Newcomb's Problem is the classical problem in decision theory.
An all-powerful computer (or psychic. It doesn't matter) who can perfectly (or near-perfectly) predict your decisions presents you with two boxes, A and B. It indicates that you may choose between two choices: to either take box B, or to take both boxes.
Box A is transparent, and you can see inside ten crisp hundred dollar bills, laid out for easy counting. Box B is opaque, and the Being tells you that it contains either one million dollars, nothing, depending on its prediction of your decision.
If the Being had predicted that you would only take box B, box B would contain the million dollars. But if the Being predicted that you would take both boxes, it would have put nothing in the box.
The second box lies there, and already has the million dollars in it, or not, and you can see the hundred dollars lying in box A. The Being has no way of changing the contents of any of the boxes.
Do you take one box, or two?
(Errata states that if you choose absolutely randomly (say, a perfect coin toss), box B contains nothing)
Casual decision theory (CDT) states that, as the Being cannot change the contents of boxes, it would always be better to take both boxes. CDT depends on causal relationships between the choice and the outcome, and, since there is no way that choosing which box(en) to take can affect the contents of the boxes, two-boxers will take both boxes. Causality.
Evidential decision theory (EDT), on the other hand, states that, as those who chose to take two boxes always walk away with a thousand, whereas those who chose to take one box always walk away with a million, it is better to take only one box. EDT states that one should choose the choice that has the best probability of giving the best outcome. Probabilities.
EDT wins in Newcomb's problem, however, that is not always the case. Decisions theory still has ways to go in finding a theory to obtain the most successful outcome in all scenarios.