A remarkably accurate predictor has already guessed what you will choose. Now two boxes wait on the table.
One box is clear and holds $1,000. The other is opaque. It contains either $1,000,000 or nothing, depending on the predictor’s earlier guess: if it expected you to take only that box, it filled it; if it expected you to take both, it left it empty. You may take one box or both.
Taking both always adds the visible $1,000, whatever is inside the opaque box. That makes two boxes look like the safer choice. But because the predictor is reliable, people who take only the opaque box tend to find the million there. One rule of choice says take both; another points toward one. Philosophers disagree about which kind of reasoning rationality demands.