Last night, in the middle of hosting a fairly lively party, someone asked me about the Monty Hall problem. I know this sounds like I’m making it up for the sake of this post, but I promise it’s true. My friend, Kailyn, had recently heard about it and someone tried to explain it to her unsuccessfully. So I guess it was my turn to take a shot.

I started with the usual explanations used to provide some intuition. But it quickly became apparent that was not going to work. So I had her play out a variation on the game. Instead of three “doors”, I made ten. I brought in another friend, Theresa, to pick a winning door and whisper it to me. Theresa picked door #7. Then Kailyn picked a door (#6). I “opened” eight of the doors: 1,2,3,4,5,8,9, and 10. Then I asked her if she wanted to stick with door #6 or switch. At this point Kailyn still felt that the probabilities were the same for either door. Time to try something else.

This is where it got kind of interesting. I decided to reverse Kailyn and Theresa’s roles. Kailyn would pick the door that would have the prize and watch Theresa play the game. I went through the exact same steps for Theresa, and when I got down to two doors, Theresa also said that the probabilities for each seemed to be the same. But now Kailyn stepped in to dispute that! By watching the game play out, but not being at the center of it, she got a sort of “birds eye” view of the situation and had her ah-ha moment.