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Journal Planesdragon's Journal: A perfect example of science's shortcomings. 23

Journal by Planesdragon

If you don't know about it already, go read up on the Monty Haul problem. Bear in mind that computer simulation proves Marilyn Vos Savant right.

Now, then, why exactly is she wrong?

A natural inclidng is to jump up and say "she's got to be wrong; there's no way that can be right." A scientific inkling is to say "Planesdragon, you've gone off on a silly Christian rant again. Why must you prove how stupid you are?"

The answer, of course, comes in a closer examination of the problem.

If you choose to always switch, you will win 2/3 of the time.

If you choose to not switch, you will win 1/3 of the time.

But, the desicion to switch does not come until Monty asks his final "will you switch" question. Either you've got the car or you've got the goat--a new possibility that has exactly two outcomes.

I'm just a lowly college drop-out, but I believe that this is an example of "the law of independent trials."

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A perfect example of science's shortcomings. More

A perfect example of science's shortcomings.

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  • I've read your post about 6 or 7 times now and I still don't understand how you are trying to say that the Monty Hall paradox is an example of scientific shortcomings.

    Are you saying that Marilyn is wrong and the odds of winning are not 2/3 if you switch every time?
    • Are you saying that Marilyn is wrong and the odds of winning are not 2/3 if you switch every time?

      No. What I was saying was that the necessary question isn't "what should I pick", but rather "what are my odds of wining?"

      If you go up onto a game show, your odds of making your final desciion are 50/50 -- one is a car, one isn't. I incorrectly failed to account for Marilyn's presumption that the host is playing fair -- somewhat augmented by lack of an actual choice among the various "emphirical tests" Wikipe
      • Under the rules of the game, the odds of winning if you switch is 2/3. If you change the rules you change the odds, obviously.

        If Monty doesn't know what door the car is and randomly opens one of the remaining doors, then you end up with a 1/3 chance of winning, regardless of whether you switch or not. This is because if Monty opens the car door, you've lost. Switching or staying with your door doesn't make a difference.

        If the sponsors can change where the stuff is after the first door is picked, then the
        • Many other assumptions are left out of everything else we read as well.

          Sometimes, this is fine. Other times--particularlly over efforts that have any opposition at all--it's a bad thing.

          Best example I can think of? The Big Bang theory (and most other astrology) presumes that the fundamental forces of the universe are constant and homogenous. While this is emminently reasonable, it's the sort of thing that needs to be pointed out when people take science's "this is what it looks like" and turn it into "we
          • I wouldn't consider the big bang theory to have anything at all to do with astrology. I don't think science trusts astrology for anything and I know Christianity doesn't.

            Probably just a typo though, so I will leave it at that.
            • 1: Yes, I meant "astronomy." But at least astrology was upfront about their assumptions. ;)

              2: Christianity has quite a history with astrology, actually. The best example would be the three wise men, but there are likely others in teh various christian bodies of lore.

              Remember, the commandment was not "forsake all but your God", it was "have no other Gods before me." If the Big man isn't answering you, there's nothing inherently sinful about turning to astrology. (There may be something inherentily foolis

  • The reason MVS is right (Score:3, Informative)

    by Marxist Hacker 42 ( 638312 ) * <seebert42@gmail.com> on Tuesday July 26, 2005 @07:40PM (#13171643) Homepage Journal
    Has nothing to do with the first choice- and everything to do with the behavior of the Game Host- who increases the percentage odds from 50% to 66% by showing you what is behind one of the three doors (of course, the original choice stays stuck at 33% chance of winning the car). The reason that the law of independant trials does not apply in this case because the trials are not completely independant- the host opening the door with the goat provides the link between the trials.
    • And to paraphrase the Wiki article, once the host shows a door with the goat, you know right away that there is a 2/3rd's chance that he picked that door because you already picked the other one (in which case switching gets you the car), and a 1/3rd chance that he picked either of the goat doors (in which case switching loses).

      The trials are not independent, and that's the non-intuitive part.

  • The trials are not independent (Score:1, Informative)

    by Anonymous Coward
    Your first selection of a door influences the host's selection of which door to reveal, so your final choice (to switch or not) is not an independent trial.
  • But, after one of the doors is open, wouldn't the chances of then selecting the winning door become 50%?

    After you have two options to choose from, you can only select either one or the other. One of the 100% chance of failure options is eliminated, leaving two options (a winner and a loser), thus a 50% chance of winning.

    At the option to switch, why does the first door have any relevance whatsoever?
    • You _are_ simplifying it too much. In fact your initial choice has an effect on what door the host opens. If you chose a goat, the host must choose the other goat to show you. You know that your odds of initially choosing a goat are 2/3, so there's a 2/3 chance that the host just showed you the second goat, leaving the door you DIDN'T pick as the one with the car.

      Kids get pounded into their heads in stats classes to watch out for independent events, but these events are NOT independent, therefore that does
    • At the option to switch, why does the first door have any relevance whatsoever?

      Because the host knows which door is the prize door.

      The picture is easier with a larger number of doors. Let's say, four. You have a one-in-four chance in picking the right door on your first time--and that's the ONLY time that the door the host doesn't open won't be the prize.

      it's nice to know I wasn't the only one who got this one wrong. Although it becomes yet another complaint against scientists that this principle wasn't
  • It's already been explained many times why independent events has absolutely nothing to do with this problem. What I'd love is a more detailed explanation about what this has to do with Christianity and Science. It's pure math, plain and simple. Even Christians believe in math. (At least, I do.)
    • Even Christians believe in math.

      Are you sure about that?

      The good Christian should beware of mathematicians and all those who make empty prophecies. The danger already exists that mathematicians have made a covenant with the devil to darken the spirit and confine man in the bonds of Hell.
      ---Saint Augustine
    • What I'd love is a more detailed explanation about what this has to do with Christianity and Science.

      Absolutely nothing more than framing the flow of the article. I could have easily said "married men" or "white guys".

  • Repeatedly they link DATES to DATE entries in the pedia. WTF? If you're going to cite MVS' article about this, YOU NEED TO LINK TO IT NOT THE DATE.

    So the basic explanation is really actually quite simple. There are three possible outcomes:

    • You picked goat 1, Monty shows goat 2, you switch and WIN
    • You picked goat 2, Monty shows goat 1, you switch and WIN
    • You picked the car, Monty shows a random goat, you switch and LOSE

    So there are three posibilities, two of which lead to you winning the car, hence a 2/3's p

  • In such a game you have a flat 50% chance of winning, as the host always opens one of the losing doors after your first choice. In effect, there are only two choices, one wins and one loses. The fact that one of the two losing choices is removed from the second round of guessing dictates that the chance is indeed 50%.

    IE, you have choice 1, 2, 3.

    The correct choice is 2, 1 and 3 being false.

    If you pick 1, 3 is revealed, and vice versa.

    You never have a 33% chance of winning, nor a 66% chance. You have a 33%
    • No, I was wrong. Spent more than a few hours yesterday and today convincing myself of it, too.

      There are four variables involled--winning door, first choice, door shown, and second choice. If you map out all of the possibilities, you wind up with even choices of each--but that doesn't account for the host knowing which is the right door.

      It is precisely because the host knows which door is the prize--and so will not pick that one if you haven't--that tilts the odds in the favor of the switcher. Replace the

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