No, randomness is kind of a red herring. I shouldn’t have brought it up.
At one point I thought I had a kind of Dutch Book argument against Omega—if he could predict some future “random” event which I intended to use in conjunction with a mixed strategy, then I should be able to profit by making side bets “hedging” my choice with respect to Omega. But when I looked more carefully, it didn’t work.
No, randomness is kind of a red herring. I shouldn’t have brought it up.
At one point I thought I had a kind of Dutch Book argument against Omega—if he could predict some future “random” event which I intended to use in conjunction with a mixed strategy, then I should be able to profit by making side bets “hedging” my choice with respect to Omega. But when I looked more carefully, it didn’t work.
Yay: honesty points!