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.
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.
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.
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.
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.
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.
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