I don’t get paid on the basis of Omega’s prediction given my action. I get paid on the basis of my action given Omega’s prediction. I at least need to know the base-rate probability with which I actually one-box (or two-box), although with only two minutes, I would probably need to know the base rate at which Omega predicts that I will one-box. Actually, just getting the probability for each of P(Ix|Ox) and P(Ix|O~x) would be great.
I also don’t have a mechanism to determine if 1033 is prime that is readily available to me without getting hit by a trolley (with what probability do I get hit by the trolley, incidentally?), nor do I know the ratio of odd-numbered primes to odd-numbered composites is off-hand.
I don’t quite have enough information to solve the problem in any sort of respectable fashion. So what the heck, I two-box and hope that Omega is right and that the number is composite. But if it isn’t, then I cry into my million dollars. (With P(.1): I don’t expect to actually be sad winning $1M, especially after having played several thousand times and presumably having won at least some money in that period.)
I don’t get paid on the basis of Omega’s prediction given my action. I get paid on the basis of my action given Omega’s prediction. I at least need to know the base-rate probability with which I actually one-box (or two-box), although with only two minutes, I would probably need to know the base rate at which Omega predicts that I will one-box. Actually, just getting the probability for each of P(Ix|Ox) and P(Ix|O~x) would be great.
I also don’t have a mechanism to determine if 1033 is prime that is readily available to me without getting hit by a trolley (with what probability do I get hit by the trolley, incidentally?), nor do I know the ratio of odd-numbered primes to odd-numbered composites is off-hand.
I don’t quite have enough information to solve the problem in any sort of respectable fashion. So what the heck, I two-box and hope that Omega is right and that the number is composite. But if it isn’t, then I cry into my million dollars. (With P(.1): I don’t expect to actually be sad winning $1M, especially after having played several thousand times and presumably having won at least some money in that period.)