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Math Help - Expected Value Question

  1. #1
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    Expected Value Question

    This problem was presented in a philosophy class. I don't have much prob/stat background, so I want to make sure I understand it correctly.

    A game at a casino consists of the following:
    • You roll a dice.
    • If it lands on a 6, then you win $60.
    • Otherwise, you lose $12.

    What is the expected utility of agreeing to play this game?
    I did some googling and found this resource on Expected Utility:

    If there is a  p% chance of  X and a  q% chance of  Y , then EV=pX+qY
    Based on that Theorem, here is what I have done:

    X = \text{Gain } \$60
    p = \frac{1}{6} \times 100
    Y = \text{Lose } \$12
    q = \frac{5}{6} \times 100

    Plug these values into

    EV=pX+qY

    Then we have

    EV=\frac{1}{6} \times 100 \times 60 + \frac{5}{6} \times 100 \times -12
    EV=1000 - 1000
    EV=0

    So, based on that formula the expected value would be zero. So you don't stand to gain anything by playing.

    Is that correct?
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  2. #2
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    You can make it simplier by saying

    \displaystyle EV=\frac{1}{6}  \times 60 + \frac{5}{6} \times -12
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  3. #3
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    Quote Originally Posted by centenial View Post
    This problem was presented in a philosophy class. I don't have much prob/stat background, so I want to make sure I understand it correctly.
    I did some googling and found this resource on Expected Utility:
    Based on that Theorem, here is what I have done:
    X = \text{Gain } \$60
    p = \frac{1}{6} \times 100
    Y = \text{Lose } \$12
    q = \frac{5}{6} \times 100
    EV=pX+qY
    Then we have
    EV=\frac{1}{6} \times 100 \times 60 + \frac{5}{6} \times 100 \times -12
    EV=1000 - 1000
    EV=0
    So, based on that formula the expected value would be zero. So you don't stand to gain anything by playing. Is that correct?
    That is absolutely correct.
    But I have a question: "Why is this a question in a philosophy class"?
    No question that has definite answer is a philosophical question.
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  4. #4
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    Quote Originally Posted by Plato View Post
    That is absolutely correct.
    But I have a question: "Why is this a question in a philosophy class"?
    No question that has definite answer is a philosophical question.
    Thanks! We were talking about Pascal's Wager and the professor brought up some other Expected Utility games.
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  5. #5
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    Quote Originally Posted by centenial View Post
    Thanks! We were talking about Pascal's Wager and the professor brought up some other Expected Utility games.
    Oh yes, now I quite well understand.
    It is often said “Pascal could have been a great mathematician but religion got in the way”.

    Others say “Pascal could have been a great theologian/philosopher but mathematics got in the way”.
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