It seems to me that no rationalist should accept the ‘givens’ in this scenario without a lot of evidence.
So what am I left with. Some being who hands out boxes, and 100 examples of people who open 1 box and get $1M or open both boxes and get $1k. I am unwilling to accept on faith a super-intelligent alien, so I will make the simplifying assumption that the being is in fact Penn & Teller. In which case, the question simplifies to “Am I willing to bet at 1000:1 odds that Penn & Teller aren’t able to make a box which vanishes $1M if I choose both boxes.” To which I respond, no.
No reversal causality required. No superintelligent prediction required. I simply know that I can’t beat Penn & Teller at their own game 999 times out of 1000.
If I was advising an AI on how to solve this question, I might recommend guessing many sets of three random numbers, and just looking at the ratio of ‘yes’ to ‘no’. A result of 1⁄6 yes, could then be matched against various rules and there ratios. This would greatly reduce the solution set, and ordering would likely jump to the front as a likely possibility.
If I were answering the question for myself, I would likely try to break it, by that I mean get you to either add a new rule, or to say ‘I don’t know’. { e, i, pi }