Basic (I think) games theory question

Discussion in 'General Math' started by Eric, Nov 10, 2005.

  1. Eric

    Eric Guest

    I owe a friend $10. He's feeling generous and tells me I can pay $5 to
    settle my debt to him. Or I can play a game where I have X% chance of
    winning. If I win, I pay him nothing. If I lose, I owe him the full
    $10.

    Am I correct that if X is greater than 50, I play the game; if X is
    less than 50, I pay the $5; and if X equals 50, I am indifferent
    towards playing and paying? Or am I missing something in this equation?

    Thanks.

    Eric
     
    Eric, Nov 10, 2005
    #1
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  2. Expecation is 5x - 5(1 - x) = 10x - 5.
     
    William Elliot, Nov 10, 2005
    #2
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  3. I am afraid I didn't get the logic. As I see it, there are three
    possibilities(certainties?) here :

    1. If you choose not to play, you are set back by $5.
    2. If you choose to play and you win, you are set back by $0.
    3. If you choose to play and you lose, you are set back by $10.

    So, if you choose not to play, your expected gain is $ -5.

    If you choose to play, your expected gain is $ x.0 + (1-x).-10 =
    $ 10x -10, which seems to validate Eric's surmise about choosing
    when to play depending on the value of x.

    Could you tell me what is wrong here?

    Thanks,
    Philip
     
    Geevarghese Philip, Nov 29, 2005
    #3
  4. Eric

    jimz Guest

    Play the game no matter what X.
    If you lose, kick his ass and take his wallet.
     
    jimz, Nov 30, 2005
    #4
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