A predictor with a long record has already filled the boxes and gone. Box A is transparent and holds a thousand. Box B holds a million if it thought you would take only B, and nothing if it thought you would take both. Two arguments settle this, both valid, and they disagree.
Take one box. Work out the expectation. If the predictor is right ninety-nine times in a hundred, one-boxing averages nine hundred and ninety thousand. Two-boxing averages eleven thousand. This is not a theory about what would happen. One-boxers walk out rich and you can watch them do it below.
Take both boxes. The money is already in the room. The predictor left before you arrived and nothing you do now can reach into a sealed box and change what is inside it. If B holds a million, taking A as well gets you a million and a thousand. If B is empty, taking A gets you a thousand instead of nothing. Two-boxing wins in every possible state of the world, which is about as solid as decision theory gets.
Nozick's observation, when he published this in 1969, was that almost everybody finds one of these obviously right, and that people divide roughly evenly on which.
This is not really about boxes. It is the cleanest case where two theories of rational choice give different answers, and it forced them apart into named positions.
Evidential decision theory says pick the action that is the best news about your outcome. Learning that you took one box is excellent news, so take one box. Causal decision theory says pick the action that causes the best outcome. Your choice causes nothing about a box that was sealed yesterday, so take both.
Causal decision theory is the mainstream position, and it earned that by winning elsewhere. The standard case against evidential reasoning is the smoking lesion: if a gene caused both smoking and cancer, and smoking itself were harmless, evidential decision theory would tell you not to smoke, because smoking is evidence of the gene. That is plainly the wrong advice. So causal decision theory is the sensible view, and it says take both boxes, and the people who take both boxes reliably leave with a thousand dollars.
One-boxers ask: if you are so rational, why are you not rich?
Two-boxers answer that the scenario rewards a disposition rather than a choice. A demon who hands a million to anyone who believes two and two make five does not thereby make that belief rational.
Rationality would recommend becoming the kind of agent who then acts irrationally. Something has gone wrong.
That reply is strong but not clean, because you can commit to one-boxing in advance and a good predictor will read the commitment. So the advice is to make yourself into a one-boxer and then, at the moment of choice, do the thing you have decided in advance is the wrong thing to do.
Functional decision theory, developed largely in AI alignment work rather than academic philosophy, argues you are not choosing an action but the output of a decision procedure, and the predictor is running that same procedure. Your decision logically fixes the prediction without causally influencing it, which gets one-boxing without abandoning causation. Academic philosophy has largely not adopted it, so treat it as a live minority position rather than a settled repair.
Lewis (1979) argued that a prisoner's dilemma against someone relevantly like you just is a Newcomb problem: your choice is correlated with theirs by the same sort of mechanism, causal decision theory says defect, and both of you end up worse off. So this is not a curiosity about a strange predictor. It is the general structure behind cooperation among agents who can model one another, which is most of what the rest of this site is about.
A decision problem is not a game, and there is no population here evolving towards anything. What runs above is a tournament: the two policies played against the same predictor many times, with the accounts kept. It can show you that one-boxers end up richer. It cannot tell you whether that makes one-boxing rational, which is the entire dispute.