Comments on: I Knew You Would Say That

By: Gabriel Enck

Gabriel Enck — Tue, 23 Sep 2008 08:00:11 +0000

Only before the opening of a losing door is there a 2/3rds chance of having chosen a losing door. Once Monty reveals either Doors 2 or 3 to be a loser, the outcome with that door being a winner is impossible (0% chance). The probability matrix (http://www.marilynvossavant.com/articles/gameshow.html) doesn’t reflect that. If a goat is shown to be behind Door 2, (and you chose Door 1), the “GOAT, AUTO, GOAT” outcome is no longer possible, and thus is not part of probability. The only viable outcomes are now either “AUTO, GOAT, GOAT” or “GOAT, GOAT, AUTO”. A 50/50 chance. No matter which door you initially choose, Monty will show a losing door, and then you will have to decide between the two remaining doors which to choose. The choice “to switch” or not isn’t any different than just choosing one of two doors from the outset.

By: Kevin Cline

Kevin Cline — Fri, 25 Jul 2008 19:54:21 +0000

On the show, life was not so simple. Myers analysis assumes that the host always opens one door and then gives the contestant the option of switching. But on the show, Monty Hall was much sneakier than that. See the Wikipedia article for more information: http://en.wikipedia.org/wiki/Monty_Hall_problem

By: Doug Brooks

Doug Brooks — Thu, 10 Jul 2008 02:09:01 +0000

Thanks for setting me straight. I take some solace from the Marilyn Vos Savant postings – looks like I was in pretty good company in my error.

By: Ian Robinson

Ian Robinson — Sun, 06 Jul 2008 02:31:01 +0000

This issue of the three doors was thoroughly analysed in the Sceptical Inquirer about ten years ago and conclusively resolved. Myers is right and Brooks is wrong. [All my back copies are in storage pending a move, or I could give you chapter and verse.] Like Brooks I didn’t believe it at first but then I did the math.

Ian Robinson
President
Rationalist Society of Australia

PS Check out http://www.marilynvossavant.com/articles/gameshow.html

By: Thuy Ngo

Thuy Ngo — Sat, 28 Jun 2008 17:29:08 +0000

I disagree with Mr. Brooks. The chance of you picking the wrong door in the first round is higher (2/3), so it’s better to switch door in round two even if it seems (intuitively) that switching doesn’t matter.

By: Doug Brooks

Doug Brooks — Thu, 26 Jun 2008 20:55:08 +0000

There is something that has always bothered me about the problem discussed in the first two paragraphs of your review (I am sure I have seen it somewhere before) – my intuition tells me that once Monty opens door number 2, it doesn’t matter whether I switch or not, and I am not satisfied by the explanation in the second paragraph.

I think the problem is that by opening door #2, Monty has changed the rules mid-stream – or started a new game. The game starts as a 1 out of 3 chance to win the car; my assumption is that once I make my choice, Monty will let me know whether or not I have won. But instead, he starts a new game. Now the game is a 1 out of 2 chance to win the car. The fact that in a previous game I happened to have chosen one of those doors is irrelevant to what I should do now. My previous choice of door #1 does not magically imbue that door with any quality that changes my odds of winning the new game from 50/50, any more than a roulette wheel player’s successful choice of red on one spin does not change the odds of the wheel hitting red on the next spin.

I don’t think this analysis would change even if I knew that after I make my first choice, Monty is going to open one of the other doors. I know that once I make my choice, at least one of the remaining doors will have a goat, and that unless Monty wants the game to end, he will open a door that has a goat. Depending on my initial choice, Monty will have either two doors to choose from (if door #1 has the car), or just one. However, unless I can interpret some “tell”, Monty’s choice is not going to affect my odds of winning the new game, or whether I should switch doors.

By: Jerry Hesch

Jerry Hesch — Wed, 25 Jun 2008 15:53:08 +0000

“Intuition is not subliminal perception; it is subtle perception and learning — knowing without knowing that you know.”
I love that definition. I always described intuition as an unconscious choice made by a person who has a wealth of experience and may be acting on subtle clues, as opposed to something in the realm of mind reading. Maybe I would add the term at the very end…”or why you know.”
I intuit that I will put your definition with my addendum on my bulletin board.