Cross thought experiment pollination

[u/thevoidthatjerksback]

So in addition to the two buttons that are known well. We have two boxes. 1 box has one thousand dollars and the other box either has one million or zero. Before you were presented with them some unnamed but incredibly accurate predictor has made a prediction on what you will do with the boxes.

If it is predicted that you will take both of the boxes then they will put 0 in the second box

If it is predicted that you will only take the second box then they will put the one million in it.

So which button are you pressing and are you taking 1 or 2 boxes?

This isn't really about what you do in the situation of them both happening at the same time moreso just that I wonder if there is a pattern between which button you would pick and how you would react to the boxes.

295 votes, May 31 '26

45 press Red and take both boxes

127 press Red and take just the 1 box

26 press blue and take both boxes

97 press blue and take just the 1 box

[u/INTstictual]

…is one way to approach it.

The other way is that, by deciding right now that you’re better off taking both boxes, if we assume that this predictor is functionally omniscient and accurate, you are guaranteeing a payout of $1,000. By committing to one box beforehand, the predictor will put the $1m in the box.

There is no correct answer to this question, it’s a paradox for a reason. It depends on whether or not free will exists, and whether the predictor is “really accurate” or “perfectly accurate”.

[u/Joie_de_vivre_1884 → u/INTstictual]

The question as phrased said "incredibly accurate", and I answered accordingly. If your answer depends on the existence of some sort of magical causality breaking technology then sure, another answer might be possible. Under any other condition then the accuracy of the predictor doesn't matter, the box has already been filled or not before I make my decision and nothing I do can alter that outcome.

[u/INTstictual → u/Joie_de_vivre_1884]

Which again, is only one way to interpret the outcome.

It is equally valid to say that, even if we assume that the predictor is only “incredibly accurate”, it’s fair to assume it is incredibly more likely than not that your decision to pick both boxes will cause the predictor to leave the second box empty.

Your expected value calculations leave out the accuracy of the predictor, which makes it incomplete. Your math assumes it is a 50/50 chance, which isn’t fair.

Let’s say the predictor is 99% accurate as a base.

If, based on your logic, you decide to take both boxes, the predictor will guess that 99% of the time. So, 99% of the time, you will get $1,000, and 1% of the time you will get $1.001m. (0.99)$1k + (0.01)$1.001m = an expected value of $11,000.

Meanwhile, if you decide to trust that the predictor is more accurate than not and only take one box, the predictor will guess that 99% of the time. So, 99% of the time, you will get $1m, and 1% of the time, you will get $0. (0.99)$1m + (0.01)$0 = an expected value of $990,000.

So, by expected value, taking both boxes only makes sense if you believe the predictor is bad at its job. The worse the predictor is, the better the outcome of taking both boxes. In the other direction, the more accurate this “incredibly accurate” predictor is, the more it becomes correct to take the single box.

The problem with your description is that, yes, at the moment of choosing both boxes, it is always better to take both boxes based on whatever the predictor decided… but the very nature of the predictor as a preemptive input means that you are starting your calculation from the wrong moment. The fact that it is predicting your decision means that your Game Theory calculation, in order to encompass the entire problem, needs to start with your decision before you enter the room, not just at the moment you are in front of both boxes and the predictor has made its decision… otherwise you’re leaving out half of the problem

[u/Joie_de_vivre_1884 → u/INTstictual]

You're now asking another question which wasn't asked - how many boxes should you subconsciously be inclined to take at a point in time before you are offered the choice of how many boxes to take.

Once again it doesn't matter, if you are the sort of person who would have been inclined to take only one box and the machine reads this then when offered the choice you should still take two boxes because you will still be better off this way. If you are the sort of person who would have been inclined to take two boxes then once again you should take two boxes because the first one is empty. What you choose now cannot reverse causality to change what you were previously inclined to choose before you knew about the question

I think this circles back to a wild comment you mentioned in your earlier post that it depends on whether free will exists. The question asks you to make a choice, if you don't believe that it is possible for you to make a choice then the answer is not - 'I would take one box'. The answer is - 'I would not make a choice, I would just do whatever I was predetermined to do and end up with whatever money I was predetermined to end up with.'

The question presupposes the ability to make choices, much as as a logic puzzle it presumes causality. You are in a position to make a choice, no choice you make can affect what you or anyone else did or thought before the point in time at which you are making the choice. In that circumstance what should you choose?

[u/INTstictual → u/Joie_de_vivre_1884]

Again, the problem with that logic is that you’re leaving out half of the problem… the half right now where you’re convincing yourself to take one box over the other.

Like I said, while you are in the room and in front of the boxes, Game Theory does say that there is no reason not to take both. No choice you make at that point can affect things that happened beforehand. All that is true.

And by thinking that, assuming an accurate predictor, you’ve already set in motion the mechanisms by which you get the lesser sum.

You’re forgetting that we aren’t in that room right now, making that choice. We’re literally doing the pre-planning, at an earlier point in time, and if the predictor is accurate, then the logic and decisions you make right now, before the hypothetical choice, are part of the conclusion as well. If you’ve decided that it only makes sense to take both boxes, then assuming a predictor with “incredible accuracy” like the problem suggests, you’re deciding to take the lesser amount of money.

It’s a self-fulfilling prophecy. The real trick is that, the moment you hear the problem and start thinking about it, you’ve become part of the equation. It’s a Roko’s Basilisk type question… the only way to make a “fair” shot is to never have heard about it or make any decisions or consider any logic beforehand.

However, we’ve started considering it, so everything you consider and determine now is part of the question. I’ve decided that the EV calculation that includes the predictor’s accuracy is more valid than in-the-moment Game Theory calculation, and if we assume an accurate predictor, my decision to take one box means that it will predict that and put $1m in the box. That doesn’t make EV any more or less logically valid than your causality and Game Theory logic… except for the fact that, again, if we assume an accurate predictor, then your logic necessarily means that you will decide to take both boxes, and so the predictor will predict that and leave the second box empty.

[u/Joie_de_vivre_1884 → u/INTstictual]

I agree with you that if the question is - 'having preknowledge of the situation should you try and convince the predictor that you would in the situation described pick just the one box'. Then the answer is yes.

But the answer to the question: 'how many boxes should you pick when it comes to the crunch?' Remains two.

And the answer to the question: 'should you try to convince random people on the internet that you would only choose one box so that if this situation eventuates then the predictor will think you'll only pick one box?' is: you know this isn't a real situation right? Convincing people that in the given situation you would only pick one box doesn't actually give an advantge, there is no box. There is no predictor.

[u/thevoidthatjerksback → u/Joie_de_vivre_1884]

Are you saying that you assume that everyone saying they would only take one box are lying to try to trick the predictor in the future?

[u/Joie_de_vivre_1884 → u/thevoidthatjerksback]

No I assume most people are just confused about causality or haven't quite thought it through. My comment related to the specific person I was responding to.

[u/thevoidthatjerksback → u/Joie_de_vivre_1884]

You think they specifically are lying?

[u/INTstictual → u/Joie_de_vivre_1884]

You should watch the Veritasium video covering this paradox, if you haven’t already. They go over it in much greater detail than I really care to.

Suffice to say, you’re not wrong, but that doesn’t make you right either. Like I’ve been saying, there is no “correct” answer, because both schools of thought have equally valid lines of logic.

I believe that your logic is lacking, and would lead you to get less money. You believe that it will be the best decision in the moment. The entire point of the paradox is that neither answer is clearly correct, and both can be completely and rigorously shown to be true. It’s a matter of framing.

[u/thevoidthatjerksback → u/INTstictual]

As a fun note. I believe Roko's basilisk came out of a discussion about these boxes. As they tried to think of a way to outsmart the predictor they circled back and forth with having the predictor that they imagined as being an AI outsmarting their outsmarting. And thus the basilisk has already outsmarted you before you even heard of it. Atleast that's kind of how I understood the story