The Monty Hall Puzzler

The Puzzler

New Puzzler, 10/11/97: Behind Door Number One...

RAY: OK. Now, here's the puzzler for this. I thought about this a lot and I have a whole bunch of puzzlers, but I have to revisit this puzzler, from yesteryear, for a variety of reasons. Number one --

TOM: I know one of them. You found out the right answer.

RAY: Number of reasons plus one.

TOM: Plus one.

RAY: Number one it was perhaps, it is perhaps one of the best puzzlers of all time, I think.

TOM: Monty Hall?

RAY: Number two, we haven't used it in so long that the people that heard it then, are dead.

TOM: They're dead. Or they forgot.

RAY: Here it is, in its simplest form.

TOM: Yeah.

RAY: You may remember the game show. What was that game show? Let's Make a Deal.

TOM: Let's Make a Deal. Yeah.

RAY: Where the contestant was presented with three doors - door number one, door number two and door number three. Behind one of the doors was a wonderful prize and behind the other two doors were crummy prizes, known as zonks.

TOM: Yeah.

RAY: And very simple.

TOM: Like a couple of candy bars or some such thing.

RAY: Exactly.

TOM: Something not worth much.

RAY: Exactly. A '63 Dodge Dart. Anything like that. Here's the deal. You are the contestants.

TOM: I'm the contestant.

RAY: Monty Hall says, "Pick a door." Your chances of picking a zonk are two and three and your chances of picking the winner are one in three.

TOM: Right.

RAY: He says, "OK. You pick door number two. I'm going to show you what's behind one of the doors that you didn't pick. Now, because there are two zonks and one winner and he knows where the winners and the zonks are. He shows you one of the doors that you didn't pick that's clearly a zonk.

TOM: So, he says, "I'm going to show you what's behind door number one."

RAY: Right.

TOM: And he looks behind door number one --

RAY: And it's six candy bars.

TOM: Six candy bars.

RAY: He then says to you, "Would you like to keep door number two, which you've chosen or would you like to switch to door number three?" That's the question - should you switch or not switch? Now, if you think you know the answer or just feel sorry for the Post Office in this age of e-mail and you want to give them something to do, send your answer to Puzzler Tower, Car Talk Plaza, Box 3500, Harvard Square, Cambridge --

TOM: Our fair city.

RAY: MA 02238. Or, if you prefer, you can e-mail us your answer from the Car Talk web site. Just click on the Talk to Car Talk section. Now, if we choose your correct answer at random, from among all of the correct answers that we receive, you will get a Car Talk sistine wrench T-shirt. Car Talk's first attempt, and probably last, at fine art.

TOM: And we don't say when you'll get it. You will get it.

RAY: You shall get it. You might.

TOM: At some time --

RAY: You probably will.

TOM: At some time in the future.

Answer: 

Monty Hall Puzzler


How It Started

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!!


A Quick Flashback

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.

Historical Proof Check out the mathematical proof from our pal Steve Selkin. (Steve: thank God you bailed us out. We're not saying we understood all that garbage you wrote, but all those symbols sure looked good.)
Be Enlightened--sort of Read the letter from Monty Hall himself, or the other mail we've gotten about this puzzler!

 


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