==> decision/newcomb.s <== This is "Newcomb's Paradox". You are presented with two boxes: one certainly contains \$1000 and the other might contain \$1 million. You can either take one box or both. You cannot change what is in the boxes. Therefore, to maximize your gain you should take both boxes. However, it might be argued that you can change the probability that the \$1 million is there. Since there is no way to change whether the million is in the box or not, what does it mean that you can change the probability that the million is in the box? It means that your choice is correlated with the state of the box. Events which proceed from a common cause are correlated. My mental states lead to my choice and, very probably, to the state of the box. Therefore my choice and the state of the box are highly correlated. In this sense, my choice changes the "probability" that the money is in the box. However, since your choice cannot change the state of the box, this correlation is irrelevant. The following argument might be made: your expected gain if you take both boxes is (nearly) \$1000, whereas your expected gain if you take one box is (nearly) \$1 million, therefore you should take one box. However, this argument is fallacious. In order to compute the expected gain, one would use the formulas: E(take one) = \$0 * P(predict take both | take one) + \$1,000,000 * P(predict take one | take one) E(take both) = \$1,000 * P(predict take both | take both) + \$1,001,000 * P(predict take one | take both) While you are given that P(do X | predict X) is high, it is not given that P(predict X | do X) is high. Indeed, specifying that P(predict X | do X) is high would be equivalent to specifying that the being could use magic (or reverse causality) to fill the boxes. Therefore, the expected gain from either action cannot be determined from the information given.