Here are 2 articles that may help analyze the problem
and provides some insight

why peoples' intuition
get this wrong and why the better choice is to switch
choice,

if you get the first choice wrong.

http://en.wikipedia.org/wiki/Monty_Hall_problem
http://saliu.com/monty-paradox.htmlEnjoy
the reading. If Game Theory interests you, I just
finished an excellant read in

Bruce Bueno de
Mesquita's "The Predictioneer's Game". It is a facinating
read on Game

Theory and how "predictions" can
be made of people choices as Bruce book states

"Using the Logic of Brazen Self-Interest to See
and Shape the Future." They had a

show on Bruce's
work 2 years ago on TV. The US Govenrment State
Depatrment and

CIA has rated Bruce's prediction
of world political and other events at better than
90%.

This is increadible statistics on future
predictioneering.