  The rational solution of the Monty Hall problem unsettles many people. Most
people, including the authors, think it feels wrong to switch the initial
choice of one of the three doors, despite having fully accepted the
mathematical proof for its superiority. Many people, if given the choice to
switch, think the chances are fifty-fifty between their options, but still
strongly prefer to stay with their initial choice. Is there some sense behind
these irrational feelings?
  We entertain the possibility that intuition solves the problem of how to
behave in a real game show, not in the abstract textbook version of the Monty
Hall problem. A real showmaster sometimes plays evil, either to make the show
more interesting, to save money, or because he is in a bad mood. A moody
showmaster erases any information advantage the guest could extract by him
opening other doors which drives the chance of the car being behind the chosen
door towards fifty percent. Furthermore, the showmaster could try to read or
manipulate the guest's strategy to the guest's disadvantage. Given this, the
preference to stay with the initial choice turns out to be a very rational
defense strategy of the show's guest against the threat of being manipulated by
its host. Thus, the intuitive feelings most people have about the Monty Hall
problem coincide with what would be a rational strategy for a real-world game
show. Although these investigations are mainly intended to be an entertaining
mathematical commentary on an information-theoretic puzzle, they touch on
interesting psychological questions.
