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The Puzzler

Puzzler Answer: Behind Door Number One...

RAY: OK. Look. It's time, finally, to answer the questions and Monty Hall's been dying to know the answer to.

TOM: Yeah.

RAY: And I didn't want to embarrass you by asking you what --

TOM: Of course, I knew it was Monty Hall.

RAY: We've milked. We've used this puzzle now for two weeks and it's time to give the answer.

TOM: Yeah. Yeah. I've been dying to find out what the answer is.

RAY: I'll restate the puzzler

TOM: I wish you would.

RAY: As briefly as I can. Everyone remembers the game show, Let's Make a Deal, where the contestant was presented with three doors, Door Number One, Number Two, and Number Three. OK.

TOM: Yeah.

RAY: Behind one of the doors is a wonderful prize and behind the other two doors were crummy prizes, known as zonks. OK?

TOM: Yeah. I got it.

RAY: Here's the puzzler. You are the contestant. Monty Hall says, "Pick a door." Go ahead, pick a door.

TOM: Three.

RAY: No, you have to pick two.

TOM: Two.

RAY: OK. Monty Hall says, "OK. You've picked Door Number Two." Now, in the real game, he offered you cash, whatever. We simplified it.

TOM: Yeah.

RAY: He says, "I'm going to show you what's behind one of the doors that you didn't pick." Now, because there's only one prize needless to say, I won't even say it, those two doors have one, either two zonks --

TOM: Or one prize and one zonk.

RAY: Right.

TOM: Yeah.

RAY: And those are the only choices.

TOM: Yeah.

RAY: OK.

TOM: And I'm going to show you what's behind one of the doors.

RAY: So, he knows where the zonks are. So, he says, "I'm going to show you what's behind Door Number One" and he shows you that, '63 Dart. He then says, "Do you want to switch your choice from Door Number Two to Door Number Three?" And your logic is what?

TOM: What's the difference?

RAY: What's the difference? I had a one in three chance of winning before.

TOM: Right. I could have just as easily have chosen Three the first time. What's the difference? I'm sticking with Two.

RAY: And that's the answer you should stick. It's a stupid puzzler. No, that isn't the answer. The answer is you should switch. Now, I know this is going to generate all kinds of gnashing of teeth and all kinds of controversy and --

TOM: Oh, especially among all the college professors who've been teaching probability theory, all their lives and think they understand it.

RAY: Well, I know I don't understand anything.

TOM: I was one of them.

RAY: You should switch because if you don't switch, your chance of winning is one in three. We already know that. You just pick a door. No matter what he does, your chance is one in three.

TOM: Exactly.

RAY: If you do switch, this is the part that's hard to believe. Your chances become two in three. You double your chance.

TOM: Impossible. I can hear it all over the country. I can hear them all.

RAY: And hear it reverberating.

TOM: Impossible.

RAY: From sea to shining sea.

TOM: The guy's so blimped out now, they've gone over the edge. I won't stand for it. What's their e-mail address?

RAY: From Springfield to Springfield to Springfield.

TOM: To Fairview to Fairview to Fairview.

RAY: Here's the simplest way I can explain it. What Monty Hall is basically offering you is this, he says, "You've chosen Door Number Two. Would you like to switch for Doors One and Three?"

TOM: Exactly.

RAY: Because he knows where the zonk is he's obviously going to show you the other zonk which is Door Number One and, but he can't show you Door Number Three because the prize might be there.

TOM: It might be.

RAY: And if it is there, he can't show you that so, what he's basically saying is "You pick Door Number Two. I'm going to give you One and Three."

TOM: If he had not shown you what was behind Door Number One and simply said --

RAY: Would you like...

TOM: Would you like to switch from Door Two to Doors One and Three, would you always switch. Of course, you would.

RAY: Right. And if he said to you, if you showed you nothing and asked if you would switch from Door Number Two, your answer would be no, but because he has shown you one of the zonks.

TOM: Now, you believe that it doesn't matter.

RAY: Doesn't matter. Pretty good, huh? Who's our winner this week?

TOM: Wow! Tired just thinking about it. The winner is Victoria Montag. Sounds like something's left off the end of that name. Montag-goo or Montag-nah or Montana. Victoria Montag from Floral City, Florida and for having her correct answer chosen at random, from all the dozens if not hundreds if not two correct answers we receive this week, our victor Victoria wins our newest CD. Brand new. Brand new. A whole album of calls about couples and their cars. It's called Men are from GM, Women are from Ford and it's guaranteed to cement any relationship.

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