The Game

The game has the following form. You will be presented with two boxes:

Box A will contain $10,000.
Box B will contain $1,000,000 or nothing.
You will not be able to see inside the boxes, so you won't know whether Box B contains $1,000,000 or nothing. You will then be given the choice between taking home both boxes or just Box B.

There are two crucial things to take into account when making your decision.

The amount of money in Box B will be determined by Perfect Predictions’s most accurate clairvoyant - approaching 100% accurate – on the following basis. If she predicts that you will take home both boxes, then no money will be put into Box B. If she predicts that you will take home only Box B, then $1,000,000 will be placed into the box.
The prediction will already have been made by the time the game starts, and the amount of money in Box B already fixed.

Assuming you want to win as much money as possible, should you take home both boxes or just Box B?