Robert J. Marks: Pigeons can solve the Monty Hall problem. But can you?

The dilemma pits human folk intuition against actual probability theory, with surprising results:

Let’s Make a Deal was a television game show first hosted by Monty Hall (1921–2017) in 1963. There have been various remakes since then. The basic idea is that there are three doors and a contestant’s job is to barter with Monty for the most valuable prize behind the doors. The Monty Hall problem, loosely based on the quiz show, was popularized by Marilyn vos Savant (pictured) in her Parade Magazine column, “Ask Marilyn,” in 1990. A reader wrote to ask:

“Suppose 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 pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, ‘Do you want to pick door No. 2?’ Is it to your advantage to switch your choice of doors?” Marilyn Vos Savant, “Game Show Problem” at Parade

Vos Savant, reputed at the time to have the world’s highest IQ, said yes—switching doors improved the chance of winning. Untutored intuition on the other hand often says it doesn’t matter—you have a 50–50 chance no matter what.

Robert J. Marks, “Pigeons can solve the Monty Hall problem. But can you?” at Mind Matters News

Vos Savant is right and untutored intuition is wrong. Marks explains why at the link.

But the howler is that pigeons tended to get this right more easily than humans – at least in one study. (Another study found that it depended on the humans’ age.)

The problem isn’t likely that pigeons are smarter than us. Rather, precisely because we have intellects, we have folk ideas about how the world works that are sometimes wrong. The pigeon just wants bread crusts and has no theories about it. So he learns some things quicker.

Note: Yes, it’s that Robert J. Marks, from the Evolutionary Informatics Lab.

5 Replies to “Robert J. Marks: Pigeons can solve the Monty Hall problem. But can you?”

1. 1
Viola Lee says:

I used to give students this problem when we studied probability. After some discussion, I then had them write an explanation of their understanding of the answer to the problem. It was a good exercise in both thinking and written explanation.

2. 2
ET says:

Viola Lee- You should have demonstrated the problem by having your students conduct an experiment with say 100 iterations. One Ivy League school did that and came out with over 70%, instead of the predicted 66.666%.

3. 3
Viola Lee says:

I didn’t have enough students to do that, but we set up a simple spreadsheet and simulated the situation to run thousands of times, which confirmed the 2/3 probability of success when switching. My guess is that with just a 100 iterations even the spreadsheet would show a small deviation from 2/3.

4. 4
ET says:

All you need is one student. Then you play it out 100 times. Then you can do that for 100 days.

5. 5
Viola Lee says:

True, I could have done that.