The Monty Hall Dilemma and Opening Your Mind

Two of the things I love most about having been an option trader for the past 30 years is 1) I basically sit around and solve puzzles all day—which is kinda fun; and 2) I get to be around a bunch of smart people who also like to solve puzzles.

Enter: The world of Game Theory.

Game Theory

Game theory is a collection of, basically, thought models to get the thinker to arrive at the most logical solution. They are logic puzzles. Often there’s some math involved. And they are really fun games for people like me who like to solve problems.

One of my favorite game theory puzzles is called The Monty Hall Dilemma. I talked about it a bit in Episode 3 of the Wealth Building with Options Podcast. Now I’m going to expand upon it and share the answer and logic, and we’ll muse about why many people struggle with this one.

The Monty Hall Dilemma

It goes like this: Imagine you’re on a game show and there are three doors. The game show host, Monty Hall, explains that behind one of the doors, there is a brand-new car. Behind each of the other two doors there is a goat.

Then Monty asks you to choose a door. Now, of course, this is completely blind and random. Unless you have some sort of ESP, it doesn’t matter which door you choose. You have a 1 in 3 chance of winning the car. So… you choose one of the doors—hoping for the car and not a goat. Let’s say it’s door No. 1.

Game shows need drama. So, before revealing what’s behind door No. 1—the one you chose—Monty says something like, “Are you sure that’s the door you want to choose?”

You say, “Yes, Monty. I’m sure.”

Then he says, “Well, what if I show you what’s behind door No. 2?” Then he proceeds to open door No. 2 and guess what’s there? A goat.

The crowd oohs and aahs. You nervously smile and shake your head.

Then Monty says, “After seeing what’s behind door No. 2, one of the doors you didn’t pick, would you like to change your mind and pick a different door?”

Here’s where it gets interesting… and a little weird.

There is, in fact, a right answer. And it’s not super intuitive. In fact, I talked about this on the podcast.

A while ago. I was giving a free workshop to a traders group in the San Francisco Bay Area. And to be fair, they were a pretty smart group–though there were a good handful who thought they were smarter than they actually were. But, whatever.

And after I shared the answer there were a couple of people who wouldn’t accept the mathematically precise answer. They got a little over assertive and argumentative. So, yeah. I don’t talk about this in live workshops anymore.

But I can see why they didn’t get it. It’s, well, like I said, a little weird.

The correct answer is that you should switch from door No. 1, which you originally chose, and instead pick door No. 3.

What?! Wait! Why?

There are a couple of ways to look at it. But the simplest way is this:

When you first picked door No. 1, you had a 1 in 3 chance of the goat being behind that door. That means, logically, you’d have a 2 in 3 chance of the car being behind one of the other doors. The new information you gained, seeing that there’s a goat behind door No. 2, doesn’t change those odds.

If you switch doors, you would then have a 2 out of 3 chance of winning the car.

This is what’s called a veridical paradox, which means the answer is counter to most people’s natural intuition.

Professor Steve Selvin first posed and solved the dilemma back in 1975 in a letter to American Statistician. But it really gained notoriety in 1990 when a reader raised the question in a letter to Parade magazine. In her response, columnist Marilyn vos Savant said the contestant should switch doors. After the letter was published, the magazine received 10,000 letters from readers arguing Savant was wrong—and that included nearly 1,000 people with PhDs.

In fact, Paul Erdos, known as one of the most prolific mathematicians at the time, was unconvinced until he was shown a computer simulation proving Savant’s logic.

Opening Your Mind

Investors run into a lot of the same veridical problems in their trading activities.

“I didn’t lose money because I didn’t close the trade yet.”

“I lost money on my covered call because the stock rose through the strike price.”

“Covered calls are conservative, cash-secured puts are risky.”

And I could list a lot of trading concepts that run counter to intuition. But overcoming these mental obstacles is what can turn an investor from struggling to consistently winning.