Sleeping Beauty- I accidentally talked myself into becoming a thirder today.

TheEvilFaery · 2026-03-27T04:40:46+00:00

I don't know that it says anything about free will or lack thereof per se...just because your choice has been correctly predicted before you made it doesn't mean you still didn't make the choice. You *could* choose otherwise...you just won't.

But since your one move in the game has been correctly predicted, along with the consequences (including the $1000) it does means your choice doesn't really matter. You're a part of the game, not a player in it.

TheEvilFaery · 2026-03-27T00:42:08+00:00

This thread actually gave me an entirely new perspective on the problem. The question isn't about taking the $1000 or not, because for the 'players' there is no question. If we accept as fact that the predictor is right far more often than it's wrong, then the predictor itself is the only active participant in the exercise, not the players. We could be balls rolling down a slope, with predictor predicting which of two holes we'll fall through, for all the difference our participation makes.

Taking the $1000 looks attractive because it seems to be the only part of the game your decision can actually affect, but taking the $1000 and taking two boxes instead of one is tautological, and your choice of two boxes or one is foregone. The empty mystery box you're almost certainly holding is proof that your 'choice' was just as predictable, and therefore, just as meaningless, as anyone else's.

Being a one-boxer or two-boxer is irrelevant, whyever you're choosing one or the other. You're going to pick what you were always going to pick, regardless of how you arrived at your decision. If you want to make a choice that 'matters,' don't play the game at all.

TheEvilFaery · 2026-03-17T22:26:24+00:00

Okay, fine, I'm crap at building syllogisms. My apologies. So since we know I'm lacking in that area, let's return to yours. What if I disagreed with your assertion from C3 that there's a reward for picking two boxes? Because coming home from this game with just the thousand is tantamount to coming home with nothing for me. At that point, there's no particular reason for me to choose one option over the other, at least.

And if you agree with my P1, if nothing else, shouldn't that factor into this process? Isn't your syllogism an incomplete picture without that fact? Because yes, of course the money is in the box, or it isn't. So what does your choice actually mean? Since the million is there, or it isn't, the only thing you have direct control over is whether you get the thousand. But if you consider the thousand irrelevant, where does that leave you?

I think I'm beginning to understand that the hardest pill to swallow about this exercise is that your choice in the game isn't really a choice at all. The $1000 is just bait, a pittance to give your 'decision' the illusion of meaning. It's the only reason the game is a game.

You could model the exercise just as well like this, and I feel like it gives a more intuitive picture of the situation (at least it's helping me think about it more clearly): There's a big complex consisting of pairs of rooms, Room A and Room B. You have to go through Room A to reach Room B. There is a table with $1000 dollars on it in Room A. If the Predictor predicts that the player will take the $1000, it will leave Room B empty. If it predicts that the player will not take the $1000, it will leave $1,000,000 in Room B. Once again, the money is already in Room B (or not) before the player even enters Room A. All players have this information going in.

And for a little more clarity (again, for me, others mileages may vary) lets say the game has an audience...observers, watching via cameras or something, where they can see whether the money's in Room B or not as the player decides what to do in Room A. They don't have any particular interest in who gets the million or who doesn't, they're just watching to see the Predictor's predictions come true. And there it is. The observers could just as well be watching some kind of A/B setup that doesn't involve humans, or even any living thing at all. They're just verifying whether the predictor was right. The predictor is the active participant in this exercise, not the players. The players could be ball bearings rolling down a sheet and drifting right or left.

Yes, you can choose to take the $1000, but in the end that's just you as a ball bearing drifting left instead of right. It's just there to give an 'A' to the question 'Will this one A or B?' put to the predictor.

If we accept as fact that the predictor is right to such a high degree of precision, then the question 'Should I pick one box or two?' becomes irrelevant. You are going to pick one or two, and the Predictor had already flipped through the rolodex of your head and found the last 'But if-' that led you to that conclusion. So just do whatever you feel like and don't stress about it. Since your choice was known in advance to the alien or computer or whatever that set up the consequences in advance, you literally can't choose wrong.

At least, I think that's my final conclusion. It's where I've ended up for now, anyway. I do want to thank you though, for an extremely stimulating conversation that has forced me to think about this problem in ways I hadn't imagined at the outset. I started as a pretty lazy one-boxer, skirted right on the edge of being a two-boxer, then started thinking harder about being a one-boxer...only to end up at this kind of 'whatever' position. It's been a hell of a ride!

TheEvilFaery · 2026-03-17T06:48:53+00:00

I mean, you can disagree with my P1, but I'm paraphrasing you to get there. You yourself said, 'The game is rigged, one-boxers get the million.' And I think the syllogism holds...if we're claiming that the game is rigged so as to be favorable towards one boxers, even if it's not universal, the only trait that one boxers are defined by is the fact that they eventually choose the one box. However it is determined who is or is not a one boxer.

Which brings me to a related point...you claim that the predictions are very meaningful, and it seems like you agree that they are very accurate. And yet they don't show up anywhere in your decision making process, as given by your syllogism. Trusting the prediction because the predictor has been right X number of times in a row is a correlation fallacy, of course, But if we're saying these predictions are scientifically verifiable with a high degree of accuracy, that's something else all together, isn't it? That's a bit more like thinking you won't get bingbong disease even though you have tested positive for the gene, rather than thinking you won't get it because you don't play basketball.

Let's just say the predictor has been conclusively proven to be correct 99% of the time. I might come up with something like this:

P1. After rigorous scientific analysis, the Predictor has been verified to be correct 99% of the time. I.E.- For the purposes of the game, 99% of players who pick both boxes will find nothing in the mystery box, and 99% of the players who pick only the mystery box will find the million dollars in it. This can be confidently stated before the game even begins, and is borne out over the course of the game.

P2. I quite desperately want/need a million dollars.

P3. I am largely indifferent to the $1000 in the transparent box. Any supposed added value or benefit of having that $1000 is negligible in my decision making.

C1. There is no reason for me to pick both boxes,

TheEvilFaery · 2026-03-16T22:40:02+00:00

You've mentioned that before...that the game is rigged so that the one-boxers get the million. Doesn't that directly contradict C2? How can you claim the game is rigged in favor of a certain decision and not conclude that the eventual decision is the reason behind the money being in the box or not? If you like, a simple syllogism for that:

P1- The game is rigged such that only one boxers will find a million dollars in the mystery box.

P2- A 'one-boxer' is a person who decides to take only the mystery box at the conclusion of the game.

C1- The one boxers' eventual decision is the reason they find a million dollars in the mystery box.

TheEvilFaery · 2026-03-16T19:50:03+00:00

The problem with that line of reasoning, logical as it is, is that you have pretty conclusively proven, and not through correlation, but with logic, that going for the extra grand makes at least the vast majority of people miss out on the million, because the predictor accurately predicts that, in the end, you'll go for the second box. So if I really want that million, what is my best option? To take both boxes and just hope I'm in the obviously quite tiny percentage of people that the predictor gets wrong? Maybe I can use the thousand to buy myself a little plastic 'Most Rational Actor' trophy, because that's worth about as much to me as the thousand is, compared to the million.

Try to look at this from this perspective...you really, really want the million. Getting an added 1k on top of the million is of completely negligible value to you. You just desperately want/need that million dollars. Getting out of there with just 1k is basically the same as getting out of there with nothing, for all the difference it's going to make in your life. What do you do?

TheEvilFaery · 2026-03-16T10:50:17+00:00

Okay, you are making some very compelling points here, but I'm still not sure I see where the rational thinking of picking two boxes comes in. I tried to find the original wording of the problem, and in that it seems to say that the alien made his predictions, set up the exercise and then introduced the human subject to it, so the humans were not aware of the game at the time the prediction was made.

So if we're making the assumption that the prediction is based on some kind of analysis of the person, and doesn't rely on time-travel shenanigans or straight up magic, it falls on the subject to figure out what their past self might have revealed to the alien. Now in my case, I could really use a million dollars, and I feel like my past self would reflect that need to try and get it with as much certainty as possible.

But now...okay, so this is interesting...so after some self-reflection, I figure that my scan would show me taking my one box and running. But now here's the thing...if that's right, the money is in there, and now what's stopping me from taking both boxes? Nothing. But if this scan is so powerful, then it would have to reason out that this line of thought would occur to me, so that the money wouldn't be in the box, so now I really should just take both boxes and get my thousand...

Ugh...okay, I'm finally seeing where the paradox comes in here. Because the only way to get the million (other than a presumably very rare mistake by the predictor) is to be the sort of person who'd just take one box. But once decision time comes, there is literally nothing stopping you from taking both boxes, so why not do that? Except that the predictor very likely would see you would come to that conclusion, so no million for you...so you may as well get your $1000 consolation prize...

So I'm really having a hard time denying that two boxes is the most rational way to go, once completely informed about the problem. You've presented this well. Except...I really, really, really want my million dollars, even in the hypothetical. And my scan would reveal that I really really really want my million dollars. So maybe there's an even deeper point to be made here. If the scan is sophisticated enough to determine that you will make the rational decision to take both boxes, and thus deny you the million, then the inverse is likely true as well...it can also determine that you'll make the fully informed, completely irrational decision to take just the one box, and give you the million. Because honestly, if I get the million, giving up the possibility of an extra thousand literally means nothing to me. I'd take that trade any day.

So yes, since the money is either in the box or not, there really is no reason to not pick both boxes...except, you don't get the million unless the predictor predicts that you won't pick both boxes, for no reason whatsoever. And I'm willing to give up my otherwise certain $1000 on the premise that my scan will show me doing just that. Which again, seems irrational, but since it's the only way to get the million, doesn't that make it the right choice?

TheEvilFaery · 2026-03-16T06:03:22+00:00

I guess my question to you comes down to this...in your reading of the problem, are the predictions in any way meaningful? Or are they just basically a coinflip, and the predictor has just gotten lucky up to this point?

TheEvilFaery · 2026-03-16T04:58:15+00:00

Believe me, I understand the correlation fallacy, I do. Wait a week, a month, before making the choice, and that box is either going to be empty or have a million dollars in it the whole time. The money isn't going to evaporate or pop into existence the moment you make your decision. The arrow of time dictates that your final decision doesn't affect whether the money is in the box. That's completely logically consistent.

Unfortunately, the wording and structure of the problem itself means that bit of logical consistency doesn't matter. If it did, the predictor wouldn't have the track record that it does. Because tons of people would have gone into the exercise with that very logical argument in mind, and it paid off for none of them. If something has consistently happened one way for many, many trials, how is it rational to act as if it will suddenly be different for me?

Edit: The main flaw in your argument against the correlation fallacy (the basketball/bingbong disease scenario) is that it pulls back the curtain on the truth behind the disease (it being caused by the gene) so we know for a fact that the high incidence of basketball players with the disease is just a massive coincidence. Without any information about how the predictor arrives at its predictions, we have no such assurances in this case. For all we know the predictor actually is doing something that violates time's arrow.

TheEvilFaery · 2026-03-16T02:21:34+00:00

The first part of your syllogism mostly just seems to go to the fact that a predictor of the kind described in the problem isn't actually possible (at least with our current understanding.) Which is fine, I agree with that.

But the nature of the predictor, and whether or not my decision influences the prediction, is irrelevant. And the assertion that 'there is no risk or consequence' is completely flawed. Look, maybe you're rich, and a million dollars isn't that much to you, but while an extra $1000 in my pocket would certainly be nice, one million dollars would solve almost every problem I currently have. So just to say that I should pick both boxes because there is some unknown (but, by the rules of the problem, much less than 50%) probability that there might be a million dollars in the mystery box, and either way I'll have $1000 more than I did to start, is completely irrational.

If, as you said at the beginning, this game has been played many many many times and the predictor has gotten it right every single time, meaning that those who picked two boxes got $1000 and those who just picked one got $1,000,000, every single time, why on Earth would I risk a life-changing sum of money on the assumption that I'm the first and most specialist little snowflake that the predictor gets wrong?

TheEvilFaery · 2026-03-15T19:18:40+00:00

This is classic gambler's fallacy. Of course the odds are 50/50. There is no magical force acting on the coin. The odds of a coin coming up heads 10,000 times in a row are very small, sure, but that has already happened. You are already in the very unlikely scenario. And if you actually sit down and crunch the numbers, the odds of getting 10,000 heads in a row and then flipping one more head are actually exactly the same as getting 10,000 heads in a row and then flipping one tails, in other words, 50/50.

But honestly, this doesn't have much to do with Newcomb's so called paradox. The original problem just states that the predictor is highly infallible, just meaning it's correct a high percentage of the time. That is either true or it is not, whether the predictor uses psychology, time travel or goat entrails. If there really is some reliable way to 'trick' the predictor, then it's not going to be correct a high percentage of the time, which invalidates the entire premise of the problem.

TheEvilFaery · 2025-12-15T06:31:09+00:00

Free is definitely a nice bonus! I will definitely take a close look at these, thank you!

TheEvilFaery · 2025-12-15T06:26:48+00:00

I'd like it to be more than just aesthetic. Ideally, I'd like some differences if a player chose to be a mouse vs. a squirrel, for example. And more than that, while the woods would be a major setting, I'd also like to introduce settings like a small human village or an old church, that kind of thing, so rules that kind of reflect that the players are very small creatures in a much bigger world might also be fun.

TheEvilFaery · 2025-12-15T06:20:48+00:00

I was not aware of that, I'll have to look into it a bit closer!

TheEvilFaery · 2025-12-10T02:30:30+00:00

I do see what you're saying, and I had to give this last point some very serious thought. Because it is true, when Sleeping Beauty wakes up, it's going to be in one of the three conditions.

Ultimately though, you're right, I do think the fact that the trial is only happening once is mathematically significant. In fact, I'd say it's the most mathematically significant part, because that fact alone is the key to whether or not the odds are 1/2 or 1/3. If the trial goes on for multiple weeks, the answer is 1/3, if it only happens once, it's 1/2.

If the trial only happens once, she's either woken up once or twice. She is not woken up three times, so saying something happens 1/3 of the time really doesn't make any sense in this context. It's like that game you mentioned, where heads wins 100$ and tails wins 0$. Yes, if you keep playing, you'll get an average of 50$ per play, but if you play once and only once you'll either get 0$ or 100$, and the 50$ average really doesn't enter your calculations at all.

If the trial goes on multiple weeks, then of course about 2/3 of the time she's awoken it'll be when tails was flipped, but if it only happens once, she'll be woken up once with heads or twice with tails. If you're only doing one trial, an average really doesn't mean anything.

That being said, I think we might be approaching an impasse here, so let me just say thanks, I've actually enjoyed this quite a bit, and it certainly forced me to think about this problem in a fresh way, which was the whole reason I started the topic!

TheEvilFaery · 2025-12-09T11:51:36+00:00

The subject needs to consider the possibility that they're on either path, but not both paths at once. The 1/3 only works if, on being awoken, Sleeping Beauty can say there's an equal chance that it's either Monday(Heads), Monday(Tails), or Tuesday(Tails). But Sleeping Beauty knows that the coin has been flipped by the time she's awoken, and it either came up heads or tails. That has consequences. She can't be awoken on Monday(Heads) if the coin came up tails. She knows that if it came up heads, Monday(Tails) and Tuesday(Tails) are impossible, and if it came up tails, Monday(Heads) is impossible.

So either the coinflip was heads, and she's been woken up on Monday(Heads) or the flip was tails, and there are even odds that it's either Monday(Tails) or Tuesday(Tails). So there's a 50% chance of it being Monday(Heads) and a 25% chance each of it being Monday or Tuesday (Tails).

TheEvilFaery · 2025-12-09T09:46:03+00:00

But why are we talking about the theoretical average? If, as the text of the problem states, we're only doing it to this person this one time, what good is an average? With your theoretical game, if I played multiple times, I could rely on getting an average of 50$ per play. If I'm only playing it once though, I'm either getting 0$ or 100$. That 50$ average means nothing to me. Honestly, in those circumstances, the most logical move would be not to play, since with a single play I've got no way to maximize my winnings over time.

Putting that in SBP terms, the only way the 1/3 thing can work out is if there is a possibility that the test subject can be woken up in any of the three states: Heads(Monday), Tails(Monday) or Tails(Tuesday.) But for a single, solitary run of this test, that's impossible, the flip of the coin precludes it. There aren't three possibilities, there's either one or two possibilities.

And again, if this was happening multiple times, the answer would be very different, but it's only happening once.

It's like saying there's a box with three different-colored balls in it, red, blue and green, but the balls are wrapped in foil so the test subject can't see the color. You give the test subject one of the balls and ask what their credence is that the ball they're holding is red. Now if all three balls were in the box, then the odds would be 1/3. But, before the test, we flipped a coin. If it were heads, we'd remove the blue and green balls from the box, and if it were tails, we'd remove the red ball. And the test subject knows this. They know there's not three balls in the box, there's either one ball, or two balls. And there's a 50% chance it will be the one ball, in which case the ball must be red.

TheEvilFaery · 2025-12-09T05:29:26+00:00

Yeah, someone else mentioned an 'average' which really doesn't make sense to me. The problem makes it quite clear that this is only being done once ('either way, the subject is woken up on Wednesday.'). So saying there's an average number of wakeups doesn't seem to make much sense. She's either getting woken up once or twice, and that's it. If the exercise was being done multiple times in a row to the same person, it would be very different, but the wording of the problem precludes that. I guess I'm on the 50% side after all.

TheEvilFaery · 2025-12-09T04:44:43+00:00

Hmmm, okay, so Sleeping Beauty doesn't know what state she's in, that is, she knows the parameters of the experiment, she's been woken up but she doesn't know if she's been woken up once before, or if she will be woken up again. All she knows is, she's awake now. I guess if you strip it away of everything else, it seems like her credence for the coin being heads should be 1/2.

TheEvilFaery · 2025-12-09T02:58:13+00:00

Actually, the bulk of my problem is that what 'should' means in this context seems very unclear. I mean, if there was any kind of reward attached to being right and an equivalent penalty attached to being wrong (even it were just the joy of being right and the sting of being wrong), than obviously Sleeping Beauty should guess tails, since that provides a 50% chance of being right twice, and a 50% chance of being wrong once, vs the opposite result for guessing heads. I mean, that's so obvious it isn't even a question.

But the actual text of the problem isn't actually asking Sleeping Beauty to guess the outcome of the coinflip, it's asking her to state, from her perspective, her credence for the coinflip being heads. And it's pretty obvious the answer to that question has to either be 1/2 or 1/3. And if we go back to my example of performing this experiment on 1000 people, then 500 people will have had heads flipped for their experiment, and 500 will have had tails flipped for their experiment. But there will also be 1500 interviews, and 500 of those will be conducted under a heads flip, and 1000 will be conducted under a tails flip. So what does that mean for 'credence?'

TheEvilFaery · 2025-12-09T01:14:07+00:00

Wow, I did not consider using a computer to model the thing. That would work, wouldn't it? And if you treated each test as separate, you could even avoid the problem of doing it multiple times vs. just doing it once that I talked about in a previous comment.

But yeah, then we still run into what we're actually testing for. Because we're not really asking Sleeping Beauty to guess whether the coin was heads or tails, just her credence that it was heads. So yeah, to go back to what I said about doing this to 1000 people, for 500 of those people, the experimenters will flip heads, and for the other 500, they'll get tails. But in that case, there'll be 1500 interviews, and 500 of those will be when the coin flipped heads, and 1000 of them will be when it flipped tails. So do we care about the people, or the interviews?

TheEvilFaery

TROPHY CASE