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Thread: Another probability puzzle for Don Schlesinger ( or anyone else)

  1. #14


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    If there really was a 50/50 chance of it being 200 or 50 then switching definitely has a positive expectation, just like if I paid $100 to flop a coin where heads I get $200, and tails I get $50, that would be a good game and I would play.

    But it is not possible for the envelope to have either $200 or $50. It only has one or the other.

    I guess the other envelope could be randomly selected, for example pulled out of a bin of envelopes where half were filled with $200 and half with $50.

  2. #15


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    Oh my goodness Three.

    Instead of giving in, you're trying to redefine the paradox so you'll be right. You're being adolescent.

    I give up. I also give in. I don't care a bit about this paradox, other than it's an amusing brain teaser. You can have the win.

    You are 100% correct.

    I was completely in error.

    I am a mouth breather.

    My apologies.

    Feel better?

  3. #16
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    Quote Originally Posted by Meistro123 View Post
    If there really was a 50/50 chance of it being 200 or 50 then switching definitely has a positive expectation, just like if I paid $100 to flop a coin where heads I get $200, and tails I get $50, that would be a good game and I would play.
    So you agree that scenario 1 above you should take the envelope rather than a sure $100.
    Quote Originally Posted by Meistro123 View Post
    But it is not possible for the envelope to have either $200 or $50. It only has one or the other.

    I guess the other envelope could be randomly selected, for example pulled out of a bin of envelopes where half were filled with $200 and half with $50.
    No stipulation on how the envelopes were filled except that it was totally random and one contains twice as much as the other. Now what about scenario 2. Does the guy showing up sooner and being told that one envelop contains twice as much as the other and one is opened in some random process that has an equal probability to have either envelope opened make you decide different than the decision you made in scenario one? If so why? Remember the goal isn't to make the right decision the more frequently. This is one trial with one known amount exposed. You want to maximize EV as was the stipulation in Gram's problem. If you wanted to sim it for EV you could but each time the amount that is known must be $100 which had a 50% chance of either being the envelope with twice as much or the other envelope. This is one of the givens for the problem. I don't think we need to sim it.

  4. #17
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    120 posts and counting on "probability"?

    Will the real T3, please stand up?

    https://www.youtube.com/watch?v=SycxTpgVFk0

  5. #18
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    Quote Originally Posted by RCJH View Post
    Oh my goodness Three.

    Instead of giving in, you're trying to redefine the paradox so you'll be right.
    No I am not. The other thread was about this query as the OP:
    Quote Originally Posted by Gramezeka
    In one box, 2 times more money than in another. We opened one of them, there is $ 100, should we open the second one? How to maximize EV ?
    Now I think we all can agree that when fixing the sketchy English translation from Russian that it should read:
    In one box there is 2 times more money than in another. We opened one of them and find it contains $ 100, should we keep the $100 or take the unknown amount in the second box? How do we maximize EV ?

    Everyone else tried to change the problem to something else and say that for the other problem it didn't matter so it must not matter for Gram's problem. I laid out a slight refining of choices that should start with an analogous problem. Then go to the same problem. Then get as different as possible without changing the givens. Then change the problem entirely to what caused the paradox. Then we can see at what point the the decision breaks down when looking at Gram's query. Do you have to completely change Gram's query as everyone tried to do. The only thing Gram didn't specify was the one opened was chosen in an unbiased process that wouldn't make the smaller amount or the larger amount more likely to be selected. I believe it was intended to be assumed in Gram's query so I added it. Obviously if the odds of choosing the larger amount was high enough choosing the unknown amount would not be the right answer to Gram's. So does setting the likelihood of choosing either envelope to open as equal make a difference in your answer?

  6. #19
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    I can't believe that not one person has went through the series of scenarios to see when their logic used to take the unknown envelope ceases to be applicable.

  7. #20


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    Quote Originally Posted by Three View Post
    I can't believe that not one person has went through the series of scenarios to see when their logic used to take the unknown envelope ceases to be applicable.
    Im sure they're many with my perspective of - who gives a shit - and can't be bothered.

  8. #21
    Random number herder Norm's Avatar
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    No more squabbling. This ends. Do you people understand?

    Closed.
    "I don't think outside the box; I think of what I can do with the box." - Henri Matisse

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