# Thread: Expected Value and Roulette

1. ## Expected Value and Roulette

2) A roulette wheel has 38 slots. 36 of them are the numbers 1 - 36. The remaining 2 are "0" and "00". You can bet on a single number and if the ball lands on your number you win 35 chips plus the chip you bet.

a. If each chip is worth $1, what is the expected value for a player who bets the number 17 for a long period of time? 2. Hello, mdenham2! 2) A roulette wheel has 38 slots. 36 of them are the numbers 1 - 36. The remaining 2 are "0" and "00". You can bet on a single number. If the ball lands on your number, you win 35 chips plus the chip you bet. a. If each chip is worth$1, what is the expected value for a player
who bets the number 17 for a long period of time?

We have: . $\begin{Bmatrix}P(17) &=& \dfrac{1}{38} \\ \\[-3mm] P(\text{other}) &=& \dfrac{37}{38}\end{Bmatrix}$ . $\Rightarrow\quad \begin{Bmatrix} P(\text{win \36}) &=& \dfrac{1}{38} \\ \\[-3mm] P(\text{lose \1}) &=& \dfrac{37}{38}\end{Bmatrix}$

Therefore: . $E \;=\;\left(\frac{1}{38}\right)(+36) + \left(\frac{37}{38}\right)(-1) \;=\; -\frac{1}{38} \;=\;-0.026315789$

[If he plays 3000 times, he can expect to lose about \$79.]