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  • #31
    Originally posted by Sparko View Post
    either way the odds would remain the same for the person choosing. It would be better to switch most of the time because the host will not open a curtain that contains the prize.
    Have fun...

    http://educ.jmu.edu/~lucassk/Papers/MHOverview2.pdf

    (High-Numbered Monty). As before, we have three identical doors
    concealing one car and two goats. The player chooses a door which remains
    unopened. Monty now opens a door he knows to conceal a goat. This time,
    however, we stipulate that Monty always opens the highest-numbered door
    available to him (keeping in mind that Monty will never open the door the
    player chose.) Will the player gain any advantage by switching doors?

    For reasons of concreteness, we will assume once more that the player
    initially chooses door one. Any time door one conceals a goat, Monty has no choice regarding which
    door to open. He can not open door one (since the player chose that door),
    and he can not open the door that conceals the car. This leaves only one
    door available to him.
    The interesting cases occur when door one conceals the car. Unlike Classic
    Monty, who now chooses randomly, High-Numbered Monty will always open
    door three when he can. It follows that if we see him open door two instead
    we know for certain that the car is behind door three.

    And if High-Numbered Monty opens door three? Since Monty is certain
    to open door three whenever the car is behind door one or door two, we now
    have no basis for deciding between them. It really is a fifty-fifty decision in
    this case.
    That's what
    - She

    Without a clear-cut definition of sin, morality becomes a mere argument over the best way to train animals
    - Manya the Holy Szin (The Quintara Marathon)

    I may not be as old as dirt, but me and dirt are starting to have an awful lot in common
    - Stephen R. Donaldson

    Comment


    • #32
      Originally posted by Bill the Cat View Post
      Have fun...

      http://educ.jmu.edu/~lucassk/Papers/MHOverview2.pdf

      (High-Numbered Monty). As before, we have three identical doors
      concealing one car and two goats. The player chooses a door which remains
      unopened. Monty now opens a door he knows to conceal a goat. This time,
      however, we stipulate that Monty always opens the highest-numbered door
      available to him (keeping in mind that Monty will never open the door the
      player chose.) Will the player gain any advantage by switching doors?

      For reasons of concreteness, we will assume once more that the player
      initially chooses door one. Any time door one conceals a goat, Monty has no choice regarding which
      door to open. He can not open door one (since the player chose that door),
      and he can not open the door that conceals the car. This leaves only one
      door available to him.
      The interesting cases occur when door one conceals the car. Unlike Classic
      Monty, who now chooses randomly, High-Numbered Monty will always open
      door three when he can. It follows that if we see him open door two instead
      we know for certain that the car is behind door three.

      And if High-Numbered Monty opens door three? Since Monty is certain
      to open door three whenever the car is behind door one or door two, we now
      have no basis for deciding between them. It really is a fifty-fifty decision in
      this case.

      The problem is that you are assuming you know Monty's strategy is to open the highest number door. If you don't know his strategy, all you can know is that he won't open the curtain with the car behind it, so as far as you can tell, the game is the same as before. And if you did know the strategy, then you only occasionally (if he chooses door 2 to open) know which door has the car. And since such a strategy makes no sense for Monty to employ, there is no reason he would ever use it.

      Comment


      • #33
        Originally posted by Sparko View Post
        The problem is that you are assuming you know Monty's strategy is to open the highest number door. If you don't know his strategy, all you can know is that he won't open the curtain with the car behind it, so as far as you can tell, the game is the same as before. And if you did know the strategy, then you only occasionally (if he chooses door 2 to open) know which door has the car. And since such a strategy makes no sense for Monty to employ, there is no reason he would ever use it.
        Probability doesn't have to make sense.
        That's what
        - She

        Without a clear-cut definition of sin, morality becomes a mere argument over the best way to train animals
        - Manya the Holy Szin (The Quintara Marathon)

        I may not be as old as dirt, but me and dirt are starting to have an awful lot in common
        - Stephen R. Donaldson

        Comment


        • #34
          I wonder about the more common scenario where you get a prize and then are allowed to keep the prize or trade it in on curtain 2 or 3 (neither which is opened) - and curtain 2 or 3 (or both) could contain the goat, or a better prize.

          So let's say you get a new TV. You can trade it in on curtain 2 or 3. Perhaps curtain 2 contains a goat and curtain 3 contains a car. Or one contains a boat and the other a car, or both contain goats.

          Comment


          • #35
            Keep the boat - you can sell it and get whatever car you want. Or whatever goat you want, depending on your idea of 'better'.
            "He is no fool who gives what he cannot keep to gain that which he cannot lose." - Jim Elliot

            "Forgiveness is the way of love." Gary Chapman

            My Personal Blog

            My Novella blog (Current Novella Begins on 7/25/14)

            Quill Sword

            Comment


            • #36
              Originally posted by Teallaura View Post
              Keep the boat - you can sell it and get whatever car you want. Or whatever goat you want, depending on your idea of 'better'.
              Depends on the boat.

              For instance, one of your Alabamistani "boats"




              Comment


              • #37
                Originally posted by Sparko View Post
                Depends on the boat.

                For instance, one of your Alabamistani "boats"



                <looks at label>
                "Made In Kentuk"

                Well, it's genuine Kentucky manufacture - notice the misspelling only Kentuckians would make.

                "He is no fool who gives what he cannot keep to gain that which he cannot lose." - Jim Elliot

                "Forgiveness is the way of love." Gary Chapman

                My Personal Blog

                My Novella blog (Current Novella Begins on 7/25/14)

                Quill Sword

                Comment


                • #38
                  Originally posted by Teallaura View Post
                  <looks at label>
                  "Made In Kentuk"

                  Well, it's genuine Kentucky manufacture - notice the misspelling only Kentuckians would make.

                  sorry but if you actually look at the guy's shirt and the chair back they both do say "Alabama" on them.

                  Besides we don't have shirts in kentucky, or water. Just moonshine.

                  Comment


                  • #39
                    Originally posted by Sparko View Post
                    sorry but if you actually look at the guy's shirt and the chair back they both do say "Alabama" on them.

                    Besides we don't have shirts in kentucky, or water. Just moonshine.
                    No, I looked at the shine jug fuel tank in back. Of course the chairs say Alabama - only an idiot would buy a chair made in Kentucky....
                    "He is no fool who gives what he cannot keep to gain that which he cannot lose." - Jim Elliot

                    "Forgiveness is the way of love." Gary Chapman

                    My Personal Blog

                    My Novella blog (Current Novella Begins on 7/25/14)

                    Quill Sword

                    Comment


                    • #40
                      Teallaura,
                      re: "I think because the host could have chosen the lowest number instead..."


                      That could only be the case if neither curtain 2 nor 3 has the car behind it.

                      Comment


                      • #41
                        Originally posted by rstrats View Post
                        Teallaura,
                        re: "I think because the host could have chosen the lowest number instead..."


                        That could only be the case if neither curtain 2 nor 3 has the car behind it.
                        You misread the post - I was answering Bill and we were talking about the host's initial choice of a door with no car behind it. Bill stated the host could have chosen the highest number or randomly of the two choices. I don't see why he couldn't have instead chosen the lowest number of the two choices.

                        My answer to the OP was that switching gives the best chance of winning.
                        "He is no fool who gives what he cannot keep to gain that which he cannot lose." - Jim Elliot

                        "Forgiveness is the way of love." Gary Chapman

                        My Personal Blog

                        My Novella blog (Current Novella Begins on 7/25/14)

                        Quill Sword

                        Comment

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