Well, this one really intrigued me because my background is Statistics.
The contestant definately improves their chances to 2/3 by choosing the other door, if they have been shown a third door that is a goat. That's really why it's not 1/2 chance, the conditional probability is based on having been shown a third door that is a goat. It would be different if Monty told you that you won the car every time you picked the correct door from the get-go.
I have a fun little program that proves it...I tried to upload it but I hit the max lines limit. Hopefully, this zip will work...
It will let you run door by door, or in auto mode and in auto mode, let's you try both ways....always choosing the alternate door (66% or always sticking with your original door (33%)
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