(If Omega can choose whether to let you play the game, which is the only game available to you, and the game has the rule that the numbers must be equal, then you should two-box to improve your chances of being allowed to play when the Lottery number is composite, and thus capture more of the composite Lottery outcomes. This works not because you are increasing the conditional probability of the number you get being composite (though you do), but because you are increasing the prior probability of playing the game with a composite Lottery number.)
Okay. I feel much more confident in my answer, then :P.
Double-checking: What if the lottery picks primes and composites with equal frequency?
… then, on average, you’ll get into half the games and make twice the money, so you should still two-box. I think.
So, assuming you/Manfred don’t poke holes into this, I’ll edit the original post. Thanks—having a clear, alternative two-box problem makes understanding the original much easier.
(If Omega can choose whether to let you play the game, which is the only game available to you, and the game has the rule that the numbers must be equal, then you should two-box to improve your chances of being allowed to play when the Lottery number is composite, and thus capture more of the composite Lottery outcomes. This works not because you are increasing the conditional probability of the number you get being composite (though you do), but because you are increasing the prior probability of playing the game with a composite Lottery number.)
(Responded before your edit, so doubly-curious about your answer.)
Okay. I feel much more confident in my answer, then :P.
Double-checking: What if the lottery picks primes and composites with equal frequency?
… then, on average, you’ll get into half the games and make twice the money, so you should still two-box. I think.
So, assuming you/Manfred don’t poke holes into this, I’ll edit the original post. Thanks—having a clear, alternative two-box problem makes understanding the original much easier.