Contradicting the premises is a common failure mode for humans attacking difficult problems.

Failing to question them is another. In the political world, the power to define the problem trumps the power to solve it.

Within the terms of this problem, one is supposed to take Omega's claims as axiomatically true. p=1, not 1-epsilon for even an unimaginably small epsilon. This is unlike Newcomb's problem, where an ordinary, imaginable sort of confidence is all that is required.

Thinking outside that box, however, there's a genuine issue around the question of what it would take to rationally accept Omega's propositions involving such ginormous numbers. I notice that Christian Szegedy has been voted up for saying that in more technical language.

Consider someone answering the Fox-Goose-Grain puzzle with "I would swim across" or "I would look for a second boat".

These are answers worth giving, especially by someone who can also solve the problem on its own terms.