Monty Haul Problem

["Michael McGeachie" <mmcgeach@>]

Friends, Stataites, Labmembers.

I come to you with a problem.  An economist friend of mine thinks that even
seasoned statistical reasoners have difficulty solving the following
problem, or if they can, then they have difficulty explaining it.  This is a
modified version of the Monty Haul problem:

Modified Monty:

Monty presents you with three identical boxes, one of which contains a prize
and two of which are empty.  You first choose one box, but do not open it.
Monty then opens one of the remaining unchosen boxes, and shows you that it
is empty.  Since there are two empty boxes, Monty can always do this.  Monty
then gives you a choice: you may open the box you have already chosen, or
trade with Monty for the remaining unopened box, and open that one.  What
then, is the best strategy, and what is the probability of winning the
prize?

And in a modified spirit of the CSAIL-Discuss mailing list, the three or
four of you who have yet to unsubscribe are invited to respond (not to the
whole list, please) with answers and explanations, the best of which earns a
free beverage at this evening's 3rd Stata Centered...

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