The role of probability in solving the Monty Hall problem

[Mr.wizard]

I would keep the initial door I picked.  Though my chances of being correct have changed from 1 in 3 to 50/50, it will not change what is behind the door that I chose.  By opening door #3 and showing me a goat, it affirms the possibility that I chose the right door, but gives me no reason to assume that I chose incorrectly (or correctly).

Game-wise however, I would assume that I had picked the right door as they would rather I chose the goat and will try to get me to change my mind.

The probability does not become 50/50 right after one goat is open, its's still 33%. Think of 100 doors, you pick 1 and the host opens 98 doors revealing goats, the probability you choose correctly initially does not become 50/50, it is still based on 1/100, because the host knows where the car is and he is going to open only goats.