Newcomb’s problem is a thought experiment where you’re presented with two boxes, and the option to take one or both. One box is transparent and always contains $1000. The second is a mystery box.
Before making the choice, a supercomputer (or team of psychologists, etc) predicted whether you would take one box or both. If it predicted you would take both, the mystery box is empty. If it predicted you’d take just the mystery box, then it contains $1,000,000. The predictor rarely makes mistakes.
This problem tends to split people 50-50 with each side thinking the answer is obvious.
An argument for two-boxing is that, once the prediction has been made, your choice no longer influences the outcome. The mystery box already has whatever it has, so there’s no reason to leave the $1000 sitting there.
An argument for one-boxing is that, statistically, one-boxers tend to walk away with more money than two-boxers. It’s unlikely that the computer guessed wrong, so rather than hoping that you can be the rare case where it did, you should assume that whatever you choose is what it predicted.
The point is to reveal the different frames of analysis people use to make the decision.
This thought process, “The decision’s already been made, either way it’s always a free $1000,” is one way of looking at it. But another way of looking at it is, “Those who choose one box tend to walk away with more money, so the evidence shows that taking one box is the better approach.” These approaches sort of “talk past each other,” because they’re looking at completely different parts of the problem in order to draw their conclusions, and those different parts indicate very opposing conclusions.