I think your last paragraph is more or less correct. The way I'd show it would be to place a node labelled 'decision' between the top node and the left node, representing a decision you make based on decision-theoretical or other reasoning. There are then two additional questions: 1) Do we remove the causal arrow from the top node to the bottom one and replace it with an arrow from 'decision' to the bottom? Or do we leave that arrow in place? 2) Do we add a 'free will' node representing some kind of outside causation on 'decision', or do we let 'decision' be determined solely by the top node?
In the smoking problem, there's usually no causal arrow from 'decision' to the bottom; in Newcomb's, there usually is. Thus, if we're assuming an independent 'free will' node, you should one-box but smoke.
Unknowns seems to be pushing the case where there's no 'free will' node; your decision is purely a product of the top node. In that case, I say the answer is not to waste any mental effort trying to decide the right choice because whether or not you deliberate doesn't matter. If you could change the top node, you'd want to change it so that you one-box and don't smoke, but you can't. If you could change your decision node without changing the top node, you'd want to change it so you one-box and smoke, but you can't do that either. There's no meaningful answer to which impossible change is the 'right' one.
This is like saying a 100% determinate chess playing computer shouldn't look ahead, since it cannot affect its actions. That will result in a bad move. And likewise, just doing what you feel like here will result in smoking, since you (by stipulation) feel like doing that. So it is better to deliberate about it, like the chess computer, and choose both to one box and not to smoke.
I am currently learning about the basics of decision theory, most of which is common knowledge on LW. I have a question, related to why EDT is said not to work.
Consider the following Newcomblike problem: A study shows that most people who two-box in Newcomblike problems as the following have a certain gene (and one-boxers don't have the gene). Now, Omega could put you into something like Newcomb's original problem, but instead of having run a simulation of you, Omega has only looked at your DNA: If you don't have the "two-boxing gene", Omega puts $1M into box B, otherwise box B is empty. And there is $1K in box A, as usual. Would you one-box (take only box B) or two-box (take box A and B)? Here's a causal diagram for the problem:
Since Omega does not do much other than translating your genes into money under a box, it does not seem to hurt to leave it out:
I presume that most LWers would one-box. (And as I understand it, not only CDT but also TDT would two-box, am I wrong?)
Now, how does this problem differ from the smoking lesion or Yudkowsky's (2010, p.67) chewing gum problem? Chewing Gum (or smoking) seems to be like taking box A to get at least/additional $1K, the two-boxing gene is like the CGTA gene, the illness itself (the abscess or lung cancer) is like not having $1M in box B. Here's another causal diagram, this time for the chewing gum problem:
As far as I can tell, the difference between the two problems is some additional, unstated intuition in the classic medical Newcomb problems. Maybe, the additional assumption is that the actual evidence lies in the "tickle", or that knowing and thinking about the study results causes some complications. In EDT terms: The intuition is that neither smoking nor chewing gum gives the agent additional information.