RichardKennaway comments on The Number Choosing Game: Against the existence of perfect theoretical rationality - Less Wrong Discussion
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There is no such thing as an actual unrealistic situation.
They do not have to pick a number, because the situation is not real. To say "but suppose it was" is only to repeat the original hypothetical question that the agent has declared unsolved. If we stipulate that the agent is so logically omniscient as to never need to abandon a problem as unsolved, that does not tell us, who are not omniscient, what that hypothetical agent's hypothetical choice in that hypothetical situation would be.
The whole problem seems to me on a level with "can God make a weight so heavy he can't lift it?"