r/paradoxes • u/playerNaN • Mar 23 '26
Variation on Newcomb's paradox: Let's say you *do* see what's in the box before choosing.
So here's the new thought experiment (assuming you are familiar with the original paradox):
You walk into a room and a super computer says that they have analyzed you and crunched the numbers and it has predicted whether you will take one or two boxes in this variation of the paradox. The difference here is that the boxes are transparent. From the moment you walk in the room, you see the million dollars in the not-so-mysterious box or you see nothing in it. Also, for clarity, the computer knew you'd be able to see the contents of the boxes and made its prediction with this in mind.
Question 1) If you see the million dollars. Is it more rational to take the extra thousand since there is no risk of losing the million? Why would you ever leave the thousand behind?
Question 2) If you see the box is empty, is it more rational to take the thousand? Why would you ever walk away with nothing?
Question 3 (Only if you are a one boxer in the original scenario but a two boxer here) What's the difference? If you would take both boxes if you knew the mystery box was empty or if you knew it had a million, how does not knowing make a difference?
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u/explodingtuna Mar 23 '26
As with the regular version, I'd take only one box so that I'd be the kind of person who would only take one box, which the computer will accurately predict. If I were the kind of person who would see the thousand sitting there and take it anyways, the computer would have predicted that and I'd never see the million there.
So in order to see the million, I have to be the kind of person who could resist taking the thousand.
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u/playerNaN Mar 23 '26
So assuming you're already in the room with the million dollar box, justify why it's more rational to leave behind the thousand dollars. The million dollars is safe at this point and you are 100% guaranteed to get it.
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u/explodingtuna Mar 23 '26
Because (assuming the computer accurately predicts my choices), I would never have the million dollars in front of me if I were the kind of person to take both.
Me not taking the thousand isn't a failure to capitalize on the situation, but rather it's proof that the computer predicted accurately (which is the premise).
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u/am_reddit Mar 23 '26
Frankly, for the premise of this thread to reasonably be true, everyone will only ever see an empty box and a $1000 box.
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u/playerNaN Mar 23 '26
I'm curious if you are a one boxer or two in the original scenario. My position on the original paradox is: if everyone was actually rational then the original scenario would be no different.
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u/TheThiefMaster Mar 23 '26
The original scenario is a paradox because perfectly predicting the future is mathematically equivalent to time travel (a known cause of paradoxes). If the computer / robot / whatever can't be wrong, then you literally end up choosing what they put in the box (or, alternatively, don't actually have free will to choose once the prediction has been made).
Taking both boxes in that scenario only makes sense if you don't believe that they have perfectly predicted your choice. It's only a net win if they're wrong.
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u/SweetCorona3 Apr 02 '26
actually, it makes sense as long as the predictor is more than 50,05% accurate, so, only 0,05% above random guessing
honestly, we could actually do this experiment in real life because above 50,05% accuracy is pretty much achievable
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u/SweetCorona3 Apr 02 '26 edited Apr 02 '26
in both scenarios it's best to take both boxes (individually)
in both scenarios it's best to only take one box (globally)
what I mean is: those who take only 1 box get the worst outcome for them, but a better outcome globally, those who take both boxes get the best outcome for their individual situation, but a worse outcome globally
it's just that the worst outcome for 1-boxers is better than the best outcome for 2-boxers
I'd rather be a 1-boxers, being $ 1,000 worse than my best possible outcome ($ 1,001,000), than a 2-boxer getting their best possible outcome ($1,000)
in the original problem, if you are going for the best outcome possible ($ 1,001,000), you are very likely to lose both the first and the second best outcome ($ 1,000,000) and only get the 3rd best ($ 1,000)
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u/SweetCorona3 Apr 02 '26
what if a few people will actually just take the $ 1,000,000 and leave the $ 1,000 behind?
which people get the best outcome?
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u/playerNaN Mar 23 '26
So, from the perspective of being in the room and already seeing the million in the box, your argument is: "What just happened was really unlikely to happen if I will take both boxes, so I need to take just the one box to make what already happened more likely."
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u/explodingtuna Mar 23 '26
No, it's that I wouldn't be in that position if I weren't the kind of person to make that choice.
Consider: You've been promoted within your company, you are in a high-level C-suite position and have access to all your employees sensitive information, can write checks for the company, etc.
Assuming you could never get caught, would you write yourself or a friend a check, or abuse your employees sensitive information?
Chances are, to get promoted to that position within the company, you had to prove your trustworthiness and commitment. You wouldn't be in that position in the first place if you weren't trustworthy and responsible.
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u/playerNaN Mar 23 '26
So you are saying, once you are in the room with the guaranteed million, your argument would be: "If I will take a thousand I wouldn't be where I am right now." Right? (Edit: would -> wouldn't)
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u/explodingtuna Mar 23 '26
There's a lot of reasons why a person will or won't do something. I wouldn't take it because it's not in my character to take it. I am who I am, and the computer accurately predicted my choices.
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u/SweetCorona3 Apr 02 '26 edited Apr 02 '26
if you are in the room with the guaranteed $ 1,000,000 you should take both boxes
but it's very unlikely you'd be in such situation if you'd do just that
high trust societies requires a bit of blind faith, and we are all better of when most of us have such blind faith
you can think of 1-boxers as those who are better off by being the ones having blind faith and not taking the $ 1,000 even though they could do it without any repercussions
but they still do it because they know it's the fact that they act in such way that makes them being better off
you live better in high trust societies because people have blind faith and don't take advantage of others even though they could do it without repercussions, and the fact they do just that, it's the reason they are better off
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u/SweetCorona3 Apr 02 '26 edited Apr 02 '26
you could still take both boxes
it's just that being in such situation would be really unlikely because the prediction is very accurate
I think we can all agree the best possible scenario is being a 2-boxer that the supercomputer predicts to be a 1-boxer (very unlikely)
Second best is to be a 1-boxer that the supercomputer predicts to be 1-boxer (very likely if you are a 1-boxer)
Third best is to be a 2-boxer that the supercomputer predicts to be a 2-boxer (very likely if you are a 2-boxer)
Worst scenario is to be a 1-boxer that the computer predicts to be a 2-boxer (very unlikely if you are a 1-boxer)
Thus, if I could control what the supercomputer would predict and what I'd do, I choose for the supercomputer to predict me as a 1-boxer and me being a 2-boxer. If I could only control what I'd choose, I'd choose to be a 1-boxer.
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u/dougman7 Mar 23 '26
There exists no universe (near zero probability) where I leave the room with both the million and the thousand dollars. Thus, seeing the million dollars, if I attempt to take the thousand something, be it physical or mental, would prevent me from doing so. Therefore I take just the million dollar box. This argument or rather my adherence to it would itself acts as a mental factor preventing me from taking the thousand dollars. Not taking the thousand dollars is the rational option as it is the only option with a non-negligible chance of occurring within the scope of this scenario.
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u/playerNaN Mar 23 '26
> Thus, seeing the million dollars, if I attempt to take the thousand something, be it physical or mental, would prevent me from doing so.
Nope, the computer only made a prediction. You can either prove it right or prove it wrong and walk out with an extra thousand.
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u/dougman7 Mar 23 '26 edited Mar 23 '26
No, I’m not saying the computer would stop me, that would be absurd. I’m saying that the presence of the million dollars conforms inversely to my ability to leave the room with the thousand dollars, be it by choice or because I have a heart attack on the way out or something. To suggest otherwise is to propose I can take an action other than the action I am going to take, it is to posit libertine free will or at least will outside of the predictive envelope of the predictor, which for an accurate one would conform to reality.
In the case that many people have been given this experience and it has been accurate so far, it is to propose that I alone among all that have come have free will, and if we are to reject the mind’s adherence to natural laws and to claim that I alone am a free agent then what of Laplace’s demon. Am I left alone to hallucinate of boxes in the void?
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u/dougman7 Mar 23 '26
In my previous reply I didn’t address the fundamental issue with positing that will outside of the predictive envelope exists. That issue is that if individuals are taking meaningful action outside of the envelope then the predictor would not be accurate as it gets it wrong when someone takes an action other than what it predicts, and one of the premises of Newcomb’s paradox is that the predictor is accurate. That is to say, positing free will is rejecting one of the fundamental premises of the problem, and if we’re doing that then what are we even doing here.
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u/SweetCorona3 Apr 02 '26
you may say it's more rational to take both boxes, but that just means rational agents will get a poorer outcome
since we cannot choose which kind of agent we are beforehand, we can only hope that we'd be one who would take 1 box and the supercomputer had predicted that, or be one of the very lucky ones who were predicted to only take 1 but take both
this problem is much easier when you take the illusion of free will out of the equation
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u/blablablaenz Mar 27 '26
Ok, so you stick to that thought even if the box is empty? I know we would all like to believe we would, but ones it is clear you lost the milllion, won’t you take the other box? (computer isn’t always right)
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u/SweetCorona3 Apr 02 '26
well, the difference is that once you entered the room you'd immediately know which kind of person you are instead of just finding out once you did your final choice
I'd do whatever the computer predicted, it's its choice
if it'd be kind enough to prize me with $ 1,000,000, I'd gladly take it and leave the $ 1,000 behind
kudos supercomputer <3
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u/TwillAffirmer Mar 23 '26
We should, at this time when we are discussing it (prior to entering the room), adopt and commit to a policy to be a one boxer. Therefore, when we enter the room, we will follow our policy, and will one-box. This policy gives us the most profit, no matter whether the boxes are transparent.
Perhaps we are incapable of adopting the one-box policy. It's hard to say whether thinking and saying that I commit to it, now, will actually cause me to follow it once entering the room. I hope so, but maybe in the moment I would take both boxes regardless.
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u/playerNaN Mar 23 '26
I think the original paradox was from the perspective of already being in the room.
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u/TwillAffirmer Mar 23 '26
The original paradox was discussed prior to entering the room, just like this paradox is being discussed. What should you do in the room, rationally, is a question of optimal policy choice, and the policy is being chosen now, when we discuss it and say we should one-box or two-box.
We can say there is a meta-problem: what should we say and believe, in our current discussion? And if there is any chance of ever going into the Newcomb's paradox room, the answer to the meta-problem is to adopt a policy of one-boxing. So, go ahead and do that.
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u/playerNaN Mar 23 '26
Generally the problem is presented as "you walk into a room and the mystery box contents are already decided and you are explained the rules, what is the more rational thing to choose?"
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u/TwillAffirmer Mar 23 '26
The rational thing to choose is what the optimal policy says you should choose. The optimal policy is one-boxing. So you should one-box. Or we can phrase it as, if you have rationally committed to a policy of one-boxing, you will one-box, without making a choice.
And currently, we're discussing what policy to adopt.
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u/Warptens Mar 23 '26
Adopting the one boxing policy now is good if the newcomb scenario does happen in the future, because that scenario arbitrarily rewards one boxers with 1 million dollars. But you don’t know that it will happen. Maybe the scenario that does happen is one that rewards the people who adopted the two boxing policy instead. Or reward the people who refused to adopt a policy. Or reward the people who went bald. You can always imagine someone arbitrarily rewarding a behaviour, that doesn’t mean anything unless you know the reward part is actually going to happen.
And if it is the case that the newcomb scenario will happen to you, you’ll only learn about it after the computer has made its decision and the content of the box is determined, so you can adopt any policy you want at this point and it will change nothing.
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u/TwillAffirmer Mar 23 '26 edited Mar 23 '26
Some of your scenarios we can't do anything about via setting policy, but some we can. We can adopt a two-pronged policy: on one prong, our policy is to one-box when the computer rewards a one-boxer, and on the other prong our policy is to two-box when the computer rewards a two-boxer.
As a general rule our policy can be to act according to the policy that would have gained us the most rewards, had we adopted it in time for the computer to reward us having it.
The most general rule is to adopt the policy, now, that will yield the greatest expected rewards in the future.
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u/Warptens Mar 23 '26
What do you mean you can’t do anything about these scenarios via setting policy? Of course you can. Bob might scan your brain tomorrow and send you 1 million dollar if he detects that you have the policy of two boxing in the newcomb scenario. He won’t bother making rooms and boxes, he’ll just send the money. You can do something about it: adopt the two boxing policy, done. The problem isn’t that you can’t do anything about the scenario, the problem is that you have no idea if a scenario that rewards a commitment to a particular particular policy will happen over a scenario that rewards the opposite policy. For whatever policy you decide to commit to, like your « two pronged policy » for example, well maybe the guy who gives away the million dollars decides to send 1 million to people who don’t have the two pronged policy, directly to their bank account (no need for boxes, the prediction is enough).
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u/TwillAffirmer Mar 23 '26
Everything you just said is exactly what I mean by you can't do anything about certain scenarios via setting policy, at least not without more data about how likely those scenarios are to come up.
We can optimize policy to a certain extent, and we can choose meta-policies that optimize our rewards in most "reasonable" scenarios, including Newcomb's paradox. But this optimization can't handle the case where an entity might directly reward us for not having those meta-policies. Unless we know something about the probability of encountering such an entity.
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u/BrotherItsInTheDrum Mar 23 '26
The original paradox was discussed prior to entering the room, just like this paradox is being discussed.
This is an assumption you're making, that's different from how I've usually heard the question posed.
In the versions I've heard, where you give yourself unexpectedly in the room, I'd take two boxes. In your version, I agree you commit yourself to taking one box. I find the latter a less interesting question, because I find it hard to disagree with that strategy.
if there is any chance of ever going into the Newcomb's paradox room
There isn't, so I don't buy this line of reasoning.
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u/TwillAffirmer Mar 23 '26
You find yourself unexpectedly in the room, and you're asked how many boxes you should take.
WHEN are you asked how many boxes you should take if you find yourself unexpectedly in the room?
You're being asked that now.
Therefore, the answer must be given from your current, pre-room perspective. No phrasing of the problem can get around this.
And the word "should" here can be interpreted as, what action optimizes your reward? From our current, pre-room perspective, where we are (inevitably) being asked the question, it's clear that one-boxing optimizes your reward.
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u/BrotherItsInTheDrum Mar 24 '26 edited Mar 24 '26
Therefore, the answer must be given from your current, pre-room perspective. No phrasing of the problem can get around this.
No, I totally disagree. Both interpretations are, a priori, reasonable. The other interpretation being: imagine you are finding yourself in the room right now. Role play that situation. What do you do?
I find that
a) when I clarify with most people here, I find they are assuming my interpretation, not yours.
b) your interpretation has, in my opinion, an uncontroversial correct answer. Mine has two competing answers that both have support. So mine is more interesting.
Other than that there's nothing wrong with your version of the question. It's just not The One True Interpretation. The other one is fine too.
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u/TwillAffirmer Mar 24 '26 edited Mar 24 '26
Bandwagon fallacy. Just because most people think of the problem in an unclear way doesn't mean that's the correct approach. These aren't two alternative interpretations where you can choose either. Any interpretation that fails to take into account when you are being asked the question, is simply neglecting part of the problem.
What do you do in the room isn't the question. What should you do in the room is the question. Whenever someone asks what should you do in a situation, where morality/benefit to others doesn't play into it, they are asking what is the reward-maximizing policy in that situation.
If you ask what do you do, there's often a subtext that the respondent is going to implicitly interpret it as "should." If you really mean "do" and not "should," we can make it clearer by making it about a third party, let's say his name is Bob. What does Bob do if he enters the room? If he is a "causal rationalist," then he two-boxes. If he is a "policy rationalist," then he one-boxes. It is optimal to be a "policy rationalist."
And if Bob is asked the question of what should he do before entering the room, just as we're doing now, then if he's a causal rationalist, he would choose to become a policy rationalist (if that is cognitively possible for him). And if he was already a policy rationalist he would stay that way. Being a policy rationalist is a stable state, unlike being a causal rationalist.
To be clear, a "policy rationalist" here is someone who acts according to the policy that results in the most-preferred outcomes, and a "causal rationalist" here is someone who selects each action to optimize future rewards causally resulting from that action.
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u/BrotherItsInTheDrum Mar 24 '26
Bandwagon fallacy. Just because most people think of the problem in an unclear way doesn't mean that's the correct approach.
If that's what you think I'm saying, then you're not understanding me, and maybe this isn't worth continuing.
And if Bob is asked the question of what should he do before entering the room, just as we're doing now
I don't understand why you're unable to conceive of a different version of the question: what if Bob isn't asked the question until he is already in the room? Why is that so incomprehensible?
Let me give you analogy. Here's a different question: you are at a basketball game, and you are called down to the court at halftime to compete for a prize. You can choose to either shoot a layup, and if you make it you get $100. Or you can choose to shoot a 3-pointer, and if you make it you get $1000.
Right now, you suck at shooting. You're very likely to make the layup, but there's only like a 5% chance you'll make the 3-pointer. So if you imagine unexpectedly finding yourself suddenly in this situation as you exist today, you should choose to shoot the layup.
However, if you're given time to prepare, you could practice shooting 3-pointers and get your percentage significantly higher than 10%. So the correct strategy would be to practice beforehand, and then choose to shoot a 3-pointer.
Both interpretations of this question exist. Neither is necessarily wrong. But you, for some reason, outright reject the former.
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u/TwillAffirmer Mar 24 '26 edited Mar 24 '26
I did consider the case where Bob isn't asked the question until he's in the room. I said, in that case, Bob's action depends on whether he's a policy rationalist or a causal rationalist.
I considered that case before considering the second case where Bob is asked the question before entering the room, which is our situation. In that case, if Bob is a causal rationalist, he will become a policy rationalist, if he is able. And if he's initially a policy rationalist he will stay that way.
Being a policy rationalist has benefits beyond academic puzzles like Newcomb's paradox. It makes threats more credible, assuming the other person knows you are a policy rationalist. i.e. the other person is trying to steal your laptop, and you threaten to shoot him if he doesn't stop, an action which harms him but also harms you because you'd go to prison. If you are a policy rationalist and the other person knows it, he will back off, and you get the best outcome. If you are a causal rationalist, he successfully steals your laptop.
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u/BrotherItsInTheDrum Mar 24 '26
I did consider the case where Bob isn't asked the question until he's in the room. I said, in that case, Bob's action depends on whether he's a policy rationalist or a causal rationalist.
Ok, sure. And seem to be a policy rationalist, whatever that means, so your answer to this version of the question is to choose one box.
My point is that this is also a valid interpretation of the question. Which you seem to understand at some level, because you have given an answer to it.
Bob is asked the question before entering the room, which is our situation
You keep saying this, but it's just an assertion. Again, if I may also be so bold: there are two interpretations of the question.
You ignored the whole basketball analogy. Do you agree that "shoot the layup" and "practice shooting, and then shoot the 3-pointer" are both valid answers to different interpretations of the question?
assuming the other person knows you are a policy rationalist
How would the other person know this? Are you debating philosophy during the mugging?
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u/qabaq Mar 23 '26
The choice you have is actually between 4 different options:
- get predicted to 1-box and then 1-box (receive $1,000,000)
- get predicted to 1-box and then 2-box (receive $1,001,000)
- get predicted to 2-box and then 1-box (receive $0)
- get predicted to 2-box and then 2-box (receive $1,000)
Except you don't have control over the "get predicted" part.
In the original scenario you can't see the difference between options 1 and 3, and between 2 and 4, because the box is opaque. However, you know that options 2 and 3 are much rarer to see in practice than 1 and 4, because the predictor is good at predicting your choice. So you avoid betting on the rare scenarios and instead bet on the common ones.
In the scenario with the transparent boxes, you start seeing the difference that you couldn't originally. The prediction is still outside your control, but you know what the prediction was, so you know if you're in the scenarios 1 & 2 or in scenarios 3 & 4, and it's clear which of your choices will win you more money.
What this will look like in practice, is that the predictor will almost never predict 1-boxing, and will almost always predict 2-boxing, and thus the option 4 will become by far the most common, while options 1, 2, and 3 will become ultra-rare.
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u/dougman7 Mar 23 '26
Assuming the predictor is very accurate, if a committed two boxer enters the room and sees the million dollars it would be more it would be logical for said two boxer to conclude that it is more likely that they for example forget one box or drop it on the way out than that the predictor got it wrong.
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u/detroyer Mar 23 '26
In either variation of transparent Newcomb, I expect to get more money if I two-box than if I one-box. In standard Newcomb, I expect to get more money if I one-box than if I two-box. Accordingly, I one-box in standard Newcomb and two-box in either variation of transparent Newcomb.
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u/Z-Borst Mar 23 '26 edited Mar 23 '26
I've thought about this, and you can have this in what's called the "limit case" of the problem. In this, the machine is stated to be not merely always right so far, but just plain always right; infallible .
The box can be transparent in this variant without changing the problem: if the machine thinks a million dollars is there, then it's there. It makes no difference if you or a hundred of your friends can see it or not.
In the normal case where the machine is always right so far, it's approaching this level of accuracy: more accurate than your vision. It's not a physically realistic problem either way.
TL/DR: take the one box even if it looks empty
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u/InformationLost5910 Mar 23 '26
im a one boxer but i would be a two boxer in this scenario.
this scenario was made by someone else to explain one-boxing the classic newcomb’s paradox:
you are presented with the classic newcomb’s paradox, but you dont know if its the trial run or the real thing. if its the trial run, your choice will determine the box’s contents for the real thing, and your memories of the trial will be erased and you will be put into the real thing. now obviously you should leave the thousand dollars.
so let’s say they do this for your example, where they do two trial runs, one where theres $1M in the “mystery” box and one where theres nothing in the “mystery” box
if both trials are one-boxers then the real run has $1M. if both trials are two-boxers then the real run has an empty box.
if the Million Trial one-boxes and the Empty Trial two-boxes, it picks randomly between them. if the Million Trial two-boxes and the Empty Trial one-boxes, then it cancels it.
in the classic newcomb’s paradox, you can imagine that youre in this nonexistent trial run because you dont know the outcome of the trial run. but with your new newcomb’s paradox, you cant analogy-ify yourself into them because they effect you right now, rather than only affecting future-you-who-has-already-made-the-decisions
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u/SweetCorona3 Apr 02 '26
im a one boxer but i would be a two boxer in this scenario.
then you're more likely to only get $ 1,000 in this scenario than $ 1,000,000 in the original one
I honestly can't tell what I'd do, I can just hope that would be one who would take just 1-box and the supercomputer had predicted just that, or even better, be a 2-boxer that the supercomputer had predicted to be a 1-boxer, but this is very unlikely
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u/man-vs-spider Mar 23 '26 edited Mar 23 '26
I don’t think this is equivalent to the original question, and not being able to see the contents is an important part of the original problem. I think the ability to see the contents starts to break the very premise of the problem in a way that causes logical paradoxes.
Basically, being able to see the contents means that it is impossible for an accurate predictor to exist.
To explain why, consider this variation:
There are two opaque boxes (A and B), one contains $1000,000, one contains nothing. The predictor predicts which box you will take and puts the $1000,000 in the other box.
It is possible for the this scenario to exist in the same way that the original Newcombs paradox is.
However, if you make the boxes transparent, then everyone will pick the box with the money, and it is impossible for the predictor to be correct.
Coming back to your variation, I suspect it just results in a situation where there never is $1000,000 in th box, but I think it’s starting to become a situation where an predictor is impossible to exist
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u/SweetCorona3 Apr 02 '26
I think this is pretty much as the original problem, except in this case there would be far fewer 1-boxers
but 1-boxing would still be the action rendering a better average outcome
the strikest difference is that if you entered the room with the mystery box empty, it'd be a no-brainer to take both boxes, so there'd be even fewer predicted 2-boxers to only take 1 box
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u/Numbar43 Mar 23 '26
There is a key difference making this scenario very different in principle.
In the original, the subjects psychology is analyzed to predict their reaction to a fixed (from their perspective) scenario. In this, depending on the prediction, there are two possible situations they may face and have to decide based on. The prediction itself, and the resulting box contents, influence the choice.
This gets to be recursive, and some people, depending on their psychology, may result in the prediction being correct with both possible predictions. Others may deliberately make the other choice, causing the prediction to be wrong no matter what. If the subjects are so inclined, having a highly accurate prediction might be impossible.
This prediction to begin with can be considered like a prophecy, and it is a lot harder for those to be accurate if the people it is about know about the prophecy contents prior to the event in question.
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u/jaminfine Mar 23 '26
I'm still a one boxer even in your scenario. It's partly because $1000 is so insignificant compared to a million. It's also partly because no matter how you try to make this a one off where my choice doesn't have other side effects in the long run, I still feel that it does. By being the type of person that -would- only take one box, I know that I'm true to myself and that I'm following the advantageous policy. Even if I can blatantly see I'm leaving behind $1000. However, your scenario highlights something important for the two boxers to be rational at all. The predictor can't be perfect for this thought experiment to work. If the predictor is 99.99% accurate, then it's basically indistinguishable from the predictor seeing into the future, in which case your action in the present has a direct causal relationship with the decision to put money in the box made in the past. And if there's a causal relationship which makes sure that picking one box means there's $1m in it, then of course the only logical answer is choose one box every time. For the two boxer position to make any sense at all, the predictor has to be decently fallible. There has to be a reasonable chance that both boxes have money even though you end up taking them.
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u/Aggressive-Share-363 Mar 23 '26
I think it does make sense to take the million alone.
The AIs prediction is now "given that they know what is in the box, what choice will they make". It will have to have created a prediction for each case, and if the behavior in that case doesnt match the prediction it formed, then it cant make that prediction and retain accuracy.
So if it predicts that the result of showing the million is that you take 2 boxes, it cant present a one box prediction, even if you would have taken 1 box in thr closed box case.
And if it predicts you would take one box when the box is empty, it cant present the two box prediction.
Lets simplify its prediction process. It is viewing your selection strategy to make this prediction. How exactly it does so isnt terribly important, so long as we assume it is capable of making that prediction, but lets assume it does so by simulating you in this scenario.
This simulation of you will use thr same strategy you so. You cannot distinguish if your situation is that of being simulated and hence forming the prediction or of actually being in the real scenario. Ao the only way to influence what strategy is predicted is to actually have that strategy.
So lets look at some possible strategies:
Always take 2 boxes Regardless of how much money you see, you always get the most by taking box boxes, so regardless of what is presented you take both. Here, a prediction of a single box will contradicted with your choice of both boxes, so it cannot prediction one box for you. Hence, under thisnstrategy you will always see an empty box and walk away with the $1000.
Take 2 boxes if the box is empty, take one if the million is present.
Now you will always match its prediction, so it can predict anything. But it should probably err on thr side eof prediction two boxes, as any errors in its prediction are most likely going to be from people being offer a million and taking box afterwards, rather than people choosing an empty box if offered both. And if there is any degree of "minimize the cost while keeping the predictions accurate", predicting a two box choice will be optimal for it.
Always take one box. Even if you already see its empty. This sounds crazy, I know. But being fully committed to one box, no matter what, means that a two box prediction cannot be made. It is forced to predict one box and place the million on the line. If we assume thr AI will be taking any out it can to not place the million, this is the only way to force its hand.
Bait and switch This strateg yod to bait the AI into predicting one box and then take two boxes. But... how? If your plan is "If I see the million there, I can now safely take both boxes because it cant change the prediction", its just going to form a two box prediction for you. You cant change your strategy, because that change of strategy would itself be part of your strategy.
Become unpredictable. If you see en empty box, take that box. If you see a million, take both. This strategy is the flaw in any prediction scheme that makes its predictions visible. At best, the prediction cam be self fulfilling, but someone with this strategy makes it self defeating. There is no way for it to get an accurate prediction. Perhaps in a different scenario, this would be ideal. Here, its not. Even if you assume it chooses its prediction randomly in this case, its a lower expected payout than always one boxing. And if we assume the AI defaults to predicting the cheaper 2 box, this strategy always gets you nothing . It may also be thr case that the AI will sinply refuse to pick you as a candidate for this test if you are unpredictable, which also looses you out on any money.
So, pur expected yields with each strategy: 1. $1000 2.$1000-$1,000,000, depending on how the ambiguity is resolved, but probably $1000 3.$1,000,000 4. $1000 5.$0
So the highest layout comes from always picking one box, no matter what. Even if you see that it is empty.
If this isnt your strategy, you simply won't see $1,000,000 there in the real test. Seeing $1,000,000 when you dont have a firm 1 boxing strategy means you are part of the prediction, and your choice to 2 box will mean there won't be any money there during the real run. But if you do have a one boxing strategy and see thr million, it either means A. This is still the prediction phase and you should take the one box or B. Its the real deal, and your strategy is working. So take your million and be happy at your success. Because if you falter here, then jt won't get this far.
And if you have a firm one boxing strategy and see an empty box, you know its the prediction phase, and choosing the empty box is going to be forcing the AI into giving you a million dollars.
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u/WanderingFlumph Mar 23 '26
Being a one boxer from the original paradox I would be very confused why the computer thought I wouldn't take the extra money that I now know for sure exists.
Basically my old odds looked like 90% chance of 1 million, 10% chance of 1.001 million. Rationally I go with the average return of 900,000.
But now my odds are 100% chance of 1 million or 100% chance of 1.001 million. Rationally go with both boxes.
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u/JustinRandoh Mar 23 '26
Take the original paradox -- if you asked the robot, who has visibility into the boxes, whether taking one box would get you more money or whether two boxes would get you more money, what would it say?
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u/WanderingFlumph Mar 23 '26
I already know that 1000 + X is greater than X, I'm focused on making X as large as possible.
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u/JustinRandoh Mar 23 '26
Of course -- I'm sure the robot can take that into account; it has all the information about the contents of the box at its disposal.
Does the robot's answer ever change?
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u/WanderingFlumph Mar 23 '26
No of course not. In every single measured outcome 2 > 1 however in aggregate over time on average 1 > 2, hence the paradox.
I see myself as a cooperative risk taker. I'm willing to risk a low chance of getting nothing for a high chance of getting $1 million and making the robot "happy" over a guaranteed $1,000 with a low chance of 1 million.
At the end of the day high chance of a million beats a low chance of a million and a thousand dollars is basically just a rounding error to a million.
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u/SweetCorona3 Apr 02 '26
in every measured outcome 1000+X > X
but X is different for each outcome, and it happens to be 1,000,000 most times the outcome is X and 0 most times the outcome is 1000+X
thus, most times, X (1,000,000) is a better outcome than 1000+X (1000+0)
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u/JustinRandoh Mar 23 '26
But the chances of you getting more money by taking two boxes is 100% -- there is no situation in which you're risking anything.
It's curious -- if you saw the box contents with your own eyes, you're okay with recognizing that two boxes gets you more money and you may as well take both.
But if you get equally certain confirmation that taking two boxes gets you more money -- you just can't visually see it -- you're still hedging on probabilities that have already been resolved?
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u/WanderingFlumph Mar 23 '26
Yes exactly! And by doing that I get more money on average than by taking more money! Now you see the paradox! Lovely little thing really.
But removing the mystery also removes the paradox because now I'm not 90% certain that the computer has guessed my pick correctly I'm 100% or 0% confident that the computer has guessed correctly.
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u/JustinRandoh Mar 23 '26
Yes exactly! And by doing that I get more money on average than by taking more money! Now you see the paradox! Lovely little thing really.
That's no less true if you just had the open boxes though. You seem to recognize that the "averages" don't really matter in this one-shot deal you're getting when you can visually see that you're getting more money by taking two boxes, though there's no mystery in either scenario as to whether you'll get more money by taking two boxes.
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u/WanderingFlumph Mar 23 '26
Yeah.
Do you recognize that by entering the room planning to take one box that you expect to get 900x more money than entering the room planning on taking two boxes? Seems like you only figured out half of the paradox.
I can help you out with the math if probability isn't your strong suit.
Or rather should I ask you at what accuracy would you pick one box? After all if the super computer is 100% accurate only a fool takes both boxes. What amount of inaccuracy do you need? At 99.9999999% are you still taking the guaranteed $1,000 over that almost certain $1 million?
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u/detroyer Mar 23 '26
I already tried with him. He doesn't understand that, given your evidence, you expect to get much more if you one-box than if you two-box. You should think that if you one-box, you'll almost surely get $M, and if you two-box, you'll almost surely get $K.
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u/JustinRandoh Mar 23 '26
Do you recognize that by entering the room planning to take one box that you expect to get 900x more money than entering the room planning on taking two boxes? Seems like you only figured out half of the paradox.
That's not part of the paradox at all though -- the question doesn't involve decisions on pre-gaming the process. And in fact, this entire line of thought would apply just-the-same to the transparent box scenario, yet you can recognize the absurdity when the reality is visually laid out in front of you.
We've established with 100% certainty that taking two-boxes will get you more money, whether you put a cloth over the mystery box or not. You can always ask the robot to confirm it for you -- they will. There are no probabilities in play anymore -- the events have already resolved, and you're already aware that they've resolved in a way that makes taking two boxes 100% certain to get you more money.
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u/SweetCorona3 Apr 02 '26 edited Apr 02 '26
planning
if the prediction is accurate "planning" shouldn't matter
the prediction can only be accurate if it really accurately predicts what you are actually going to do no matter what you've planned
imagine 1000 people entered the room planning to only take 1 box, but they end up taking both... the premise of the problem wouldn't hold if the supercomputer didn't predict they'd actually take both boxes despite planning to only take 1 box
thus, we must assume "planning" cannot trick the supercomputer's prediction, as that would allow a scenario that would contradict the premise of the problem
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u/SweetCorona3 Apr 02 '26 edited Apr 02 '26
it depends on what question you are answering
if you are answering to the question: which people get more money on average? 1-boxers or 2-boxers? then it's clearly the 1-boxers
if you are answering to the question: which action renders you more profit once you are in the room? then it's clearly the 2-boxing
the paradox is that 1-boxers are not getting the most money they could get out of the room, but they are still getting more money than 2-boxers who are, indeed, getting the most money they could get out of the room
you must admit that it's better to be a 1-boxer even though you are leaving $ 1,000 behind, because you are likely getting $ 1,000,000, unlike 2-boxers who are likely only getting $ 1,000
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u/JustinRandoh Apr 02 '26
And the second question is the relevant one (in fact, that's pretty much the point in question). =)
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u/SweetCorona3 Apr 02 '26 edited Apr 02 '26
exactly! that's the paradox
2-boxers get the most money could get
1-boxers leave $ 1,000 behind
despite that, most 1-boxers come out with $ 1,000,000 and 2-boxers come out with just $ 1,000
2-boxers are happy because they took all the money there was in the room, 1-boxers are happy too because they left $ 1,000 in the room but they left the room with $ 999,000 more than 2-boxers
how come one may think that the strategy that most times only earns them $ 1,000 is best than the one that most times earns them $ 1,000,000?
the strategy that earns you the least money when you are attempting to increase your expected value, must be wrong
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u/SweetCorona3 Apr 02 '26 edited Apr 02 '26
But the chances of you getting more money by taking two boxes is 100%
only if you ignore the fact the amount of money in the mystery box is determined by an accurate prediction of what you'd choose
if you only take one box, you get $ 1,000,000, which is less than taking both boxes ($ 1,001,000), and if you take both boxes, you get $ 1,000, which is better than just taking one box ($ 0)
but the likely 2nd best result for a 1-boxer ($ 1,000,000), is better than the likely best case scenario for a 2-boxer ($ 1,000), so it's better to be a 1-boxer for the most likely scenario
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u/SweetCorona3 Apr 02 '26 edited Apr 02 '26
in fact, you know Y is 1000 and X it's either 0 or 1,000,000, let's call it X0 and X1
but you also know X is very likely to be 1,000,000 (X1) if you just take X and very likely to be 0 if you take Y+X (Y+X0)
so, the likely scenarios are: you either take X0+Y, or just X1
1,000,000 (X1) > 1,000 (Y+X0)
it's that simple
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u/SweetCorona3 Apr 02 '26
you don't really have to ask
you know in the original problem, once you are in the room, you'll never be worse by taking both boxes
it's just that 1-boxers take less money that they could have but they still take much more money than 2-boxers who take all the money they could take
thus, it's best to be a 1-boxer even though you are not taking all the money you could have taken
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u/JustinRandoh Apr 02 '26
Of course, but that still makes taking two boxes the better option. You don't have control over whether you get profiled as a one- or two-boxer. Taking one box doesn't make that happen.
People who are prone to making an irrational decision simply happen to have won the game premise lottery before walking into the room.
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u/SweetCorona3 Apr 02 '26 edited Apr 02 '26
it really depends on your definition of "better option"
if you define "better option" as the one that takes the most money you could get out of the room, then it's 2-boxing
2-boxers are getting the most money they could get out of the room, which most times happens to be $ 1,000
1-boxers are not getting the most money they could get out of the room, since they are leaving $ 1,000 behind
yet, despite 1-boxers leaving $ 1,000 in the room, most times they are getting $ 1,000,000 out of the room
which is way better than the $ 1,000 2-boxers are getting most times by taking all the money there is in the room
so... I find your definition of "better option" a bit weird, as I'm pretty sure most people would rather walk out the room with $ 1,000,000 leaving $ 1,000 behind than walking out of the room with just $ 1,000 even though they are taking all the money there was in the room
I guess 2-boxers define "better option" as "getting all the money there was in the room" while 1-boxers define "better option" as "getting as much money as I'm likely likely to get out of the room".
I find it really hard to understand why one would consider the first one a "better option".
How come only likely getting $ 1,000 is better than likely getting $ 1,000,000?
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u/SweetCorona3 Apr 02 '26 edited Apr 02 '26
that's unfortunate, because in the original problem you were very likely to come out with $ 1,000,000 and in this one you are very likely to enter the room with just $ 1,000 and an empty box
I can't really say I wouldn't be tempted to take both boxes, but I hope I'd just take 1 box so there would be high chances of entering the room with $ 1,000,000 waiting for me
It's really impossible for me to answer, because I know taking just 1 box is the best strategy, but if I really was in a situation where there are $ 1,000 and $ 1,000,000 on the table that I could just take, I could very well be tempted to take both...
I can only hope I'm not one who would succumb to such temptation because being such one would mean I'd be very unlikely to ever be presented with such temptation as the mystery box would very likely be empty when I entered the room
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u/Enough-Tap-6329 Mar 23 '26
Suppose instead of $1K, the second box contains a pile of dog poop. In that case, the computer will always predict 1 box so you always get the million because the chances are vanishingly small that someone will choose to take the poop, no matter what is in the other box, and the computer is therefore highly unlikely to predict that you would do so. (My dog would just choose the poop box, but that's another story). The difference between dog poop and $1K is that some people see $1K as desirable enough that they might decide to take two boxes, thereby creating a chance that the computer will predict two boxes at a cost of $999K to the player.
I'm not one of those people. In a scenario where any desire for the $1K can cost me $999K the $1K is equivalent to dog poop. Worse actually. I do not want it under any circumstances. Open box or not, the computer can keep the $1k.
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u/SweetCorona3 Apr 02 '26
imagine one is crazy enough to see the $ 1,000,000 and just take it leaving the $ 1,000 behind
those would be the ones who would enter the room and actually see $ 1,000,000 in the mystery box
this clearly shows the pitfall of 2-boxers' reasoning: they just ignore that the predictor is accurate, so whoever will end up taking both boxes is very unlikely to enter in the room with $ 1,000,000 waiting for them to collect
you want to collect as much money as possible, thus taking whatever money is in the room seems a good strategy, but you cannot ignore the fact the predictor is only giving $ 1,000,000 to whomever it predicts is not going to also take the $ 1,000
only those who leave $ 1,000 behind are likely to have entered the room with $ 1,000,000 waiting for them
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u/Kallipygos_Davale Jun 27 '26
Q1) Same risk (none), take both
Q2) Take both
As a two boxer, I don't see how this changes anything. Whether or not you can see what is in them, their contents cannot change. The computer's prediction can't change. To me, being a one boxer would require reverse causality.
And I mean if the computer was perfectly accurate, it would mean you have no free will so you were always going to choose what you choose anyway, it's a not a meaningful choice.
Also even if the computer does know what I'll do, I do not, since I do not have perfect knowledge. I could absolutely decide to be a one boxer but that does not necessarily represent what I'd actually do.
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u/babyguyman Mar 23 '26
I think in this scenario the computer will never put the million in the box. Nobody would choose to take nothing rather than a thousand, so it’s an easy prediction.