The Monty Hall problem is the classic puzzle that measures IQ rather than real intelligence. That's why I love it. I won't go into the standard explanation — there are decades of discussions about it. A simple outcome table shows that switching doors doubles your probability of winning.
However, as an empirical developer, I've always been puzzled not by the explanation itself, but by the fact that it assumes conditions that aren't obvious at all. This reminds me of the gap between academia and the real world.
The hidden conditions
The original analysis leading to door-switching as the optimal strategy assumes conditions never explicitly stated by the show. Monty will always open a door. He'll never open the one you chose. He'll never open the one with the prize. The prize could be behind any door. And Monty will always choose randomly.
Monty never said he'd follow these rules. Yet we take them for granted because we have the luxury of doing so. In tests and research, theorems can be applied only when all conditions are well-defined. In real life, we must decide without that luxury.
The Trojan horse
My goal isn't to prove that switching doors is always wrong. I want to go further: to use the problem as a Trojan horse for thinking about how distant these puzzles are from the real world, and how many unproven assumptions we sometimes employ to apply seemingly bulletproof formulas.
We humans are full of biases, so pure statistics usually wins. But biases evolved as survival heuristics. In a similar situation on the street, with no certainty about the premises — and therefore no exact application of Bayes' theorem — are we sure the "high IQ" solution is correct and not the worst illusion of control imaginable?
IQ versus real intelligence
A brilliant paragraph from the in-depth analysis sums it all up: "Monty Hall is not a random event. He is not a coin to be tossed or a die to be thrown; he is a rational being with free will and certain objectives to achieve. Because a primary objective is to entertain, his choices will not be random in the way that simple probability theory assumes."
This is the gap between IQ and real intelligence. High IQ tells you to switch doors. High real-world intelligence tells you that Monty is a showman who needs to entertain, so all theoretical analyses clash with this fact. The empirically intelligent person will reason on other dimensions: "What kind of night is Monty having? Are we running over time, or is there still room for his games?"
