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JGWeissman comments on Bead Jar Guesses - Less Wrong
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You should not guess that the first bead has a 50% chance of being red, because if you do, you can have this conversation:
Omega: What is the probability of the first bead being red as opposed to non-red?
You: Fifty-fifty.
Omega: So you would consider it more than fair if I offered you three dollars if the bead is red, and you paid me a dollar if it was non-red?
You: Sure, I'll take that bet.
Omega: What is the probability of the first bead being blue as opposed to non-blue?
You: Fifty-fifty.
Omega: So you would consider it more than fair if I offered you three dollars if the bead is blue, and you paid me a dollar if it was non-blue?
You: Sure, I'll take that bet.
(...and so on for ten more colors.)
Omega pulls out a red bead. He owes you three dollars, but you owe him eleven dollars. He wins.
Me: No, because you have more information than I do, and the fact that you would offer this bet is evidence that I should use to update my epistemic probabilities.
Well, Omega doesn't really need the money. There's no reason to believe he would balk at offering you a more-than-fair bet.
Well, in the case of Omega, I would at least suspect that he intends to demonstrate that I am vulnerable to a Dutch book, even though he doesn't need the money.
If you meet an Omega, that is pretty good evidence that you are living in a simulation: specifically, you are being simulated inside a philosopher's brain as a thought experiment.