Demo guide: The Monty Hall problem

For this demo guide we’ll consider one of the most vexing case studies in all of statistics and analytics. The bad news is that it may confuse and frustrate.

The good news? It’s a game! So get ready… and come on down to this Excel demo of the infamous Monty Hall problem.

The Monty Hall Problem: Here’s the deal…

The basic scenario of this problem is as follows:

• You choose from three doors, each of which has a mystery prize behind it. Two doors contain goats; one, a car.
• You pick one of these doors.
• Monty Hall (your host) opens another door (i.e., one that you didn’t choose): it has a goat.

Now, Do you stick to the door you previously chose, or switch doors? Does it matter?

Let’s use Excel to simulate the problem several hundred times and find out whether “stick” or “stay” is a relatively better strategy. You can follow along with the video using the downloadable PDF below.

Download the PDF here.

So, what happened? (Spoilers!)

There many ways to interpret and explain this legendary problem, but one of my favorites comes a tutorial on the Numberphile YouTube channel (which you should subscribe to, by the way). I took the following illustration from that video.

The way I like to think about this is that when Monty opens that extra door and shows you a goat, he gave you additional information that changed your prior probabilities. You now know that a goat is behind a specific door. The equal one-thirds probability is not longer accurate; there’s now a two-thirds probability that the other goat is behind the third door.

The Monty Hall problem is especially beloved in Bayesian statistics, which is all about updating prior probabilities given new information. If you do any data analysis, it’s good to know a little Bayesianism. And on that note, you’re welcome to use this demo guide for educational purposes however you see fit at your school or organization.

For more on Bayesian thinking, check out Will Kurt’s Bayesian Statistics the Fun Way. You can get more demo guides and other materials at my resource library, available by subscribing below.

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