I absolutely did not write that in a deterministic world prediction is impossible—quite the opposite. I think you didn’t really make the effort to read what I wrote, but I understand you. Honestly, I don’t understand how you have the energy to read all the questions and comments and answer them.

I read it carefully, and unfortunately I didn’t understand. And I also didn’t say that you wrote what you’re writing here. You began by describing my position, which you were challenging. You began to describe my position like this:
My question concerns what you wrote in the book: that Newcomb’s paradox is a proof against determinism. Regarding the claim that if we assume determinism, then the chooser is also deterministic and cannot change his choice, and therefore the prophet knows what he will choose and accordingly what to put in the box
And about that I explained two things.
What I asked here is: what in this position requires explanation? It is obvious that if the world is deterministic, one can predict in advance what will happen.
On second thought, maybe what you mean to say is that this agreed-upon description is ostensibly a deterministic way out of the paradox—that is, that there is no proof here for free will.
I rejected that in two ways, and therefore concluded that there is no solution here, because the paradox remains intact unless you adopt a libertarian picture. Am I right?
Assuming I am, I’ll try again to understand your arguments and respond.
1. The question of what the rational decision is in such a situation is well-defined. What you’re saying is that such a prophet cannot exist together with free will. Correct. That is exactly my claim. So now we have two possibilities: 1. There is a prophet and there is no free will. But then the question returns: what is the rational decision that should be made in such a situation? 2. There is no such prophet and there is free will. After rejecting the first, the second remains.
2. This question is connected to the previous one. Assuming we are dealing with a rational player, the prophet cannot predict what he will do. If you are saying there is no rational decision and the decision is necessarily according to character, then we are back to point 1. And there I already answered.

First of all, thank you for the effort to try to understand what I was saying. Reading it now, I can see that I really didn’t write it clearly, but you understood correctly that I meant your claims about there being a deterministic way out of the paradox.
Regarding your reply to my question: I claimed that it is not correct to say to the determinist, “what decision should be made here with free will,” not even theoretically, because if there is free will then there is no prophecy. And as I understand it, you agreed with that, except that you claimed the question then returns: what is the rational decision that should be made in this situation?
My claim is that it is not correct to ask what rational decision should be made if we assume determinism, because when one asks which decision should be made, one is implicitly assuming free will. In a deterministic reality, the person does not really make a decision; rather, a decision is produced in him. And the decision produced in him is rationality minus the personal influences on it. And that the prophet can certainly predict, because all the starting points here exist and are fixed.
In other words, for every person who comes to choose which box to take, it is already fixed in advance what he will decide according to his style of thinking and his personality: whether the irrationality of the decision bothers him, and at what point he is supposed to get fed up with this mental loop. Therefore the question of what rational decision he should make is not a correct question, because each person has his own decision according to his personality pattern, and that is the decision the prophet actually predicts.

One can definitely talk about the rational decision even if we are dealing with a deterministic creature. That is exactly what I explained, and I did not find in your remarks any argument undermining that.

I went over the thread twice and didn’t find where you explained how a rational decision is relevant when there is nothing to decide because the creature is deterministic. Can you point me to it?

It was explained in the book. But what is there to explain? My claim is that there is such a thing as a rational decision in this situation, even if the chooser himself will not make it and cannot make it. There is no connection, because this is a principled question and not a question about what he will do.

That’s what I didn’t understand. A rational decision belongs between two possible alternatives, so ostensibly in a deterministic world there is no concept of rationality at all, even at the principled level. (And not only rationality; ostensibly in a deterministic world there is no concept of judgment or evaluation at all. One can only describe what happens, and that’s it.)

In my world, as an outside observer asking himself, there is rationality. The question is about me (what I would do), not about the chooser. Unless you are arguing that free choice is a contradictory concept and cannot exist. I explained there that this is not their claim, and that is not what I am addressing.