The existence of a flawless predictor means that you do not have a choice after the predictor made its prediction, the decision must already be baked into the state of the universe accessible to the predictor. It also precludes that any true randomness is affecting the choice as that could not be predicted ahead of time.

I do not think that allowing some prediction error fundamentally changes this, it only means that sometimes the choice may depend on unpredictable true randomness or sometimes the predictor does not measured the relevant state of the universe exactly enough or the prediction algorithm is not flawless. But if the predictor still arrives at the correct prediction most of the time, then most of the time you do not have a choice and most of the time the choice does not depend on true randomness.

Which also renders the entire paradox somewhat moot because there is no choice for you to be made. The existence of a good predictor and the ability to make a choice after the prediction are incompatible. Up to wild time travel scenarios and thinks like that.

There's rational and then there's common sense, if put in that situation who in their right mind would take even a 50% chance that the entity is wrong and greed it for 1000$. All I'd need to know is that it is far more likely I get the million if I go into the game thinking I'd only one-box

In some ways it is an interesting problem about whether someone can engage a question about a hypothetic question -- and for the purpose of the exercise, assume the proposed parameters of the scenario.

Assuming I have no way of testing the predictor, my decision would be to pick both boxes on the basis that $1000 is not a lot of money to me, but $1000000 is, and I wouldn't worry about the odds, because without knowing the nature of the specific predictor we're down to Pascal's Wager married to the Halting Problem:

We don't know whether or how our actions and thought processes processes might affect the outcome, and so any speculation over odds is meaningless and devolves to making assumptions we can't test, without even knowing whether that speculation itself might alter the outcome, or how.

But I don't need to speculate about the relative value of $1000 and $1000000 to me. Others might opt for the safe $1000 for the same reason.

I don't get the 'choice' : the content of the box is aldready defined when you take your decision so taking it won't change the content of the black box and the open/transparent box have no drawback. What am I missing ?

I don't know about y'all, but this paradox was resolved to my complete satisfaction in a blog post some years ago, I believe by Scott Aaronson, though I can't find the link. If the predictor has such a good success rate, then it must be simulating people's brains, but since it's not always right, the simulation isn't perfect. The best strategy for playing this game therefore is to look for indications as to whether I'm the real me or the simulation when the question is posed to me, and choose accordingly. Am I floating in a sensory deprivation tank being asked my choice by a disembodied voice with no recollection of how I got there and no memory of my childhood? In that case maybe I'm the simulation, so my answer is that I'll choose just one box. Is it an ordinary day of my life and a plausible setting with all of my faculties and recollections intact? Then I'll assume simulated me had my back and take both boxes.

For folks reasoning through the "paradox," this may be helpful:

https://arxiv.org/pdf/0904.2540

Abstract:

> ...We show that the conflicting recommendations in Newcomb’s scenario use different Bayes nets to relate your choice and the algorithm’s prediction. These two Bayes nets are incompatible. This resolves the paradox: the reason there appears to be two conflicting recommendations is that the specification of the underlying Bayes net is open to two, conflicting interpretations...

I'm been presented with this thought experiment before and I always feel like I'm missing something when other people talk about it. Why would you ever take both boxes?

The premise is that the predictor is always right. So whether you take one or both boxes, the predictor would have predicted that choice. We know from the setup that if the predictor said you would take the one box, it will have a million dollars. Therefore, if you take the one box it will have a million dollars in it (because whatever you choose is what the predictor predicted).

As an aside, I think whatever this says about free will or if you're actually making a "choice" is irrelevant in regards to if the million dollars is in the box. The way I see both choices is this:

You "decide" to take both boxes -> the perfect predictor predicted this -> the opaque box has zero dollars -> you get a thousand dollars

You "decide" to take the opaque (one) box -> the perfect predictor predicted this -> the opaque box has a million dollars -> you get a million dollars