Saturday, March 7, 2026

"What the Monty Hall Problem Reveals About Human Judgment"

From Harvard Business School's Working Knowledge, February 24:

This excerpt was adapted from the book Revealing: The Underrated Power of Oversharing, written by Leslie John. Penguin Random House, February 2026.

Pretend you’re attending the famous game show Let’s Make a Deal, which started airing in 1963.

In the show, various audience members dressed in attention-grabbing “pick me!” costumes are invited to make trades with the host, the charming and perennially well-tanned Monty Hall. (Fun fact: He’s Canadian, like me! Another fun fact: We Canadians like to point out who is Canadian!)

Imagine Monty invites you to stand and shows you three doors onstage: Door 1, Door 2, and Door 3. Behind one of the doors is a prize: something “fabulous,” Monty intones, like a “braaaaaand new car!” Behind the other two doors? Zonks, which are dud prizes, such as trips to nonexistent destinations, play money, broken appliances, ridiculously large amounts of food, and live animals—yes, most commonly, goats.

And the thing is, even when people are told the math—or intellectually grasp that switching gives them a better chance of winning the prize—they often still resist switching.

Monty asks you to choose a door. You choose Door 1. Next, Monty opens one of the doors you didn’t pick, Door 3. A dramatically ominous tune sounds out, one so ingrained in my and my brother’s memory that we still intone it when something disappointing happens and we’re trying to make light of it. Behind the door is a Zonk—round-trip tickets to Zonklandia. Now, before Monty opens your chosen door, Door 1, which you hope hides a car, he wants to know: Would you like to switch to Door 2 (which remains closed)?

If you’re like most people, you choose not to switch. You stick to your guns with Door 1. It feels right. But is this a good strategy? Will it maximize your chance of winning the prize? The answer is a resounding no. You should always switch. If this is not intuitive to you, you are not alone. But the bottom line is that staying only wins on the occasions where you happened to choose the winning door from the start.

The trick is that Monty knows where the car is, and before he asks you whether you want to switch, he always opens a goat door. That means he’s actually helping you, by taking a dud door out of the running. Think of it this way: When you first pick, there’s a 1-in-3 chance you choose the car and a 2-in-3 chance you don’t. So, most of the time, your first pick is wrong. Monty then shows you which of the other two doors is a goat, leaving the other door unopened.

If you switch, you’re betting that your first pick was wrong (which it usually is). And so, chances are, switching is a winning move. If you stay, you only win in the 1 out of 3 times you guessed right at the start. But if you switch, you win on 2 out of 3 occasions. Switching doubles your odds of winning.

The Monty Hall problem has been studied a lot (ad nauseam?) in behavioral science. And the thing is, even when people are told the math—or intellectually grasp that switching gives them a better chance of winning the prize—they often still resist switching. I myself might even insist on staying. But staying is illogical—you’re giving up a free chance to double your odds. And yet, many of us think, “Whatever, I’m sticking with my door.” Totally fair. Because there’s a deeply compelling psycho-logic to staying.

Switching, only to discover you were right in the first place, really sucks. “If I’d only just stuck with my gut!” you chide yourself. By contrast, losing the other way—by failing to switch to a winning door (when you chose a losing door in the first place) doesn’t feel nearly as bad. This is weird in a way, because in both cases, the “objective outcome” is the same: You don’t win the car. And yet one hurts much more than the other. What’s going on?....

....MUCH MORE