[extropy-chat] monty hall paradox again

[Alejandro Dubrovsky]

On Wed, 2004-05-19 at 10:20 -0600, Alan Eliasen wrote:

> > On Wed, 2004-05-19 at 00:47 -0600, Alan Eliasen wrote:
> >>   Projected earnings for either case is 3/2n, and no option (always staying,
> >>switching, whatever) improves that.
> 
> Alejandro Dubrovsky wrote:
> > So are you saying that once you opened the first envelope and it had
> > $10, you wouldn't switch?
> 
>    What I'm saying is that if you don't have any idea of the potential amounts
> in the envelopes (as cited in the problem description,) then neither option
> (switching or staying) is mathematically preferable.  I'd do just as well
> flipping a coin, or always staying, or always switching, or staying 22.8% of
> the time, or whatever.
> 
>    I'm not sure if you're getting at something different with the $10
> question.  If this is treated as a mathematical problem, my answer is as
> above.  If you're turning it into a psychological problem, in which one tries
> to guess the probable amount of a donation, you're on your own.  I can only
> predict the simple things, not the firing of an unknown benefactor's billion
> neurons.  ;)
> 
No, i wasn't implying any kind of psychological analysis was wanted.
This paradox seems especially interesting to me because unlike most
paradoxes i hear about, this one has a nice sharp practical effect which
cannot be "thought away" like others.  That is, if someone comes with
two envelopes, one containing y and the other containing 2y, you choose
one and get amount x (where x is either y or 2y but you don't know
which), do you swap?  
Now what about the following case:  someone comes and gives you an
envelope which contains x, then says you can return it and get another
envelope with amounts 2x or x/2 (equal probability of either), do you
swap in this case?
If the answers are no to the first and yes to the second question, what
is the significant difference in scenarios? (this is a real question in
that i don't understand and i would like you to explain it to me, it is
not put as a teacher's test to a student)

thanks,
alejandro