Let's play a game. Two times, I will give you an amnesia drug and let you enter a room with two boxes inside. Because of the drug, you won't know whether this is the first time you've entered the room. On the first time, both boxes will be empty. On the second time, box A contains $1000, and Box B contains $1,000,000 iff this is the second time and you took only box B the first time. You're in the room, do take both boxes or only box B?
This is equivalent to Newcomb's Problem in the sense that any strategy does equally well on both, where by "strategy" I mean a mapping from info to (probability distributions over) actions.
I suspect that any problem with Omega can be transformed into an equivalent problem with amnesia instead of Omega.
Does CDT return the winning answer in such transformed problems?