A colleague (Mike Betz, Content Manager) recently sent this email:
“You’re on “Let’s Make a Deal.” The host, Monty Hall, shows you 3 doors and tells you that there’s a car behind 1 door, goats behind the other 2. If you choose the door with the car behind it, you get to keep it. The car, not the door.Wikipedia explains the problem in depth.”
You choose door #2. Monty reveals that door #3 has a goat behind it. Then he asks, “Do you want to stay with door # 2, or switch to door #1?” What should you do?
You probably thought, “I had a 1 in 3 chance of choosing the car originally. I still have a 1 in 3 chance. There’s no benefit to switching.”
And you’d be wrong.
Counter-intuitively, you’d double your chances of winning by switching to door #1. The Monty Hall problem baffled statisticians for much of the ’90s, but the salient fact is this: Monty knows where the car is. So no matter which door you choose originally, Monty will always open a door with a goat behind it. Monty’s knowledge, and your awareness of Monty’s knowledge, affect both your odds of winning (i.e., statistics) and your ability to determine where the car really is (your perception of reality).
It struck me as interesting, partly because I too found it difficult to believe until I sat down with paper and pencil and worked it out, but mostly because it later occured to me that we sometimes run into this situation in UX design. We use a “commonly held belief” to convince ourselves that a feature or design element is desired by users – only to (hopefully) realize that – after thinking through the specific scenarios – they don’t want or need it after all.