Newcomb's Problem

Because the agent's decision in this problem can't causally affect Omega's prediction (which happened in the past), Causal Decision Theory two-boxes. One-boxing is correlated with getting a million dollars, whereas two-boxing is correlated with getting only $1000; therefore, Evidential Decision Theory one-boxes. Functional Decision Theory (FDT) also one-boxes, but for a completely different reason: FDT reasons that Omega must have had a model of the agent's decision procedure in order to make the prediction. Therefore, your decision procedure is run not only by you, but also (in the past) by Omega; whatever you decide, Omega's model must have decided the same. Either both you and Omega's model two-box, or both you and Omega's model one-box; of these two options, the latter is preferable, so FDT one-boxes.

Applied to Newcomb's Lottery Problem by Heighn at 5mo

One line of reasoning about the problem says that because Omega has already left, the boxes are set and you can't change them. And if you look at the payoff matrix, you'll see that whatever decision Omega has already made, you get $1000 more for taking both boxes. This makes taking two boxes ("two-boxing") a dominant strategy and therefore the correct choice. Agents who reason this way do not make very much money playing this game. This is because this line of reasoning ignores the connection between the agent and Omega's prediction: two-boxing only makes $1000 more than one-boxing if Omega's prediction is the same in both cases, while the problem states Omega is extremely accurate in its predictions. Switching from one-boxing to two-boxing doesn't give the agent a $1000 more, it results in a loss of $999,000.

Applied to Anti-Parfit's Hitchhiker by k64 at 6mo
Applied to "Rational Agents Win" by Yoav Ravid at 9mo