Dear Brian Hayes,
thank you for this helpful review as well as for your highly interesting regular column Comp Sci.
A lot has been written about the Monty Hall affair, however I haven't yet heard of a convincing solution that doesn’t rely on statistical reasoning but logical ones. Here is my attempt:
First it is to be realized that—according to the puzzle's concept—there are restrictions concerning the door(s) Monty Hall is allowed to open:
Neither does he open the door that hides the prize nor the one chosen by the subject.
With this in mind, three situations are to be considered:
1) If the subject initially chooses the door that hides the prize, then of course switching would not be advisable.
2), 3) If the subject initially chooses one of the two other doors, then switching the doors would be advisable. (These are the two situations in which Monty Hall has no choice of which door he opens.)
Consequently, in two of three situations switching is successful.
With best regards
posted by Helmut Gluender
July 2, 2008