Monty Hall Campaign Does Not Yield Grasp of Probability

Science

Over at Dubious Quality, Bill Harris' reliably entertaining Friday Links feature (and I don't praise it just because he linked to us last week) has a link to my old nemesis: the Monty Hall Problem. As described in this NYT article and further in this much older NYT article, the Monty Hall Problem is a highly counterintuitive probability puzzle. I've never been able to wrap my brain around the currently accepted correct answer and remain skeptical, all emerging consensus aside. I am somewhat comforted that thousands of mathematicians and scientists originally agreed with me. Read Bill's summary and the articles — they are fascinating and infuriating.

Last 5 posts by Ken White

2 Comments

2 Comments

  1. PLW  •  Apr 12, 2008 @7:36 am

    You can demonstrate that the answer it right quite easily with a deck of cards. Just have someone you trust pretend to be Monte, and hide the Ace among 5 or 6 face-down cards. Then you choose one, he uncovers all but one, and you choose whether or not to switch. If you do it enough times, you've convince yourself that it's always best to switch.

  2. N  •  Apr 13, 2008 @11:35 am

    This is one I've never been able to intuitively grasp, but brute forcing it convinces me that it can't be any other way. I wouldn't go the stastical route PLW suggests (well, maybe *I* would, but most normal humans shouldn't) — just draw out all possibilities with the simple 3-door set-up. The counterintuitive outcome is that it *is* [spoiler]better to change if offered the opportunity[/spoiler].

    I'm classically (and contemporarily) trained as a mechanical engineer. I'm really good at being a student. However I was tripped up, momentarily, by a setup quite unlike the Monte Haul (ha!) problem, but a similar moment of intuitive ungraspiness. Imagine a simple coil spring. It functions by applying a force in the opposite direction to that of its extension. Mount one end to the classical (but not contemporary) immovable wall, and pull on the other end. Spring wants to pull in the opposite direction of pull. The amount of restoring force is measured in an engineering term called Stiffness (engineers have coopted many common words used in casual language for very specific engineering purposes). Stiffness can be quantified in terms like pounds per inch (generically, force per distance). You pull a 50 lb/in spring two inches and it pulls back in the opposite direction with 100 lbs force.

    So the instructor asked us students, what happens to a spring's stiffness if you cut the spring in half. My immediate intuitive response was that *nothing* happens — stiffness is an inherent property of the spring. Well, given the lead-in to my question, you can probably imagine that I wasn't just kinda wrong, but I was all the way wrong. If you cut in half a spring, what you've done is remove half the "active coils" (the part of the spring that allow it to extend), and in essense you've made the spring much more difficult to stretch out. Quantifying that in engineering terms, you've doubled the stiffness.

    In retrospect, that was a big huge "DUH!" to me, but for a few moments there I was pissed that the instructor couldn't grasp the idea that a spring's stiffness can't change just because you changed its geometry a bit. I mean I was *pissed*. How could this joker be qualified to stand in front of a class and try to teach this garba– whoa. Oh, yeah, twice the stiffness. Neat.

    Maybe that moment is just yet-to-come with the Monte Hall problem?