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

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    Another probability puzzle for Don Schlesinger ( or anyone else)

    1) You are given a choice of $100 or an envelope that has a 50% chance of having half that amount and a 50% chance of having double that amount. Which would you pick? Is there an advantage to switching to the unknown envelope?

    2) Another guy had arrived just before you and saw two unopened envelopes, one of which was selected in a random process that had an equal chance of opening either envelope. Upon opening, its contents was $100 which gave you more information to base your choice on. You are both truthfully told the other envelope has a 50% chance of having half that amount and a 50% chance of having double that amount, since nobody knows the contents of either envelop but know that one has twice as much as the other. Which should the guy who saw two unopened envelopes pick? Is there an advantage to switching to the unknown envelope for either participant and if so why would seeing an envelope opened to reveal the $100 make a difference?

    3) You both arrive at the same time and there are two unopened one of which contains twice as much as the other. One is randomly selected as above and is opened revealing $100. The random process has an equal chance of opening either envelope. Which action would you choose if you were one of the two people that selected one of these envelopes?
    a) Should you keep the envelope you chose?
    b) Should you switch to the one you didn't choose?
    c) Should you take the $100?
    d) Should you take the amount in the unopened envelope?
    Is there an advantage to any of the switching strategies once the contents of one envelope is known?

    4) You both arrive at the same time and there are two unopened one of which contains twice as much as the other. You each pick a different envelope. You each pick an envelope but neither is opened. Would you switch if you were one of the participants?

    What made the answer to any of these 4 different? If there was no difference then why wouldn't you take the envelope in puzzle #1.

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    Seriously
    Not that this hasn't been ridiculously covered in another thread, is there any relavence to Blackjack?

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    Senior Member Gramazeka's Avatar
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    Quote Originally Posted by Three View Post
    1) You are given a choice of $100 or an envelope that has a 50% chance of having half that amount and a 50% chance of having double that amount. Which would you pick? Is there an advantage to switching to the unknown envelope?

    2) Another guy had arrived just before you and saw two unopened envelopes, one of which was selected in a random process that had an equal chance of opening either envelope. Upon opening, its contents was $100 which gave you more information to base your choice on. You are both truthfully told the other envelope has a 50% chance of having half that amount and a 50% chance of having double that amount, since nobody knows the contents of either envelop but know that one has twice as much as the other. Which should the guy who saw two unopened envelopes pick? Is there an advantage to switching to the unknown envelope for either participant and if so why would seeing an envelope opened to reveal the $100 make a difference?

    3) You both arrive at the same time and there are two unopened one of which contains twice as much as the other. One is randomly selected as above and is opened revealing $100. The random process has an equal chance of opening either envelope. Which action would you choose if you were one of the two people that selected one of these envelopes?
    a) Should you keep the envelope you chose?
    b) Should you switch to the one you didn't choose?
    c) Should you take the $100?
    d) Should you take the amount in the unopened envelope?
    Is there an advantage to any of the switching strategies once the contents of one envelope is known?

    4) You both arrive at the same time and there are two unopened one of which contains twice as much as the other. You each pick a different envelope. You each pick an envelope but neither is opened. Would you switch if you were one of the participants?

    What made the answer to any of these 4 different? If there was no difference then why wouldn't you take the envelope in puzzle #1.
    Utility function.

    https://www.investopedia.com/ask/ans...calculated.asp

    p.s.

    Three, you finally opened a big secret- Don Schlesinger writes under two nicknames on this forum. ( DSchles and Gramazeka ). It's time to confess ! The forum should live !
    Last edited by Gramazeka; 02-20-2018 at 01:38 PM.
    "Don't Cast Your Pearls Before Swine" (Jesus)

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    Quote Originally Posted by Freightman View Post
    Seriously
    Not that this hasn't been ridiculously covered in another thread, is there any relavence to Blackjack?
    Isn't this a little bit pot-kettle-black? :-)
    P.S. I'll let Don correct your spelling error.

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    Quote Originally Posted by Gramazeka View Post
    Utility function.

    https://www.investopedia.com/ask/ans...calculated.asp

    p.s.

    Three, you finally opened a big secret- Don Schlesinger writes under two nicknames on this forum. ( DSchles and Gramazeka ). It's time to confess ! The forum should live !
    Didn't guess that one. It's cool one can do multiple personalities on a forum, I guess. Even have conversations pitting one against the other. Do it in a casino and they will come and take you away. haha
    Last edited by moses; 02-20-2018 at 06:20 PM.

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    I couldn't sleep last night because of Gram's brain teaser. Then I figured out the flaw in the logic that created the paradox. This series of queries is designed to get another to figure out the flawed reasoning everyone tries to apply to Gram's version of the two envelope problem. I figured Don would figure it out. The key to figuring it out is ironically what Freighter said that he used to refute what I was saying. Actually applying what he said proved what I was saying, while displaying the flaw in the logic of those that said it didn't matter if you switched or not once you knew what was in one envelope. Maybe one of you will figure it out. I have given a few clues in this post and in the Monty Hall switching thread.

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    One more thing we do use it when we play BJ. As a matter of fact it is the cornerstone into why card counting works.

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    Senior Member Gramazeka's Avatar
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    Quote Originally Posted by Three View Post
    One more thing we do use it when we play BJ. As a matter of fact it is the cornerstone into why card counting works.
    You mean "Variance". But a more accurate answer in our case- "Utility function".
    "Don't Cast Your Pearls Before Swine" (Jesus)

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    Quote Originally Posted by Gramazeka View Post
    You mean "Variance". But a more accurate answer in our case- "Utility function".
    Nope

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    Just answers the questions honestly and in sequence in the OP. It should dawn on you. The clue that Freighter used exactly wrong to say that my logic was flawed is this is just one trial.

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    Here is a real life scenario where employees should learn blackjack skills.

    Homeowners policy is due February 2017 for $461. Customer pays it with credit card but it gets mishandled because agent screwed up. Evidently, bank notices screw up and wants money returned.

    So now home owner is ready to pay February 2018 for $487. But insurance company demands $988. Combo of two years and late charges when policy was not yet due. I will stop here. What do you think the insurance comany ended up receiving?

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    It is impossible for there to be either double or half the amount of money in the envelope. It is either going to be one or the other.

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    Quote Originally Posted by Meistro123 View Post
    It is impossible for there to be either double or half the amount of money in the envelope. It is either going to be one or the other.
    That is true in scenario 1 above. But wouldn't you refuse the $100.

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