Rationally? Only if I had sufficient evidence that I was 1-in-a-billion with regards to Omega being wrong to pull my posterior estimate to less than about 50%. In actuality? Probably if I thought there was at least a one in six chance that I could pull it off, based on gut feelings.
The problem also works if Omega’s failure rate is 1 in 1.5e10 or even much larger, so long as it’s much smaller than about 50.05%.
Assume Omega has been observed to get the predictions right 999,999,999 times every billion. Would you two-boxes in hope that it gets you wrong?
Rationally? Only if I had sufficient evidence that I was 1-in-a-billion with regards to Omega being wrong to pull my posterior estimate to less than about 50%. In actuality? Probably if I thought there was at least a one in six chance that I could pull it off, based on gut feelings.