a paradox is always the result of faulty assumptions.
the amount of time and space wasted on the discussion of newcomb's "paradox" is mind-boggling.
please to be defining your parameters completely.
of course, choosing the term "predictor", was the (intentional?) source of the confusion.
there is no such thing as an infallible "predictor" because inherent in the word prediction is the possibility of being incorrect. someone who knows what is going to happen, and truthfully states that, is not "predicting", they are simply stating a fact.
there is nothing in this problem to debate, and frankly it's rather sad that so many "intelligent" people think there is.