Someone says they've built a machine that can perfectly predict what you will do. Do you believe them?
If so, take one box.
If not, take both boxes.
But even if you don't believe them, it's got a 50% chance on a coin toss.
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.
Yeah, at least you'll have an extra box to keep your stuff in.
It's much easier if you reframe the problem:
Someone says they've built a machine that can perfectly predict what you will do. Do you believe them?
If so, take one box.
If not, take both boxes.
But even if you don't believe them, it's got a 50% chance on a coin toss.
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.
Yeah, at least you'll have an extra box to keep your stuff in.