Newcomb's Paradox

Here's a fine way to melt your neural connections. Consider the following:

There are two boxes, A and B. Box A contains $1000, whereas Box B contains either $1,000,000 or absolutely nothing. You may choose to take Box A, Box B, or both, and keep any money inside. At first, your decision is simple: take both. Can't hurt.

But here's the catch:

A wise creature (Olivia the Owl) has been known to predict the future with 99.9% accuracy. You have performed many trials to establish this fact: you have had Olivia predict what you will eat for breakfast tomorrow, whether your child will be male or female, whether the stock market will rise or depreciate, whether or not you'll get that promotion, and even what color underwear you will wear in precisely a year from now - and we have established that Olivia the Owl has excellent predictive power. (For the sake of argument, its possible for Olivia to be wrong in her predictions. Out of the one thousand trials that you conducted, she failed once.)

One hour before you make your decision, Olivia the Owl gets to decide whether Box B will contain one million dollars or, instead, the proverbial sack of coal. She tells you: "If I predict that in the future you will pick only Box B, then, right now, one hour before you make your decision, I will place the full $1,000,000 into Box B. If, however, I predict that in the future you will take both Box A and Box B, then, right now, one hour before you actually make your decision, I will leave absolutely nothing in Box B."

So: what should you do?