Wednesday, November 17, 2010

On thinking straight

This afternoon my thoughts turned to what is called the Monte Hall Problem (based on the "Let's Make a Deal" TV game show). It is a devilish little puzzle that reveals how inept most of us are at reasoning. Suppose you are a contestant and are presented with three closed doors. One hides a shiny new car, the other two conceal goats. Your hope is to pick the door with the car.

Let's say you picked Door #1. Monte, that sly dog, then opens Door #2, revealing a goat. He asks if you want to switch your choice to Door #3. (Hint: you really, really should switch.)

This perplexes people to no end. After all, our powerful intuition is that because the car is behind one of just two doors, the chances are 50-50. Switching your choice can make no difference: the odds are 1 in 2 in any case.

Wrong! If you stick with Door #1, you have a one-third chance of getting the car. If you switch to Door #3, you have a two-thirds chance - twice as good!

Here's why: At the start of the game, each door has a one-third chance of hiding the car. When you pick a door, the other two doors add up to a two-thirds chance.

It doesn't matter if Door #2 is then opened to reveal its goat. Your choice - Door #1 - still has the same one-third chance. And the other two doors still have a collective two-thirds chance. So Door #3 - the only other unopened door - has a two thirds chance of concealing the car. And you're a dummy if you don't switch.

What interested me about all this today was that when I started considering writing about it, I realized that I'd have to explain this reasoning. But my mind was blank! I knew about the puzzle. I knew the correct choice was to switch. So why couldn't I remember how come?

Well, I soon managed to figure it out again. (As they say, this isn't exactly rocket science.) But I think my initial blankness was caused by my compelling intuition, unabated by the facts, that the odds had to be 50-50. (Dammit, that is obvious!) I think somewhere up in my brain, my intuition muscled in, kicked my better knowledge into a mental closet, and took over like some schoolyard bully.

The lesson? It's hard to think straight!

1 comment:

  1. There was a great debate about this when the girl with the world's highest IQ (I forget her name) gave the correct answer. I'm still not sure I get it. I would have to factor in that if I would feel a lot worse if I switched and ended up with the goat. In taking standardized tests the advice was always to stick with your initial answer.