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Thread: Fair Play Value calculation

  1. #1
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    Exclamation Fair Play Value calculation

    A coin is weighted so it comes up head 3/4 of the time and tails 1/4 of the time. You play a game where this coin is flipped. If it comes up heads, you must pay 1 dollar. If it comes up tails, you win 2 dollars. What is the Expected Value of your winnings in this game?

    I solved this portion and had the answered verified : 3/4 x -$1 + 1/4 x $2 = -0.25

    I need help with calculating the Fair Play value. The second part goes as follows:

    Assume that you still have to pay $1 if the coin comes up heads. In order for the game to be fair (where Expected Value = 0), how much should you win if the coin comes up tails?

    Please provide the solution, not just the answer. I'll understand better that way. thanks
    Last edited by topsquark; Jul 9th 2019 at 06:02 PM. Reason: Fixed dollar signs
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  2. #2
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    Re: Fair Play Value calculation

    $E[V] = -\dfrac 3 4 \cdot 1 + \dfrac 1 4 x = 0$

    $\dfrac 1 4 x = \dfrac 3 4$

    $x = 3$
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    Re: Fair Play Value calculation

    Thank you for your response Romsek, however, I'm still not getting this, at all. Why is the 3/4 now negative? Why is the X = to 3? I've been out of school for 26 years so while this should be super simple to pick apart, it isn't. Any further break down would be really really helpful.
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  4. #4
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    Re: Fair Play Value calculation

    Quote Originally Posted by sweetconiferous View Post
    Thank you for your response Romsek, however, I'm still not getting this, at all. Why is the 3/4 now negative? Why is the X = to 3? I've been out of school for 26 years so while this should be super simple to pick apart, it isn't. Any further break down would be really really helpful.
    Paying 1 dollar is represented by -1.

    With probability 3/4 you pay 1 dollar, that corresponds to the first term $-\dfrac 3 4 \cdot 1$

    $x$ is the unknown value that we need to win upon flipping a Tail in order to make the overall expectation of winnings 0.

    With probability 1/4 we win $x$ dollars. This corresponds to the second term $\dfrac 1 4 x$

    The sum of these two terms is the expectation of the value of winnings which we set to 0 and then solve for $x$.
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