The Observation Deck

Monty Hall, who was the long-time host and one of the creators of TV’s Let’s Make a Deal, died a couple days ago. Us kids watched the show routinely back in the day. You probably did too, or maybe the reruns on Nick or wherever they are.

I’m something of a mathematician but I’m still kind of intrigued by what is known as the Monty Hall Problem. I first encountered it decades ago.

Let’s say there are three doors: #1, #2 and #3. And you are told there is a new car behind one of the three doors, and a goat behind each of the other two. You can pick any of the three doors. Let’s say you pick Door #1. But before revealing what’s behind Door #1, Monty would show you what’s behind another door, say Door #3, and there is one of the goats. Of course Monty knows where the car is.

He then offers you the chance to change your mind, to pick Door #2 instead of Door #1. Should you?

Prepare to be surprised….

And the answer is, yes you should switch your choice from Door #1 to Door #2. Why?

When you first picked Door #1, you obviously had a 1/3rd chance of being correct. No disputing that. We also know that (1) Monty knows where the car is, and (2) that it’s for sure NOT behind two doors at once. So he can always reveal a door (and not the door you picked) behind which there is not a car, and he always does. So in this instance, that we now know the car is not behind Door #3 does not increase the odds that the car is behind Door #1, because we know how Monty operates. The odds are still one in three that the car is behind Door #1. But it DOES increase the odds that the car is behind Door #2, because we now know that it’s not behind Door #3. So the probability that the car is behind Door #2 is now 2/3. So clearly you should switch.

But practically nobody ever did on the show. And when some bright minds (including mine) were first presented the Monty Hall Problem, the initial inclination was that knowing the car was not behind Door #3, that then made it a 50/50 proposition, making it pointless to switch. Wrong….

And the best part is, if you understand the Monty Hall Problem, and if you pick the right door the first time, you will lose. You will switch from the door with a car to a door with a goat.

So RIP Monty Hall. You have an intriguing “problem” (some call it a paradox) named after you. And you hosted a terrific show. And lived to be 96….

(If somebody reads this who's an admin could you please put "SOLVED" in the thread title? Thanks.)