I think a way to answer Bruce Sampsell's question might be to run a simulation with the choice being made after the host has opened the door, and show that that agrees with his prediction. Thus you show why his intuition is correct, and also why his intuition is wrong (depending on whether one's first choice is made before or after the host opens the door). I find it necessary to satisfy my intuition - if I can't show why it is wrong, how do I my "right" answer is right?
posted by Andrew Tan
August 28, 2008