Here's the Best Explanation of the Monty Hall Problem Yet

The Monty Hall Problem is a fantastic probability brain teaser based on the American television game show Let's Make a Deal—and this video is the best explanation of it you're likely to find.


The problem is simple. 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 choose one door—say, number 1—and the host (who knows what's behind the doors) opens another door—say number 3—which has a goat behind it. You're then allowed to stick with the door you picked, or choose the other one—number 2 in the example.

The question is: should you switch your choice? The answer is simultaneously blindingly simple and fiendishly counterintuitive. But the above video might be your best chance yet at wrapping your head around it. [YouTube]



I am certainly no mathematician, as I am about to demonstrate, but wouldn't the math for this be: the initial three doors each have a 33.3% chance of being the winner. One door is then eliminated, leaving two doors that could be winners. Wouldn't the odds then become 50/50? How does the fact that the contestant expressed faith in one of the doors previously somehow convey less chance for winning? Isn't that all just an arbitrary arrangement?