"Malcolm"  wrote in message
news:cikgvu$2u46$1{at}darwin.ediacara.org...
> Imagine we have a corridor with 40 doors, twenty on each side. A certain
> number of cars (let's say 10) are distributed at random. The other doors
> have goats behind them.
> 
> Now a man goes through the left hand corridor, opening every door that
> contains a goat.
> 
> Do you open a door from the right, or from the left? From the left,
> obviously, because any closed door must contain a car.
> 
> Now suppose that he makes it a bit harder. He opens only a few doors on the
> left containing goats, and leaves all the doors on the right shut. Which do
> you choose? The left, of course, because some of the goats have been
> eliminated.
> 
> Now imagine that he opens only one door, containing a goat, on the left?
> Which do you choose? There is still a slight advantage on the left.
> 
> Now let's imagine that there is only one door on the right, and 39 on the
> left. It is still to your advantage to choose a door on the left.
> 
> Now imagine that you choose which door will be labelled "right". This
> doesn't make any differeence, it is still to your advantage to choose a door
> on the left.

Thanks for this very thorough and meticulous attempt to make clear this
counterintuitive fact or reality.  

This problem (including my psyche's problem with it) still intrigues me!

Here are the rationally rickety and mildly mirthful remains of my attempt
at, with your predigestive help, masticate and digest this conundrum of
competitive gambling in a certain kind of game show: 

Is it because of the degree of randomness of the (ideally) randomly
distributed 30 goats and 10 cars behind 40 doors have been left-laterally
reduced - as if by a left-localized partial wave/game function collapse
relative to the location of the guessing-reference frame of the contestant
:) - by the removal of the uncertainty of one goat's location on the left
side and thus not equally much randomness-reduced on the right side, that
the chance of choosing a door on the left is (supposed to be!?) the luckier
choice? 

And, would it take that a contestant moves 19 unopened doors to the right
side for the advantage to shift to the right side? %-}

Yours especially probability-theoretically perfunctory,
Peter
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