The usual statement of the Monty Hall Problem involves important but unstated presumptions; without them, the alleged logic falls apart. For example, it is presumed that one begins by assigning equally quantified probability to each door, but do some reading on
the problem of reference classes (for example, look into
Bertrand's Paradox), and note the assertion of von Kries, of Keynes, of Koopman, and of Mc Kiernan that probability may be an incomplete preordering, in which case no quantification is even possible.