The Monty Hall problem is consistently misunderstood. Mathematician
Jeffrey Rosenthal argues in “Monty Hall, Monty Fall,
Monty Crawl” and Struck By Lightning that a proportionality
principle can solve and explain the Monty Hall problem and
its variants like Monty Fall and Monty Crawl better than the
classic solution. Rosenthal’s Monty Fall example and solution
are examined in detail. I show he has misidentified the crucial
assumption in the Monty Hall problem, and his own Monty Fall
problem is logically equivalent to the original Monty Hall problem.
I then present the Monty Fall* case where the probabilities
for which door to pick post tease reveal are actually 50/50 using
nothing more than Bayes’ Theorem and the standard rules of
probability to prove the results—no proportionality principle
is needed. The classic solution prevails as explanatorily more
powerful. Finally, I show that Monty Crawl is also better explained
and solved with the classic solution rather than with
Rosenthal’s proportionality principle
