50/50 Joker of "Who wants to be a Millionaire" - A "Monty Hall Problem" variation?

Monty Hall does not give you information about your preselection. Therefore the probability that your first choice is right given that it is still available after the intervention, is not changed. The 50/50 Joker does give information about it (esp. when it gets eliminated). Note that many of the misunderstandings of the Monty Hall problem arise from the missing assumption that the host always willfully opens a goat-door other than the preselected door. If you modify the Monti Hall problem so that the host opens any not preselected door at random, the general misconception that both remaining doors are "equal" becomes correct.