If Monty Hall Falls or Crawls

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