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@sh.itjust.works 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.
No information regarding the machine's accuracy is provided, but the fact that you are asked to make a choice implies that it is not perfect. The question explicitly specifies that the prediction has already been made and the contents of box B have already been set. You can't retroactively change the past and make the money appear or disappear by making a decision, so if your choice must match the prediction, then it's not your choice at all. You lack free will, and the decision has already been made for you by the machine. In that case the entire question is meaningless.
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:
Machine predicts I take both, box B is empty:
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@sh.itjust.works 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.
No information regarding the machine's accuracy is provided, but the fact that you are asked to make a choice implies that it is not perfect. The question explicitly specifies that the prediction has already been made and the contents of box B have already been set. You can't retroactively change the past and make the money appear or disappear by making a decision, so if your choice must match the prediction, then it's not your choice at all. You lack free will, and the decision has already been made for you by the machine. In that case the entire question is meaningless.