Once your calculator returns the result “even”, you assign 99% probability to the condition “Q is even”. Changing that opinion would require strong bayesian evidence. In this case, we’re considering hypothetical bayesian evidence provided by Omega. Based on our prior probabilities, we would say that if Omega randomly chose an Everett branch (I’m going with the quantum calculator, just because it makes vocabulary a bit easier), 99% of the time Omega would chose another Everett branch in which the calculator also read “even”. However, Omega seems to like messing with our heads, and so we can conclude that this is probably not the algorithm Omega used to generate this problem. Instead, Omega purposely searched for an example of that 1% of all possible worlds in which the calculator read “odd”. If we assume this behavior on the part of Omega, the bayesian weight of the evidence (the knowledge that there is at least one possible world in which the calculator reads “odd”) goes way down. It might be something, especially because we aren’t 100% certain of Omega’s motivations and algorithms, but it certainly wouldn’t be enough to adjust our prior probability all the way to a point below 50%.
Once your calculator returns the result “even”, you assign 99% probability to the condition “Q is even”. Changing that opinion would require strong bayesian evidence. In this case, we’re considering hypothetical bayesian evidence provided by Omega. Based on our prior probabilities, we would say that if Omega randomly chose an Everett branch (I’m going with the quantum calculator, just because it makes vocabulary a bit easier), 99% of the time Omega would chose another Everett branch in which the calculator also read “even”. However, Omega seems to like messing with our heads, and so we can conclude that this is probably not the algorithm Omega used to generate this problem. Instead, Omega purposely searched for an example of that 1% of all possible worlds in which the calculator read “odd”. If we assume this behavior on the part of Omega, the bayesian weight of the evidence (the knowledge that there is at least one possible world in which the calculator reads “odd”) goes way down. It might be something, especially because we aren’t 100% certain of Omega’s motivations and algorithms, but it certainly wouldn’t be enough to adjust our prior probability all the way to a point below 50%.