Today’s entry on Jeff Atwood’s weblog, “Coding Horror” talks about the time-honored probability puzzler known as the Monty Hall problem. If you are unfamiliar with the problem, it deals with devising the optimal strategy for playing a game that was common on the game show “Let’s Make a Deal“, starring Monty Hall, and has a solution that is commonly perceived as unintuitive.

Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice? (Whitaker 1990)

This, much like airplane on a treadmill, and 0.999… == 1 are common topics of long, drawn-out arguments on the Internet. But what I want to talk about is not the problem itself (which has been done to death), or Jeff’s post. Rather, I want to discuss a variant problem humorously called the “Monty Fall Problem” proposed by Professor Jeffrey S. Rosenthal of the University of Toronto, which is included in an article titled “Monty Hall, Monty Fall, Monty Crawl”, which was linked from the Coding Horror article.