Reading this (well, I'm posting at page 32) made clear the "problem" with Newcomb's problem with transparent boxes (where you can see what's in the boxes before you choose): it's not a decision-determined problem. This is because you can have an algorithm that depends on some property of the Predictor - the "tit for tat" algorithm is the most obvious.
Any optimality of basing your decision on the predictor's algorithm does not keep it from being a decision-determined problem.
If you do tit-for-tat, the predictor predicts that you will base your decision on what you see in the transparent box and therefore never fills that box. Your (conterfactual) decision (process) still determines the outcome.
I have not seen any place to discuss Eliezer Yudkowsky's new paper, titled Timeless Decision Theory, so I decided to create a discussion post. (Have I missed an already existing post or discussion?)