This Old Tv Conundrum Will Help You Escape!
Well, it will two-thirds of the time.
Monty Hall was born on this day, the 25th of August, in 1921, and was famous for hosting the game show Let’s Make a Deal. While the show still airs in the US (currently hosted by Wayne Brady of Whose Line Is It Anyway?; who knew?), Hall has since become more famous for his eponymous probability problem, derived from the final round of the show.
Kind of strangely – for a mathematical conundrum – the Monty Hall problem comes with an interesting story and, would you believe it, has a lot to say about the best approach to solving puzzles. So, on what would have been the great host’s 98th birthday, let’s explore how the Monty Hall problem can help you solve that next escape room trip you’re planning.
But first: what is the Monty Hall problem?
After making a series of successful deals and trades, the contestant advances to the final round, in which they can win a swish new car! There’s one catch: Monty Hall presents the contestant with three doors; behind one is the car, and behind the other two are goats. Evidently, in the heyday of the show, a goat was considered a bad prize. I know millennials who would kill for a goat. I certainly would. Anyway, after the contestant selects a door, Hall opens one of the remaining two doors, always revealing a goat. And then, the crux of the problem: the contestant is offered the chance to swap their selection to the one remaining door.
So the problem goes like this: should you switch? Since one of the goat doors has been revealed, that means the car is either behind the door you selected, or behind the one neither you nor Hall picked. It’s one or the other – a 50% chance, right?
Not quite, and here’s the first lesson to be learned in puzzle solving: what seems like the only intuitive solution isn’t necessarily right. You actually have a 66.7% chance of winning the car if you switch (or a two-in-three chance). Let’s rewind. Since there’s no reason to suspect the car is behind any particular door, you have to choose between the three doors at random; that means you have a one-in-three chance of having selected the car. At this point, Hall – as per the rules of the game – must select a door with a goat behind it. If you selected the car initially, whichever door Hall does not choose will inevitably contain a goat. However, if you select either of the two goats, Hall will reveal the other, leaving the car as the door you did not choose. So in the two goat scenarios, you win the car by switching; in the one car scenario, switching means you lose. Two out of three.
Is your brain burning? Don’t feel bad if it is. I find it helps to imagine that you and Monty Hall are working together. You pick a door, and Hall gives you the chance to swap to the other two – but he then helps you by getting rid of an unhelpful door, giving you the best chance of winning.
So what about this controversy?
The Monty Hall problem became famous when Marilyn vos Savant, the person with the then-highest recorded IQ in the world, tackled it in a magazine column. Savant answered correctly, but could not have predicted the tidal wave of letters disagreeing and insisting on a 50% win rate. When Savant refused to back down, restating her working in a follow-up column, the story gained national traction and featured on the front page of the New York Times. Savant claims she received over 10,000 letters vehemently disagreeing. There are several respected academics who still, incorrectly, believe Savant was wrong – and, worse, believe that she used her position as a respected mind to mislead the public about mathematics.
Even ignoring for a moment that Savant was factually correct, it all seems a bit much for a probability problem. It’s worth noting too that Savant’s most prominent critics were older men, but the gender analysis can be for another time. To cut to the point: Savant would solve an escape room, and her critics would not, and that’s nothing to do with IQ or the ability to assess probability. Instead, it’s about tackling problems by being cautious and factual, not being too set in your ways, and being willing to look at puzzles from different angles.
Escape rooms are all about teamwork, and we’ve seen countless teams fail because a domineering personality has shut down someone else with the right idea. So, the next time you’re stuck in an escape room, listen to each other: maybe switch up your approach. It’ll work 66.7% of the time!