Optimal strategies for the progressive Monty Hallproblem

摘要

In the classical Monty Hall problem you are a contestant on a gameshow confronted with three identical doors. One of them conceals a carwhile the other two conceal goats. You choose a door, but do not open it.The host, Monty Hall, now opens one of the other two doors, careful alwaysto choose one he knows to conceal a goat. You are then given the optionseither of sticking with your original door, or switching to the other unopeneddoor. What should you do to maximise your chances of winning the car?