So what would you do?

OK, here's a groovy maths problem I just came across:

I have three identical boxes and I tell you there is a diamond in one of them. You don't know which one it is because the boxes are sealed, but I tell you to pick just one box, and if it contains the diamond, you can keep it.

So you pick a box, but before you open it I tell you I'm going to open one of the other boxes. So I open one of the other boxes. It's empty, and I discard it.

That leaves two boxes. You have one, and I have one. One has a diamond inside, and one is empty. You don't know which is which, but I do. I ask you if you want to swap.

The question is, should you swap with me, or stick with the box you have?

There are no tricks or hidden meanings in the question. It's just a simple statistics and probabilities question. Answer at the bottom.

Today nothing happened in the news. Well that's not quite true. They arrested someone in connection with the murder of Milly Dowler. I don't think he'll turn out t be the murderer though. I think he had something to do with disposing of the murderer's car. But nothing else happened.

Our new mattress arrived today. The old one is probably 10 years old, and it really isn't much good any more. Plus, I've always felt odd about sleeping on it because it was used by our tenants when we let the house out. Anyway, we went to the Dreams store because they were having a half price sale. Mattresses are stupid expensive. Even half price ones were £800 or more. But the dragon went and bounced on a few before deciding she liked a cheap one. And it wasn't because it was cheap, she wasn't looking at the prices. So we ended up paying £200, which is still a lot I suppose, but much cheaper than £800.

OK, the answer to the question above:

You're twice as likely to win the diamond if you swap boxes. Think about it and I'll give you the theory next time. Goodnight.