At this moment, I agree with Psychohistorian that the apparent conundrum is a result of forcing a distinction about causality when there really isn't one.

On the one hand, we say that the contents of the boxes are not directly, causally related to our choice to one box or two box. (We assert this, I suppose, because of the separation in time between the events, where the boxes are filled before we make our choice.)

On the other hand, we say that Omega can predict with great accuracy what we choose. This implies two things: our decision algorithm for making the choice is pre-written and deterministic, and Omega has access to our decision making algorithm.

Omega bases the contents of the box on the output of our decision making algorithm (that he simulates at time (t-y)) so the contents of the box are directly, causally related to the output of our decision algorithm.

Seems wrong to say that the contents of the box are not causally related to the output of our decision algorithm at time t (i.e., our choice), but are causally related to the output of the decision algorithm at time (t-y) -- even though the decision algorithm is deterministic and hasn't changed.

In a deterministic system in which information isn't lost as time progresses, then the time separation between events (positive or negative) makes no difference to the causality ... "a causes b" if b depends on a (even if b happens before a). For example, afternoon rain will cause me to bring my umbrella in the morning, in an information-complete system.

Later edit: This represents the location in {comment space}-time where (I think) I've understood the solution to Newcomb's problem, in the context of the substantial clues found here on LW. I had another comment in this thread explaining my solution that I've deleted. I don't want to distract from Anna's sequence (and I predict the usual philosophical differences) but I've kept my deleted comment in case there are more substantial differences.

I would say that the ambiguity/double think about causality is actually the feature of Newcomb's problem that helps us reduce what causality is.