Being deterministic does NOT mean that you are predictable. Consider this deterministic algorithm, for something that has only two possible actions, X and Y.
Find out what action has been predicted.
If X has been predicted, do Y.
If Y has been predicted, do X.
This algorithm is deterministic, but not predictable. And by the way, human beings can implement this algorithm; try to tell someone everything he will do the next day, and I assure you that he will not do it (unless you pay him etc).
Also, Eliezer may be right that in theory, you can prove that the AI will not do X, and then it will think, “Now I know that I will decide not to do X. So I might as well make up my mind right now not to do X, rather than wasting time thinking about it, since I will end up not doing X in any case.” However, in practice this will not be possible because any particular action X will be possible to any intelligent being, given certain beliefs or circumstances (and this is not contrary to determinism, since evidence and circumstances come from outside), and as James admitted, the AI does not know the future. So it will not know for sure what it is going to do, even if it knows its own source code, but it will only know what is likely.