The first time you enter the room, the boxes are both empty, so you can't ever get more than $1,000,000. But you're otherwise correct.
No, I can get $1001,000. If I randomly choose to take one box the first time, then both boxes will contain money the second time, where I might randomly choose to take both.
(Unless randomising devices are all somehow forced to come up with the same result both times)
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?
Discuss.