I couldn’t resist.
1. If the problem’s purely financial to you, then you should take box B only (setting aside the fact that windfall gains often don’t end up being gains at all). Surely the diminishing marginal utility of the prize money is such that you’d hardly notice the extra $1000 you could have won?
2. If the problem’s really the issue of free will, then you should build some sort of device that generates a decision for you on the basis of the actions of one of those sub-atomic particles which behaves, to the best of our knowledge, purely randomly. You should do this because, if you beat the immortal predictor, you can relish in the fact that you quite probably don’t live in a deterministic universe. On the other hand, if you lose you can tell yourself that she just got lucky (50% chance), and that it’s still possible the universe isn’t deterministic.