Ars Mathematica

I’ve just run across an interesting thought experiment known as Newcomb’s paradox. Suppose there is a being, called the Predictor, that presents you with a choice. There are two boxes. The first box may or may not contain $1,000,000. The second box always contains $1,000. You can choose to open either one box or both boxes. While you are making your choice, the Predictor does not touch the boxes in any way — whether or not the first box contains money is already determined.

Many people have encountered the Predictor before, and have discovered that he seems to always predict what you are going to do. Anyone who has ever chosen to open just the first box receives the $1,000,000. Any who has ever chosen to open both boxes finds the first box empty, and only receives $1,000.

Which would you choose?