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Newcomb's problem presents a choice: take both boxes (getting $1,000 plus whatever a nearly perfect predictor placed in the opaque box) or take only the opaque box (getting $1,000,000 if the predictor predicted you would one-box, $0 if it predicted you would two-box). The predictor has been right 99% of the time with previous players. One-boxing gets you $1,000,000 almost certainly; two-boxing gets you $1,000 almost certainly (the predictor foresaw your greed and left the box empty). This simple setup reveals a deep split in decision theory: causal decision theory says to two-box (your choice cannot causally change what is already in the box), while evidential decision theory says to one-box (one-boxing is strong evidence that the box contains $1,000,000). The problem has no consensus solution and illuminates fundamental questions about the relationship between choice, causation, and rationality.
First understand both arguments fully — the two-boxing argument from causal reasoning and the one-boxing argument from expected payoffs. Then examine variants: what if the predictor is only 51% accurate? What if you can randomize? Each variant tests the boundaries of different decision theories. The value is not in solving the problem but in understanding what makes it hard.
From expected value decision-making, you know that rational choices should maximize probability-weighted outcomes. Newcomb's problem is the thought experiment that reveals a crack in this seemingly straightforward principle -- a case where two apparently valid forms of expected-value reasoning give opposite answers, and neither can be easily dismissed.
Here is the setup. A nearly perfect predictor -- right 99% of the time -- has placed money in two boxes. Box A is transparent and contains $1,000. Box B is opaque and contains either $1,000,000 or nothing, depending on what the predictor predicted you would do. If the predictor predicted you would take only Box B, it placed $1,000,000 inside. If it predicted you would take both boxes, it placed nothing. The boxes are sealed; the prediction is already made. You choose: take both boxes, or take only Box B?
The two-boxing argument is elegant. Whatever the predictor placed in Box B is already there -- your choice now cannot reach backward in time to change it. If Box B contains $1,000,000, taking both boxes gets you $1,001,000 (better than $1,000,000). If Box B contains $0, taking both boxes gets you $1,000 (better than $0). In every possible state of the world, taking both boxes gets you $1,000 more. This is called a dominant strategy, and it seems like the bedrock of rational choice. The one-boxing argument is equally compelling. The predictor is right 99% of the time. One-boxers almost always find $1,000,000 in Box B; two-boxers almost always find it empty. The expected value of one-boxing is roughly $990,000; the expected value of two-boxing is roughly $11,000. One-boxers walk away rich; two-boxers walk away with pocket change. How can a "rational" strategy reliably produce worse outcomes?
The problem has no consensus solution because the two arguments rely on different decision theories, and the problem is designed to pull them apart. Causal decision theory backs two-boxing; evidential decision theory backs one-boxing. What makes Newcomb's problem philosophically valuable is not that it needs to be "solved" but that it forces you to commit to a framework for what "acting rationally" means. Does rationality mean choosing the action with the best causal consequences from the point of decision? Or does it mean choosing the action most correlated with the best outcome? These usually agree, but Newcomb's problem is the knife-edge case where they diverge -- and your answer reveals which theory of rationality you implicitly hold.
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