To Switch or Not to Switch: The Monty Hall Problem
April 13, 2008
Here are three closed doors, with a car behind one and a goat behind each of the rest. If the door you pick is with a car, you win. No matter which door you pick, Monty will open another one with a goat and you get a chance to switch the door before he reveals the answer. Will you make a switch? What’s your winning chance?
You can try to play a few rounds of this game at New York Times site, and see how this works. (need free registration)
When understand the statistics behind this problem, one can understand why we make a choice among available selections. This can explain the results of the experiments on monkeys like picking M&M. Check out the whole article, “And Behind Door No. 1, a Fatal Flaw“.
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Ugh, I always hated that scenario in statistics. Because it just doesn’t make sense. It’s counter-intuitive.
Thanks for the link and a fascinating analysis. I’m reminded of the difficulty choosing the correct strength lens at the optometrist’s… at first, it’s easy to figure out which one lets me see better, but it gets harder and harder to choose. Yet, since I’m still compelled to make a choice, I have to come up with some kind of rationale on which to base it, even if it’s as flimsy as “the first choice is usually the best choice”. So it makes sense that monkeys and humans would, once compelled to create a rationale, be inclined to keep it.