🚀 go-pugleaf

The remarkable thing about the Monty Hall Problem or shell game or
whatever is, perhaps, not its mathematics but its psychology.  The
correct answer (the odds are 2:1 that you should switch) is
_most_ counter-intuitive for people with some mathematical
training--the sort of people who might apply a heuristic like `now you
have reduced the problem to two doors'.  And because the mathematical
savants know what they are doing, once they have reached the wrong
conclusion it is astonishingly hard to persuade them to the other
side.  This is why the problem surfaces again and again in places like
alt.folklore.science or the syndicated column `The Straight Dope'
(where it has appeared at least three times) and similar forums.

In `The Straight Dope', the columnist (Adams?) once came up with an
explanation that might be helpful: extend the problem to one million
doors.  You pick one.  Now Monty goes and opens 999,998 of the other
doors, showing you that none of those doors has the valuable prize.
At the rate of a door per second, he finishes this task in about 11
days; this is why we are not using goats :-) You may now switch with
that one other door that remains.  The point here is that 999,999
times out of a million (i.e., if you did not pick the right door to
begin with), Monty ONLY HAS ONE CHOICE as to which doors he opens, and
as a result, HE IS SHOWING YOU WHERE THE PRIZE IS.

Does this help anyone?  No?  Oh well...

	Mike Urban

	urban@cobra.jpl.nasa.gov