Comments on: Folk Numeracy & Middle Land

By: Jeff

Jeff — Tue, 23 Dec 2008 15:13:13 +0000

Wouldn’t this actually be a short-term/long-term thing?

By expanding this and saying you have 10 sets of three, and while the correct options are random, your choice goes throughout all, so, while set one, door one is a goat, set two door one is a car. You choose one number, and it is applied to all sets.

Well, opening all door number twos, wouldn’t that make the individual odds, for each set, either 50-50 or 0-100, but the long-term odds, that you will have more cars than goats, are 66-34?

Am I making any sense?

By: Steph

Steph — Sat, 06 Dec 2008 12:29:09 +0000

If Monty opens door number 2 and reveals a goat, then that would automatically eliminate possibility b.)bad, good, bad. So with only two possibilities, shouldn’t the odds be 50/50?

By: Ted

Ted — Tue, 18 Nov 2008 05:39:20 +0000

In the Random Walk article, the two examples, 3 doors and 10 doors, new information is introduced as the doors are opened. This changes the game. Each time a goat is revealed, the size of the game is reduced by one, and the probabilities assigned to each door must be adjusted, but all remain 1/n, where n is the number of unopened doors. When only two doors remain unopened, it is 50/50. No asymmetry has been introduced by the goat-revealing process described in the examples.

By: Chris

Chris — Wed, 12 Nov 2008 13:42:33 +0000

Cam,

You are correct that the host’s action cannot be considered random. However, he always opens a door (both in the show and in the puzzle). The only choice is which door. In the original version of the puzzle, as published in Atlantic, it was not a random choice: the host knew which door held the car and always revealed a goat. And that is what throws people about the result. If the opening was random, your odds would indeed be 50-50. (None of this discussion applies to the actual show, by the way, which operated differently.)

By: Bill Zipperer

Bill Zipperer — Tue, 11 Nov 2008 05:46:04 +0000

Narative bias is another problem: people latch onto a good story. How many times have we heard of a solution to a problem that seems simple and logical yet turns out to be wrong? Science and especially statistics(!) doesn’t commonly fit into a compelling narative that people can embrace easily.

By: Cem Egrikavuk

Cem Egrikavuk — Sat, 08 Nov 2008 11:34:02 +0000

Well, I logged in to make a comment on the second part of this article, published October 2008. It’s not here yet, but I’ll post anyhow;

I strongly believe there is an error in the version of the puzzle presented in the opening paragraph of “A Random Walk through Middle Land, Part 2,” otherwise a great article. Shermer declares that the host knows the contents of the three doors. Therefore Monty’s actions can not be considered “Random” in such a puzzle, and compared with dices and roulette table. The hosts action to reveal the contents of a door might have the intention of deceiving the player into giving up on his already correct choice.

Only if the rules of the game dictate that the host must reveal one of the doors after the player makes his preliminary choice, then the argument holds. As long as opening a door is optional, the game is non-random.

(I remember the orginal version of this puzzle had the door/box being opened at random.)

Regards,

Cem Egrikavuk
Istanbul

By: Read today

Read today — Fri, 07 Nov 2008 00:50:57 +0000

[...] Shermer continues his Folk … series with an easy to read installment on Folk Numeracy, covering statistics and confirmation [...]

By: Bill Treumann

Bill Treumann — Thu, 06 Nov 2008 08:33:36 +0000

I wrote a comment here but I wanted to send a copy to my grandson so I cut and pasted it. I didn’t realize it would disappear here. I dislike writing something a second time – so how can I send it to you?
If you don’t want your email address bandied about I promise to reveal it to no one.
Bill Treumann