I don't agree to leave Newcomb aside in considering this, because my position is that they are the same problem.
If they are the same problem, you shouldn't care about leaving one aside. The smoking lesion is a simpler and clearer problem because it doesn't need to postulate a supernatural entity.
In other words, "the condition of my brain and body" functions exactly like the lesion. It completely "predetermines" the outcome.
So you're a determinist. OK.
Nonetheless, I say I have a choice in Newcomb, because the condition of my brain and body imply that I will engage in a certain process of reasoning, considering the alternatives of one boxing and two boxing, and choose one of them.
That, to me, doesn't follow at all. You don't choose, you're just an automaton going through the motions. It is, as you say, similar to the lesion -- there might well be complicated intermediate steps but there is no choice involved. You literally do not have a choice.
In which way your choice is different from the choice of a calculator which also goes through a bunch of processes before deciding to output 4 as a response to 2+2?
This is all in the context of discussing Newcomb and the smoking lesion. It is possible that libertarian free will is true. If it is, neither Newcomb nor the smoking lesion is possible in the real world, at least in the 100% way.
So I do not assert that determinism is necessarily true (although I do not know that it is not). But if it is true, it is equally true in Newcomb and in the smoking lesion, and if it is false, it is equally false in both cases.
The situation is different from the calculator because the calculator does not consider various possible a...
You're given the option to torture everyone in the universe, or inflict a dust speck on everyone in the universe. Either you are the only one in the universe, or there are 3^^^3 perfect copies of you (far enough apart that you will never meet.) In the latter case, all copies of you are chosen, and all make the same choice. (Edit: if they choose specks, each person gets one dust speck. This was not meant to be ambiguous.)
As it happens, a perfect and truthful predictor has declared that you will choose torture iff you are alone.
What do you do?
How does your answer change if the predictor made the copies of you conditional on their prediction?
How does your answer change if, in addition to that, you're told you are the original?