At first I was going to vote this up to correct the seemingly unfair downvoting against you in this thread, but this particular comment seems both wrong and ill-explained. I'd prefer to have your reasons than your assurances.
Recall that Newcomb's "paradox" has a payout (when Omega is always right) of $1000k for the 1-boxer, and $1k for the 2-boxer. But if Omega is correct with only p=.500001 then I should always 2-box.
I do agree that there is some 1>p>.5 where the idea of Omega having a belief of "what I will choose", that's correct with probability p, is just as troubling as if p=1.
By trivial argument (of the kind employed in algorithm complexity analysis and cryptography) that you can just toss a coin or do mental equivalent of it, any guaranteed probability nontrivially >.5, even by a ridiculously small margin, is impossible to achieve. Probability against a random human is entirely irrelevant - what Omega must do is probability against the most uncooperative human being nontrivially >.5, as you can choose to be maximally uncooperative if you wish to.
If we force determinism (what is cheating already), disable free will (as in...
One day, you and the presumptuous philosopher are walking along, arguing about the size of the universe, when suddenly Omega jumps out from behind a bush and knocks you both out with a crowbar. While you're unconscious, she builds two hotels, one with a million rooms, and one with just one room. Then she makes a million copies of both of you, sticks them all in rooms, and destroys the originals.
You wake up in a hotel room, in bed with the presumptuous philosopher, with a note on the table from Omega, explaining what she's done.
"Which hotel are we in, I wonder?" you ask.
"The big one, obviously" says the presumptuous philosopher. "Because of anthropic reasoning and all that. Million to one odds."
"Rubbish!" you scream. "Rubbish and poppycock! We're just as likely to be in any hotel omega builds, regardless of the number of observers in that hotel."
"Unless there are no observers, I assume you mean" says the presumptuous philosopher.
"Right, that's a special case where the number of observers in the hotel matters. But except for that it's totally irrelevant!"
"In that case," says the presumptuous philosopher, "I'll make a deal with you. We'll go outside and check, and if we're at the small hotel I'll give you ten bucks. If we're at the big hotel, I'll just smile smugly."
"Hah!" you say. "You just lost an expected five bucks, sucker!"
You run out of the room to find yourself in a huge, ten thousand story attrium, filled with throngs of yourselves and smug looking presumptuous philosophers.