Re: Are you a "Mental Gymnast"?

[Kevin McLauchlan <kevinmcl -at- magma -dot- ca>]

On Tuesday 21 January 2003 18:33, Gary S. Callison wrote:
> On Tue, 21 Jan 2003, maggiros -at- yahoo -dot- com (Maggie
> Pierce Secara) revived the
>
> Monty Hall question thusly:
> > Pretend you are on a game show where you need
> > to choose between three doors to win a
> > prize... *********
> > Kind of an interesting twist on the same old
> > thing, isn't it.
> > They're also hiring at least one writer, who
> > isn't asked to play this game, although it
> > might be cool to do it anyway.  Presumably
> > there's no "right" answer.
>
> There is a right answer. It's in the
> rec.puzzles FAQ
> (<http://mneylon.masemware.com/puzzles/faq.txt>
> and scroll down to question 2.4) and comes back
> like a bad penny every once-a-year or so in the
> usenet newsgroup alt.fan.cecil-adams.
>
> > Thoughts?

Yes. My thought is that their answer (FAQ item 2.4)  is horse-pucky.

The fallacy is that their answer assumes some sort 
of causative connection between the two choices.

Your first choice was random, 1 of 3. Other than 
superstition, you had no reason to choose any 
one door over the others.  And it doesn't matter to 
the outcome, because you don't get your answer 
from that choice. The fact that you are even 
asked to make a choice at that point is just a red herring.

When Monty opens a door -- and he will ALWAYS 
open a non-prize door -- he simply brings you to 
your real choice... fifty-fifty.

Again, your first choice has no effect on the outcome, 
and Monty is there to ensure that that is the case.
If you pick the right door on your first try, he has 
two wrong ones that he can choose. If you pick a 
wrong door, he instantly knows to choose the other 
wrong door, leaving you with exactly the same 
choice as always.... two closed doors remaining, 
only one of which is correct.

The decision to pick one door or the other is 
completely and exclusively emotional.  When you 
get down to two doors, if Monty is doing his job, 
then you will always be facing one winning door 
and one losing door, and have no information 
as to which is which.  The weight of your fondness 
for one or the other has no effect on what's behind it.
Your previous action has no effect. It's just two doors, 
only one of which is a correct choice. Fifty-fifty.

/kevin

--
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