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MichaelVassar comments on Advancing Certainty - Less Wrong
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As in the LHC example, the criterion is making a million statements with independent reasoning behind each. Predicting a non-win in a million independent lotteries isn't what ciphergoth was thinking, so much as making a million predictions in widely different areas, each of which you (or I) estimate has probability less than 10^-8.
Even ruling out fatigue as a factor by imagining Omega copies me a million times and asks each a different question, I believe my mind is so constituted that I'd be very overconfident in tens of thousands of cases, and that several of them would prove me wrong.
Everything is dependent on everything else. I can't make many independent statements.
That's certainly true given full rationality and arbitrary computing power, but there are certainly many individual things I could be wrong about without being able to immediately see how it contradicts other things I get right. I wouldn't put it past Omega to pull this off.