# Intuition

Many people tell you to trust your intuition. Is this a good idea?

Listen to this: Suppose you have a sack of potatoes that weighs 100 pounds (not including the sack, which you can forget about). Further suppose I tell you that those potatoes are 99% water.

Several days later, after some of the water has evaporated, I now tell you that the potatoes are 98% water. How much do the potatoes weigh now?

Go ahead and try to figure it out before you turn the page. And I promise you, it’s not a trick question.

Having trouble? Then just use your intuition and take a wild guess.

Now click here for the answer.

How well did your intuition serve you?

The math is pretty simple once it’s explained, and you might even have an "Aha!" moment.

Fun, no? Here’re a couple more.

Suppose you have a stack of nickels so high, it reaches to the very top of Mt. Everest.

How big a box would it take to hold all these nickels?

[Click here for the answer]

Suppose you live in a 3,500 square foot house. And all your ceilings are 8 feet high, which is about standard. Now let’s say you filled up your house with cardboard boxes shaped like cubes, a foot on each side.

A lot of boxes. How high do you figure they’d reach if you took them outside and stacked them on top of one another.

[Click here for the answer]

These are simple. But sometime it’s not so simple. Try to remain calm as you read the following:

You’re playing Let’s Make a Deal, and there are three big doors onstage. One of the doors has a Rolls Royce behind it. The other two are empty. Your job is to pick one of the doors. If the Rolls is behind it, it’s yours.

Simple game. But there’s one small variation.

You tell Monty Hall which door you plan to pick. He then opens up one of the doors you didn’t pick, and shows it to be empty.

Then Monty does an interesting thing: He offers you the option of changing your mind, and switching to the other unopened door instead.

What should you do?

Even though the studio audience is mindlessly screaming at you to do one thing or the other, if you’re reasonably intelligent, you realize that it doesn’t make any difference what you do. Your odds of picking the correct door were one out of three, now they’re one out of two, and that’s all there is to it. Changing your mind from one of the unopened doors to the other one couldn’t possibly make any difference.

That’s your intuition talking, see? And you should trust it, right?

Nope. The fact is — and I know you’re going to start yelling and screaming about this, so hang on a little — your odds of winning the Rolls double if you change your mind and open the door you didn’t pick originally.

Now you think I’m completely nuts. Any idiot can see that changing your mind doesn’t make any difference. Your intuition simply won’t let it go. My guess is, at this point, you’d even be willing to bet a substantial portion of your bank account against me. Maybe even your whole bank account.

You’d lose. That’s not an opinion, it’s a fact, and I’ll show you why soon. But what’s important right now is that your intuition would cost you an awful lot of money.

The answer to the question concerning whether you should trust your intuition is this: only trust your intuition if you have a solid enough background in the topic at hand to have developed an intuition worth trusting.

If you’ve been fixing cars successfully for twenty years and you hear a weird sound coming from the bowels of your ’56 Chevy BelAir, a sound you’ve never heard before but you are strongly convinced is a fluttering carburetor valve, you probably won’t go too far wrong ordering the part even before you’ve taken off the air filter to look at the thing.

But if you’ve never been to the track in your life and don’t know a fetlock from a sulky, then that really strong hunch you have about the prospects of Pookie’s Potato in the ninth at Aqueduct is probably worth about as much as your intuition was on the Let’s Make a Deal problem.

Zilch.

And that’s all I have to say on the subject.

Wait a minute. I have a hunch that you don’t still don’t believe me on the game show thing. I know I promised to explain it to you, but you know what? I have a hunch that you still won’t believe me!

So try this: Get a friend to help you simulate the Let’s Make a Deal scenario. You can use opaque envelopes, or cups turned upside down, instead of doors.

Your friend puts a prize slip in one of the three envelopes without your looking. Then you get to choose one of the envelopes. Then your friend opens one of the remaining two envelopes he knows is empty. At that point, you can stick with your original choice or change your mind to the one remaining envelope. Finally, write down whether you won or lost.

Play the game two hundred times. The first hundred times, never change your mind. The second hundred times, always change your mind.

You will discover that you won the prize about twice as often when you changed your mind than when you stuck to the first envelope you picked. If you thought about it real hard while you were playing, you might even discover that it is beginning to dawn on you why it works that way. (This is what Martin Gardner calls the "Aha!" moment.)

If you don’t feel like going through all those games, I’ve got a little program that will play them for you. It’s on my Website at http://LeeGruenfeld.com/Software/monty.htm [or click here to get there automatically if you're reading this on-line], and I promise it doesn’t contain a computer virus.

So now that you really do believe me, because you proved it to yourself, I’ll give you the technical explanation in the back of the book. [or click here]

But do yourself a favor and think real hard the next time you’re tempted to trust your intuition.