∞ The Monty Hall problem

Written by

Chris Martucci:

I came across the Monty Hall Problem while reading last night, and initially, I thought the author must have been mistaken. Of course, he made no mistake. He did, however, succeed in proving the common failures of human reasoning.

It’s a brain twister.


  • Anonymous

    I’ve run into this problem before, and any time I bring it up a fight breaks out. I can definitely see the logic, and could from the first time I saw the right answer (which was not right away). Many people always insist it’s 50-50, you pick one, one has the car, one has the goat. It must be 50-50, right? Only it can only be 50-50 if it were a completely random method of determining where the car was and where the goat was.

  • http://www.theuniversalsteve.com Anonymous

    Every time I read the explanation it makes sense, but two weeks later I couldn’t explain it to you if my life depended on it. I’m a programmer at a company that does physics research. It’s not always easy to present data without accidentally creating some kind of statistical distortion.

  • Anonymous

    Cool post.

    First you have a 2/3 probability that you picked a goat.
    Then,
    Since you probably picked the goat, you have to turn the 2/3rds probability in your favor by treating the first choice as an attempt to eliminate 1 goat.
    Changing to the other box, you’re playing the odds and assumming that you eliminated one goat and monte eliminated the other goat.

    How often do you eliminate a goat with your first choice? 2/3rds of the time.

    • Anonymous

      The 1/3 probability that you picked the car is the big thing. All the rest that follows is just misdirection. No matter what Monty Hall does with his curtains, you originally had a 1/3 probability that you have the car, and (given that he definitively will not throw away the car), you still have a 1/3 chance of having it. Therefore Monty Hall has a 2/3 chance. You do better by trading.

      • Anonymous

        Lol, that’s what I said – trade.

        I say realize you’re on the low end and trade up.
        You say realize Monty is on the high end and trade up.

        Same thing.

    • Anonymous

      where the trick becomes tricker for many to logic out is that Monty likely knows where the car is and he’s either trying to get you to change because you picked wrong or trying to get you to chance because you picked right and they don’t want to actually give away the car. Which it is, these folks would say, depends on how much drama they need to keep viewers interested. 

      Basically they try to make it something psychology and scammy forgetting that Monty can’t control what the picker will do. They might fall for his game and change and be wrong or stick with their guts and stay, or change and be right

      Then again, he could also just ask that the door be opened and show the world you picked a goat. or a car