If your goal is to show that Omega is “impossible” or “inconsistent”, then having Omega adopt the strategy “leave both boxes empty for people who try to predict me / do any other funny stuff” is a perfectly legitimate counterargument. It shows that Omega is in fact consistent if he adopts such strategy. You have no right to just ignore that counterargument.
This contradicts the accuracy stated at the beginning. Omega can’t leave both boxes empty for people who try to adopt a mixed strategy AND also maintain his 99.whatever accuracy on one-boxers.
And even if Omega has way more computational than I do, I can still generate a random number. I can flip a coin thats 60⁄40 one-box, two-box. The most accurate Omega can be, then, is to assume I one box.
This contradicts the accuracy stated at the beginning. Omega can’t leave both boxes empty for people who try to adopt a mixed strategy AND also maintain his 99.whatever accuracy on one-boxers.
He can maintain his 99% accuracy on deterministic one-boxers, which is all that matters for the hypothetical.
Alternatively, if we want to explicitly include mixed strategies as an available option, the general answer is that Omega fills the box with probability = the probability that your mixed strategy one-boxes.
This contradicts the accuracy stated at the beginning. Omega can’t leave both boxes empty for people who try to adopt a mixed strategy AND also maintain his 99.whatever accuracy on one-boxers.
And even if Omega has way more computational than I do, I can still generate a random number. I can flip a coin thats 60⁄40 one-box, two-box. The most accurate Omega can be, then, is to assume I one box.
He can maintain his 99% accuracy on deterministic one-boxers, which is all that matters for the hypothetical.
Alternatively, if we want to explicitly include mixed strategies as an available option, the general answer is that Omega fills the box with probability = the probability that your mixed strategy one-boxes.