The basic Monty Hall problem has been discussed far too often to keep track. In his blog, my former teacher Ulrich Berger briefly discusses a conversation appeared on “Who wants to be a Millionaire”:

A candidate faces a multiple choice question with four possible answers, only one of which is correct. She doesn’t know the answer and attaches a probability of 1/4 to each alternative. She chooses A however, not based on any knowledge. Then, before confirming her answer, she recalls that she hasn’t made use of her 50:50 joker, a random mechanism deleting two out of the 3 wrong alternatives. If the candidate chose A for herself before applying the joker and A remains one of the two alternatives on her screen, should she stick to her choice or switch to the other alternative?