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.
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?
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 (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.
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