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Gary_Drescher comments on A problem with Timeless Decision Theory (TDT) - Less Wrong
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I think this problem is based (at least in part) on an incoherence in the basic transparent box variant of Newcomb's problem.
If the subject of the problem will two-box if he sees the big box has the million dollars, but will one-box if he sees the big box is empty. Then there is no action Omega could take to satisfy the conditions of the problem.
In this variant that introduces the digit of pi, there is an unknown bit such that whatever strategy the subject takes, there is a value of that bit that allows Omega an action consistant with the conditions. However, that does not mean the bit actually has that value, it may in fact have the other value and the problem still is not coherent.
I suspect that there is still something this says about TDT, but I am not sure how to illustrate it with an example that does not also have the problem I have described.
Edit As I was typing this, Eliezer posted his reply, including "an unsolvable problem that should stay unsolvable" that should stay unsolved which is equivalent to the problem I have described.
The rules of the transparent-boxes problem (as specified in Good and Real) are: the predictor conducts a simulation that tentatively presumes there will be $1M in the large box, and then puts $1M in the box (for real) iff the simulation showed one-boxing. So the subject you describe gets an empty box and one-boxes, but that doesn't violate the conditions of the problem, which do not require the empty box to be predictive of the subject's choice.
I drew a causal graph of this scenario (with the clarification you just provided), and in order to see the problem with TDT you describe, I would have to follow a causation arrow backwards, like in Evidential Decision Theory, which I don't think is how TDT handles counterfactuals.
The backward link isn't causal. It's a logical/Platonic-dependency link, which is indeed how TDT handles counterfactuals (i.e., how it handles the propagation of "surgical alterations" to the decision node C).
My understanding of the link in question, is that the logical value of the digit of pi causes Omega to take the physical action of putting the money in the box.
See Eliezer's second approach:
Ah, I was working from different assumptions. That at least takes care of the basic clear box variant. I will have to think about the digit of pi variation again with this specification.