A and B every time because if the machine "predicts" you take both, you get 1kk usd, if the machine "predicts" you take only B, you get 1.1kkk usd. It's a free million dollars at least. Buy a house and invest the rest.
If (Box A Taken = True)
{place ($0) in Box B}
else
{place ($1,000,000,000) in Box B}
Machine doesnt care if you also take Box B, it only cares if Box A is one of the boxes taken. If you take no boxes, Box B would still have a billion dollars, although thats kinda dumb choice from a gameshow host's perspective.
Regardless of whether the machine is right, if you don't believe it can perfectly predict what you'll do then taking both boxes is always better than just one.
Both! Critically, the contents of box B depend on the machine's prediction, not on whether it was correct or not (i.e. not on your subsequent choice). So it's effectively a 50/50 coin toss and irrelevant to the decision-making process. Let's break down the possibilities:
Machine predicts I take B only, box B contains $1B:
I take B only - I get $1B.
I take both - I get $1.001B
Machine predicts I take both, box B is empty:
I take B only - I get nothing.
I take both - I get $1M.
Regardless of what the machine predicts, taking both boxes produces a better result than taking only B. The question can be restated as "Do you take $1M plus a chance to win $1B or would you prefer $0 plus the same chance to win $1B?", in which case the answer becomes intuitively obvious.
But if it's true that the machine can perfectly predict what you will choose, then by definition your choice will be the same its prediction. In which case, you should choose one box.
Though OP never actually stated that the machine can perfectly predict the future. If that’s the case, then yes, you should just take box B. But we’re not given any information about how it makes its prediction. If @Sordid is correct in assuming it’s a 50-50, then their strategy of taking both is best. It really depends on how the machine makes its prediction.
We’ve been given no information on the accuracy of the machine’s predictions. Therefore, we have to assume it has just as good of a chance of being wrong as being right. There’s essentially a 50/50 chance that box B has $1,000,000,000 regardless of my choice, so I would choose the option that at least guarantees the smaller prize while still giving me the same chance at the larger prize.
It depends. If you mean flip a coin, then you should know that no coin flip or dice roll is truely random, it is random to us only because we couldn't predict it with our current technology. This scenario assumes that there are machines in the world that can predict the future, we just don't know whether this particular machine is accurate or not.
Now if you are talking about quantum-based randomness, I mean... I think the machine could just put $0 in the second box just to fuck with you.
The machine has already done it's prediction and the contents of box B has already been set. Which box/boxes do you take?
If my choices don't matter and the boxes are predetermined, what point is there to only taking one box? The machine already made its choice and filled the boxes, so taking both boxes is always the correct answer. Either I get $1,000,000 if the machine thought I would take both, or I get $1,001,000,000 if it didn't. This is a false dilemma, there is never a reason to take just one box.
This isn't a false dillemma. Imagine if the way the machine predicts is by copying your brain and putting it in a simulated reality, then the copy of you gets asked to choose which boxes to take, the exact same way and be given the exact same information. Under this assumption, the machine could predict with 100% accuracy what the real you would've chosen.
How do you know you are even the real you. You could just be the machine's simulation of the real you.
There is a dilemma and the dilemma is about how much you want to trust the machine.
If you are a simulation, then your choice doesn't matter. You will never get any real benefit from the boxes. It's like saying, "there is also a finite possibility that the machine is lying and all the boxes are empty". In which case, the choice is again irrelevant.
Situations in which your choice doesn't matter are not worth considering. Only the remaining possibility, that you are not a simulation and the machine is not lying, is worth considering.
I feel like unless we're talking about supernatural AI the only answer is A&B
Otherwise the box has no real way of knowing what you would've picked, so it's complete RNG.
If there was a realistic way that it could make that decision i'd choose only B, but otherwise it just doesn't make sense.
edit: I also didn't realize until after I read it that box A always has the million dollars. So there's actually no reason to pick only box B in this scenario. The paradox only makes sense if box A is significantly less than box B. It's supposed to be a gambling problem but A&B is completely safe with the changes made.
Box A and B as the prediction has already been made so the choice has no bearing on the contents at this point. You either get the guaranteed million or both.
Well what you choose may not direct affect what is inside Box B, but there is still a huge difference between the two choices.
Imagine the way that the machine did it's prediction was copying your brain and making this copied brain choose in a simulation. Assuming the copied brain is completely identical to your brain, the machine could predict with 100% accuracy what the real you would choose. In this sense, what you choose can affect what's inside Box B (or rather, what your copied brain chooses can affect whats inside Box B).
One more thing to think about: How do you know that you aren't the simulated brain that's been copied?
Here’s my solution to Newcomb’s Paradox: the predictor can be perfectly infallible if it records your physical state and then runs a simulation to predict which box you’ll pick. E.g. it could run a fancy MRI on you as you are walking through the hallway towards the room, quickly run a faster-than-real-time physical simulation, and deposit the correct opaque box into the room before you open the door. The box, the hallway, the room, the door are all part of the simulation.
Here’s the thing: a computer simulation of a person is just as conscious as a physical person, for all intents of “consciousness”. So as you are inside the room making your decision, you have no way of knowing if you are the physical you or the simulated you. The predictor is a liar in a way. The predictor is telling the simulated you that you’ll get a billion dollars, but stating the rules is just part of the simulation! The simulated you will actually be killed/shut down when you open the box. Only the physical you has a real chance to get a billion dollars. The predictor is counting on you to not call it out on its lie or split hairs and just take the money.
So if you think you might be in a simulation, the question is: are you generous enough towards your identical physical copy from 1 second ago to cooperate and one-box? Or are you going to spitefully deprive them of a billion dollars by two-boxing just because you are about to be killed anyway? Remember, you don’t even know which one you are. And if you are the spiteful kind, consider that we are already making much smaller time-cooperative trade-offs all the time, such as the you-now taking a breath just so that the you-five-seconds-from-now doesn’t suffocate to death.
What if the predictor doesn’t use a MRI or whatever? I posit that whatever prediction method it uses, if the method is sufficiently advanced to be infallible then somewhere in the process it MUST be creating conscious observer instances.
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