The Monty Hall Puzzler
Remember the age old game show, "Let's Make A Deal," with Monty Hall and Carol Merrill? Well, a couple of months ago, we posed a little puzzler inspired by said game show. The puzzler involved switching boxes and changing the odds of winning the big prize. And boy, did it cause an uproar!
We practically started World War III.
The puzzler itself was pretty straightforward. When we gave our answer-- that switching would increase your odds of winning big, all Hell broke loose. We got satchels full of mail--much of it on letterhead from prestigious universities, with inscriptions like, "The Josiah Wadsworth Endowed Professorship of Statistical Phenomenology, Department of Applied Mathematics, Somewhat Prestigious University." Many of the letters were vituperative... and some were even downright nasty. We got mail that told us we were wrong headed, mail that told us in exactly which wrong place our heads must be, and mail telling us where we could put our heads, provided they weren't there already.
Well, now we're here to prove that we're right. Why go through all this trouble? Because what could be more fun than proving a bunch of pompous academics wrong!!
Here's a refresher on how the game worked. Behind one of the boxes, was the Grand Prize. Behind the other two? Lame consolation gifts, like a year's supply of Rice-A-Roni (the San Francisco treat), or 144 boxes of Ring Dings. Your job? Pick the winner.
Once you've made your selection, Monty would reveal one of the other boxes to be what he called, a "zonk"-- that is, a dud. Now, there are two boxes: the one you picked, and the remaining unopened box.
We've now arrived at the crux:
Do your odds of winning improve if you switch to the other box? The answer, unequivocally, assuredly, beyond any doubt is.... No. Wait, we mean... YES. Yes, yes, yes! A thousand times, yes. Not only do your odds improve, but they go from 1-in-3...to 2-in-3. Case closed.