Comments on: The Monty Hall Problem

By: haribo

haribo — Fri, 13 Jul 2007 15:50:11 +0000

FX Ryan: It doesn’t work for deal Or No Deal. Swapping with Monty Hall works because he will always take away a dud prize. In DOND you have an equal chance of it being one of the two amounts left.

By: Paul Ding

Paul Ding — Fri, 13 Jul 2007 04:59:59 +0000

One factor they miss in all those elegant analyses is whether Monty wants you to win or not. You see, sometimes Monty gives contestants a chance to switch doors, and sometimes he didn’t.

If Monty knows you have picked the right door, and he wants you to win, he isn’t going to give you the opportunity to switch. If he wants you to lose, he gives you the opportunity to switch.

If Monty knows you have picked the wrong door, and he wants you to lose, he isn’t going to give you the opportunity to switch. If he wants you to win, he gives you the opportunity to switch.

Therefore, you have to figure out whether Monty is on your side. If he is, and he lets you change your mind, take it. If he isn’t, and he lets you change your mind, don’t.

By: hal

hal — Thu, 12 Jul 2007 19:03:41 +0000

I read TCIOTDITN-T, and what has been bothering me about this is that, sure, switching doors improves your chances, but what if the car is behind your first door?

By: Jef

Jef — Thu, 12 Jul 2007 17:35:18 +0000

Right, the whole reason the answer to this problem seems statistically counterintuitive is the fact that the door Monty chooses to reveal to you is not a random choice. Monty knows which door has the prize, and which doors don’t. Once you choose a (random) door, Monty will then reveal to you a door that is guaranteed not to have the prize. At this point, your chances of success are 1 out of 3 with your original door (that hasn’t changed since your initial decision), and 2 out of 3 with the door NOT revealed by Monty. So switching after Monty takes away one (known to be a booby-prize) door doubles your chances of finding the prize!

By: Lauren

Lauren — Thu, 12 Jul 2007 15:46:16 +0000

This is a great post! I’m only slightly disappointed you could write about Let’s Make a Deal but not mention the lovely Carol Merrill…

By: David

David — Thu, 12 Jul 2007 14:05:17 +0000

He was even nicer in person than he was on the show, donner. He had some very funny stories about some of the folk in the audience who used to hang on to their $25 winnings, without trading up. And some great stories about getting whacked in the face, the leg, falling down on stage — all the result of some of the more outrageous costumes people would come in with!

By: donner

donner — Thu, 12 Jul 2007 13:40:12 +0000

I LOVE Monty Hall…I’m so impressed that you got to interview him…I imagine he’s as nice in person as he was on television..i loved his show – ‘anyone have a hard boiled egg? I’ll give you $50 for a paper clip…who has a stapler?’…

By: EV

EV — Thu, 12 Jul 2007 12:52:36 +0000

The trick for seeing this (or getting people to see it) is to imagine that there are 100 doors. You pick one, Monty eliminates 98 and leaves one, and says “Do you want to stick with your door, or switch and take the door we didn’t eliminate?” One of them has to have the car behind it — odds are 1 in 100 that yours is it, odds are 99 in 100 that it’s Monty’s. With three doors the numbers scale down, but it gives you an idea of how this works.

By: F.X. RYAN

F.X. RYAN — Thu, 12 Jul 2007 12:44:10 +0000

I believe that the great mathematics puzzle maven, Martin Gardner, came up with this in one his Scientific American columns. I was thinking about this when watching â€œDeal or No Dealâ€. If you are lucky enough to get the final decision and have to choose between â€œyourâ€ case and the one on the stage, using the â€œMontyâ€ principle you would have theo swap cases. 1 in 2 chances is far better than 1 in 26.

By: Yonit

Yonit — Thu, 12 Jul 2007 12:35:01 +0000

I was actually asked to work out this problem for a job interview for a software company. I had to draw out my steps on a whiteboard so guessing wouldn’t cut it.