Let’s say you’re on Monte Hall’s “Let’s Make a Deal” gameshow. You get to pick a hidden prize behind door number one, door number two, or door number three. The trick is that two of the doors hide donkeys, and only one door hides the Maserati.
You pick door number one.
The host, in the countdown to your choice, shows you that door number three hides a donkey, and you gasp in relief. Aren’t you glad you didn’t pick that door?
Now Monte puts his arm around you in a confidential manner, and asks if you want to change your choice. Are you going to stick with door number one, or switch to door number two?
This is the question the Husband posed to me on our Date Night, and I said what many people say: “I’ll stick with my choice.” I figured I had a 50-50 chance of winning.
But the simple mathematical fact is that I’m more likely to win the car if I switch.
I had no idea people had been arguing about this for years. I can remember reading The Parade, which came as an insert in The Commercial Appeal, which was the newspaper my family subscribed to as I was growing up in Memphis, Tennessee. I mostly pulled out and read The Parade to catch up on the latest gossip about movie stars, but there was and still is a column called “Ask Marilyn,” where super-smart Marilyn vos Savant (who was in the Guinness Book of World Records as the person with the highest recorded IQ — 228) employed her exceedingly sturdy gray matter to solve problems that readers sent in.
And in September of 1990 her counsel in the 3-door situation was to switch your choice in order to increase your odds of winning. She received an estimated 10,000 letters from people telling her she was mistaken. But she wasn’t!
The Husband is a major math geek, and he’s reading a book called The Drunkard’s Walk: How Randomness Rules Our Lives, where he came across the “Let’s Make a Deal” scenario. After he told me about Marilyn and the switch, I picked up the book myself and devoured the third chapter where the explanation occurs.
And basically I failed to take into consideration the game show host. You see, Monte knows the answer. He’s not going to reveal the car, he’s going to show you a donkey. And thus he changes the odds for you.
At first you had a 1 in 3 chance of guessing right off where the car was. IF you were lucky and the car really IS behind door number one, you’ll obviously win if you stick, and the odds for that are 1 in 3. But if you guessed wrong and the car is behind door number two, you’ll win if you switch, and the odds for that are 2 in 3. That’s better odds, isn’t it? The strategy of switching is on average twice as successful as staying with the original choice.
I know, it’s confusing, and it took me a few times to get it, but once I did, I was pumped! You can play it out here and see for yourself how it works.
So. What the hell am I going to do with this miniscule tidbit of super-kewl information? I am going to be the megastar of the next party I go to, I’m telling you. Math nerds are red hot.
Um, aren’t they?
Image credit: Wikipedia
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