Exactly: what counterintuitively changes the overall probability of picking the correct door is Monty’s introduction of new information that biases the contesta

Exactly: what counterintuitively changes the overall probability of picking the correct door is Monty’s introduction of new information that biases the contestant to the right choice. Many years ago I was in such disbelief about this result that I wrote a little Monte Carlo simulation to “prove” I was right. In fact, it proved I was wrong!