 18$18

on red. If the ball lands on red, you get to keep the

$ 18$18

you paid to play the game, and you are awarded

$1919.

If the ball lands elsewhere, you are awarded nothing, and the

$ 18$18

that you bet is collected. What is the expected value of the game?

The expected value for playing roulette if you bet

$ 18$18

on red is approximately

$

Explanation / Answer

P(Red)=0.5

P(Black)=0.5

Say I bet $18.

Hence Expected Value=0.5*(18+19)+0.5(0)=0.5*37=$18.5

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