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Math Help - Expected Value and Roulette

  1. #1
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    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?
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  2. #2
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    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.]

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