We're all awesome negotiators, right? That's what we do for a living and we're really good at it - we can easily spot the advantage in a transaction. Right? Are you sure about that?
Well, let's take our brains out for a little exercise and give those negotiation neurons something to chew on.
We probably all remember Let's Make A Deal with Monty Hall, but let's take a brief refresher:
There are three doors, marked Door #1, Door #2, and Door #3. Behind one of those doors is something fabulous - maybe a new Ferrari - and behind the other two are something you could easily live without - let's make it a case of spam.
So, Monty asks you to choose a door. Go ahead and pick one. Okay, you can safely assume you now have a 1 in 3 chance of having picked the door with the Ferrari. No argument so far.
Now Monty decides to mess with you a bit. He opens one of the other two doors and shows you a case of spam (and remember that Monty already knew what is behind each door). And then he asks you if you'd like to trade the door you already have for the other remaining door.
What do you do?
You're probably thinking that it doesn't matter whether you trade or not - that you have a 50% chance of being right. You might have some feelings about first guesses or luck, but underneath, you think that the choice boils down to picking one of two doors, and you're just as likely either way to drive away in a new Ferrari. So you keep your door or trade - it doesn't make any difference statistically.
You would be wrong. In fact, you will double your odds of winning if you accept Monty's offer to trade.
That doesn't make sense, does it? You don't believe me. But I wouldn't lie to you about this. And I'm happy to try and explain it - but you're still not going to be comfortable with it.
- When Monty offered you the original choice, the door you chose had a 1 in 3 chance of being the right door.
- That means that the other two doors, combined, had a 2 in 3 chance of being the right door - double the odds that you got.
- One of those two had to have a case of spam, and Monty knew which one it was, so he showed you that one.
Try it this way - what if Monty offered to trade you the other two doors (66%) for your door (33%). You'd take that in a NY minute. But, in statistical terms, that's exactly what he did - you already knew that one of them had to have a case of spam - Monty showing you which one doesn't really change anything - the 66% chance now resides in that other door. If you take his trade, you're twice as likely to win.
This is so counter-intuitive that you're probably getting mad at me, but I'm just the messenger here. This scenario has been extensively tested in simulations - the people who traded won twice as often as those who stuck with their original choice. You can check this out - it's all over the internet - just Google "Monty Hall door problem". And hey!, if it's on the internet, it has to be true, right?
Now, about that counterproposal you submitted.......
Mary & Dick Greenberg