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drnickbone comments on Problematic Problems for TDT - Less Wrong
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Fair point - how does Omega tell when the sim's choosing probabilities are exactly equal? Well I was thinking that Omega could prove they are equal (by analysing the simulation's behaviour, and checking where it calls on random bits). Or if it can't do that, then it can just check that the choice frequencies are "statistically equal" (i.e. no significant differences after a billion runs, say) and treat them as equal for the tie-breaker rule. The "statistically equal" approach might give the TDT agent a very slightly higher than 10% chance of winning the money, though I haven't analysed this in any detail.
If the subject can know the exact code of TDT, Omega can know the exact code of TDT, and analyse it however it likes. That means it can know exactly where randomness is invoked - why would it have to sample?
This was my first thought: Omega can just prove the choosing probabilities are equal. However, it's not totally straightforward, because the sim could sample more random bits depending on the results of its first random bits, and so on, leading to an exponentially growing outcome tree of possibilities, with no upper size bound to the length of the tree. There might not be an easy proof of equality in that case. Sampling and statistical equality is the next best approach...