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  • Monty Hall, we have a PROBLEM

    And any other offerings * #

    I'm reading this book called "the curious incident with the dog in the nighttime" and the protagonist explains the "Monty Hall Problem". Several thoughts at once:
    1. If Let's Make a Deal had offered this scenario to its contestants a dozen or so times, it would lose its insurers and sponsors.
    2. I have a healthier respect for the field of statistics and probability
    3. PhD's can be pretty lazy
    and more besides.

    The answer makes no intuitive sense. But s&p is impersonal like all the other maths, and doesn't care about human reason .

    Goes like this:
    You're on a game show where there are 3 doors presented. A car is behind one door, and behind each of the other doors is a goat.
    After you pick a door, and before the host (who knows where the car is) opens your chosen door, he reveals what's behind another door - a goat. He offers you the choice of sticking with your first choice, or switching your choice to the other unrevealed door. What choice gives you the better chance of winning the car?

  • #2
    Re: Monty Hall, we have a PROBLEM

    I'll post my reply in white so it's not a spoiler for others.

    When you first pick a door, your chances of it being right are one out of three.

    When Monty shows you what's behind one of the other two doors, that action occurs AFTER you already made your choice.

    The chances of your choice being right do not change as a result of something that happens subsequently.

    Therefore, your chances of being right, if you stick with your original choice, are still one out of three.

    Since there is now only one other door available, the chances of THAT door being right must be 1 minus 1/3, or two out of three.

    Therefore, you should always pick the other door, not the one you started with. Your chances of winning are twice as good if you switch than if you don't switch.


    Most people's intuition gets bollixed up at step 3.
    "Hope is a good thing; maybe the best of things."

    "Beer is a sign that God loves us and wants us to be happy." -- Benjamin Franklin

    "Being Irish, he had an abiding sense of tragedy, which sustained him through temporary periods of joy." -- W. B. Yeats

    "People generally are most impatient with those flaws in others about which they are most ashamed of in themselves." - folk wisdom

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    • #3
      Re: Monty Hall, we have a PROBLEM

      A couple other ways of thinking of it:

      Imagine you pick your door. However, Monty doesn't show you any goats. Instead, Monty offers to trade BOTH his doors for your door. It's the exact same problem. Since there's two goats, we already know for sure that one of them's going to be a goat no matter what.

      Or imagine it this way:

      There's a million doors. You pick one. Monty opens 999,998 of the other doors to reveal goats, leaving just your door and one other door that he conspicuously skipped for some reason. Hmm, wonder where the car is?

      The key to the whole problem is this: Monty knows where the goats are. He will ALWAYS have at least one goat left and will ALWAYS reveal a goat.
      Michigan Tech Huskies Pep Band: There's No Use Trying To Talk. No Human Sound Can Stand Up To This. Loud Enough To Knock You Down.

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      • #4
        Re: Monty Hall, we have a PROBLEM

        As long as we're playing game theory:

        You find yourself in a truel (three-way Mexican standoff from the old westerns.) Your opponents are a man in a white hat and a man in a black hat.

        The man in the white hat is the best shot in the West. He hits his target 100% of the time.

        The man in the black hat is an average shot. He hits his target 66% of the time.

        You are an awful shot. You only hit your target 33% of the time.

        However, they have offered you the first shot before they begin shooting.

        Who do you shoot?

        Answer whited out below:

        No one. Waste your bullet. The white and black hat will view each other as the greater threat and one of them will take the other out. You actually have up to a 40% chance of winning this way.
        Michigan Tech Huskies Pep Band: There's No Use Trying To Talk. No Human Sound Can Stand Up To This. Loud Enough To Knock You Down.

        Comment


        • #5
          Re: Monty Hall, we have a PROBLEM

          Originally posted by Twitch Boy View Post
          As long as we're playing game theory:

          You find yourself in a truel (three-way Mexican standoff from the old westerns.) Your opponents are a man in a white hat and a man in a black hat.

          The man in the white hat is the best shot in the West. He hits his target 100% of the time.

          The man in the black hat is an average shot. He hits his target 66% of the time.

          You are an awful shot. You only hit your target 33% of the time.

          However, they have offered you the first shot before they begin shooting.

          Who do you shoot?

          Hmm...without having viewed your answer, i surmise you "accidentally" shoot yourself someplace where it won't do any lasting harm, and then ask to be disqualified because of your injury??
          "Hope is a good thing; maybe the best of things."

          "Beer is a sign that God loves us and wants us to be happy." -- Benjamin Franklin

          "Being Irish, he had an abiding sense of tragedy, which sustained him through temporary periods of joy." -- W. B. Yeats

          "People generally are most impatient with those flaws in others about which they are most ashamed of in themselves." - folk wisdom

          Comment


          • #6
            Re: Monty Hall, we have a PROBLEM

            Originally posted by Twitch Boy View Post
            A couple other ways of thinking of it:

            Imagine you pick your door. However, Monty doesn't show you any goats. Instead, Monty offers to trade BOTH his doors for your door. It's the exact same problem. Since there's two goats, we already know for sure that one of them's going to be a goat no matter what.
            When Monty reveals the goat it's both a red herring and an odds-enhancer. The contestant would tend to eat the herring. He thinks his odds have been raised to 50%, when in fact he's been given a chance to double his 33%.

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            • #7
              Re: Monty Hall, we have a PROBLEM

              Game Theory is awesome. It messes with your mind so much.
              Never really developed a taste for tequila. Kind of hard to understand how you make a drink out of something that sharp, inhospitable. Now, bourbon is easy to understand.
              Tastes like a warm summer day. -Raylan Givens

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              • #8
                Re: Monty Hall, we have a PROBLEM

                You just died.

                Don't worry, no matter what you believed during life, there IS an afterlife.1 and it's totally non-sectarian, too! All you need is a good heart and a clear mind.

                The reason no one comes back, is that right after you die, you are given a choice.

                Before you there are two doors. They are absolutely identical in every respect, there is no way to distinguish one from the other.....until you pass through!

                One is the door to heaven, and the other is the door to hell.

                In front of each door, there is a guardian. The door to heaven is guarded by an angel. It embodies everything good, which means it always tells the truth.

                The door to hell is guarded by a devil. It embodies everything evil, including duplicity.2 It looks just like the angel in every respect, except that it always lies.

                You have one question and can ask only one of the two guardians your question. What question do you ask to ensure you open the door to heaven?








                1 I think it was Bertrand Russell, though it may have been a different famous logician, who said: "if you are not sure whether there is an afterlife or not, it is more logical to believe that there is. If you believe that there isn't and you are wrong, the consequences are much more severe than the converse."

                2 The most insidious thing the devil ever did was to trick us into believing he does not exist.
                "Hope is a good thing; maybe the best of things."

                "Beer is a sign that God loves us and wants us to be happy." -- Benjamin Franklin

                "Being Irish, he had an abiding sense of tragedy, which sustained him through temporary periods of joy." -- W. B. Yeats

                "People generally are most impatient with those flaws in others about which they are most ashamed of in themselves." - folk wisdom

                Comment


                • #9
                  Re: Monty Hall, we have a PROBLEM

                  Originally posted by FreshFish View Post
                  You just died.

                  Don't worry, no matter what you believed during life, there IS an afterlife.1 and it's totally non-sectarian, too! All you need is a good heart and a clear mind.

                  The reason no one comes back, is that right after you die, you are given a choice.

                  Before you there are two doors. They are absolutely identical in every respect, there is no way to distinguish one from the other.....until you pass through!

                  One is the door to heaven, and the other is the door to hell.

                  In front of each door, there is a guardian. The door to heaven is guarded by an angel. It embodies everything good, which means it always tells the truth.

                  The door to hell is guarded by a devil. It embodies everything evil, including duplicity.2 It looks just like the angel in every respect, except that it always lies.

                  You have one question and can ask only one of the two guardians your question. What question do you ask to ensure you open the door to heaven?
                  Answer in "white"
                  You ask one of the guardians whether both of them always tell the truth.
                  Last edited by owslachief; 08-08-2013, 08:54 AM.

                  Comment


                  • #10
                    Re: Monty Hall, we have a PROBLEM

                    A different, correct, answer in white:

                    You ask one of the guardians which door the OTHER one would say led to heaven.
                    If you don't change the world today, how can it be any better tomorrow?

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                    • #11
                      Re: Monty Hall, we have a PROBLEM

                      The following problem has driven me nuts, and I've never solved it. The phone rang or it was time to fix dinner or something always came up.....

                      Any takers?

                      Five friends, Andrew, Bernard, Claude, Donald and Eugene, each have a son and a daughter. Their families are so close that each has married his daughter to the son of one of his friends. Consequently, the daughter-in-law of the father of Andrew's son-in-law is the sister-in-law of Bernard's son, and the son-in-law of the father of Claude's daughter-in-law is the brother-in-law of Donald's daughter. But although the daughter-in-law of the father of Bernard's daughter-in-law has the same mother-in-law as the son-in-law of the father of Donald's son-in-law, the situation is simplified by the fact that no daughter-in-law is the sister-in-law of the daughter of her father-in-law. Who married Eugene's daughter?
                      "Hope is a good thing; maybe the best of things."

                      "Beer is a sign that God loves us and wants us to be happy." -- Benjamin Franklin

                      "Being Irish, he had an abiding sense of tragedy, which sustained him through temporary periods of joy." -- W. B. Yeats

                      "People generally are most impatient with those flaws in others about which they are most ashamed of in themselves." - folk wisdom

                      Comment


                      • #12
                        Re: Monty Hall, we have a PROBLEM

                        Originally posted by FreshFish View Post
                        The following problem has driven me nuts, and I've never solved it. The phone rang or it was time to fix dinner or something always came up.....

                        Any takers?
                        You sadistic ****

                        Comment


                        • #13
                          Re: Monty Hall, we have a PROBLEM

                          Originally posted by FreshFish View Post
                          The following problem has driven me nuts, and I've never solved it. The phone rang or it was time to fix dinner or something always came up.....

                          Any takers?
                          Her husband.
                          Michigan Tech Huskies Pep Band: There's No Use Trying To Talk. No Human Sound Can Stand Up To This. Loud Enough To Knock You Down.

                          Comment


                          • #14
                            Re: Monty Hall, we have a PROBLEM

                            Originally posted by FreshFish View Post
                            The following problem has driven me nuts, and I've never solved it. The phone rang or it was time to fix dinner or something always came up.....

                            Any takers?
                            $Texas
                            It's never too early to start the Pre-game festivities

                            Go Cats!!! GO BLACKHAWKS!

                            Cuck the Fubs... Let's Go WHITE SOX!!!

                            Wildcat Born, Wildcat Bred....

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                            • #15
                              Re: Monty Hall, we have a PROBLEM

                              Originally posted by FreshFish View Post
                              The following problem has driven me nuts, and I've never solved it. The phone rang or it was time to fix dinner or something always came up.....

                              Any takers?
                              You realize that A, B, C, D & E are all bigots because they did not allow same sex marriages.
                              CCT '77 & '78
                              4 kids
                              5 grandsons (BCA 7/09, CJA 5/14, JDL 8/14, JFL 6/16, PJL 7/18)
                              1 granddaughter (EML 4/18)

                              ”Any society that would give up a little liberty to gain a little security will deserve neither and lose both.”
                              - Benjamin Franklin

                              Banned from the St. Lawrence University Facebook page - March 2016 (But I got better).

                              I want to live forever. So far, so good.

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