how to do something with really small probability?

From: Wei Dai (
Date: Thu Nov 01 2007 - 14:30:46 MDT

Suppose an SI wants to do something with a very small, but non-zero
probability, say 0 < p <= 1/3^^^3 (in Knuth's up-arrow notation). How would
it go about doing this? The answer seems to be "it can't", because
algorithmic information theory says there is no way that it can generate a
sufficiently long random number that it can know is truly random. Can anyone
see a way around this limitation?

This problem came up in the context of Eliezer's "Torture vs. Dust Specks"
dilemma (, but I
think it might be of interest outside that context.

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