Game Show Mechanics: Why It’s Better To Change Your Mind Often Than Stick To A Plan

When you were growing up, did you ever get this advice?

You hear it when you’re a kid and thinking about quitting the baseball team. You hear it when you’re an adult trying to pick a career. Even presidents and heads of state use it to determine the course for whole countries full of people.

It’s classic leadership advice. It’s also completely wrong. At least, according to, well, math.

I shouldn’t be so harsh; it’s at least half-right: getting what you want from life does often take hard work. But the idea that making a decision and sticking to it is the way to prosperity isn’t just misinformed, it’s dead wrong.

And it can all be explained with a simple, real-life example—from a game show no less. Follow along to see how you fare.

Game Show Challenge: Which Door Should You Pick?

You’re on a game show and are faced with the classic dilemma:

The host asks you, “Which door has the yacht behind it?”

You have no idea—you’re going to make a random guess with 33% odds—but you squint your eyes and pretend like you’re channeling your x-ray vision. You pick Door #1.

Now, the host waves his hand, and one of the doors you didn’t choose opens. It’s a jar of pickles. Hooray, you haven’t lost yet!

The host asks, “Do you want to change your mind?”

You think for a moment and remember back to your childhood when you told your dad you wanted to quit the baseball team and do gymnastics. He was opposed to it, but didn’t want to be overbearing. So, he gave you that talk about sticking to the decisions you make and left it up to you. Oh, and if you quit baseball, you couldn’t have ice cream for a month. You stayed on the team.

Now the host is snapping his fingers at you and pointing at his watch. He needs a decision and your little flashback has put you 5 seconds into the commercial break. You panic and shout out, “I love ice cream! I’m sticking with Door #1!”

How Changing Your Mind Improves Your Odds Of Success

Was that the right move?

You might think it makes no difference. Your odds are at least better now: 50/50, right? Wrong!

You made a random choice with 33% odds of winning. Revealing one of the losing doors changes nothing about that. Unless you strike dumb luck, you’re going home with a jar of pickles.

But here’s what you might not have realized (and will probably argue about in the comments):

Had you changed your decision and switched to the other door, you would have doubled your odds of winning to 67%. You’d almost certainly be sailing the Mediterranean with a crew of sexy celebrities.

How is this possible? Isn’t your choice still random? A 50/50 toss-up? No, it isn’t.

Had you walked in to the game show late and the host had already eliminated a door you never saw to squeeze in an extra Metamucil commercial, you would be making a 50/50 guess. But, because you got to see one of three choices removed, you’re now privy to new information you didn’t have when you made your first choice. And that information changes everything. Well, not everything, but it does raise your odds of winning.

The reason for this is because the remaining door—the one you didn’t pick—isn’t random anymore. Instead, it’s the “winner” of a round of elimination.

This is easier to understand when the game gets bigger. What if, instead of three doors, there were 100? 99 jars of generic pickles! You make your choice, and you have a 1 in 100 chance of getting it right. Now, 98 of those doors—the ones with pickles behind them—are opened, and you’re left with two doors again.

Would you still stick with your first pick—the one with a 1% chance of winning? Or would you pick the other one—the one that just beat out 97 other doors and is still standing? The choice becomes more obvious.

New Information Should Change Your Decisions

Whatever it is you might be working on—figuring out what direction to take your career, where to go on vacation, or what house to buy—new information that comes along in the process should change the decisions you make.

The first decision opens the door to new discovery, and the new things you discover can and often will completely change what the best decision to make is. Don’t discard valuable information just to stick to your guns.

That’s not what Smart Riskologists do, and neither should you. If you want to quit the baseball team, we’ll all support you. Even if Dad says you can’t have ice cream for a month.

Additional Sources:
Bayesian Probability
Understanding The Monty Hall Problem
The game show example is adapted from the popular television show, Let’s Make A Deal, where the prize is a car and the consolations are goats.