I came up with a version of this a while ago (can't remember if I posted it) where Omega is going to (possibly) put a diamond in a box, and it has predicted the probability with which you expect there to be one, and it then uses that probability to decide pseudorandomly whether to put the diamond in the box.
I would say that a self-modifying timeless agent would immediately modify itself to actually anticipate the diamond being there with near-100% probability, open the box, take the diamond, and revert the modification. (Before applying the modification, it would prove that it would revert itself afterwards, of course.) And I would say that a human can't win as easily on this, since for the most part we can't deliberately make ourselves believe things, though we often believe we can. Although this specific type of situation would not literally be self-deception, it would overall be a dangerous ability for a human to permit themselves to use; I don't think I'd want to acquire it, all other things being equal.
Omega appears to you in a puff of logic, and presents you with a closed box. "If you open this box you will find either nothing or a million dollars," Omega tells you, "and the contents will be yours to keep." "Great," you say, taking the box, "sounds like I can't lose!" "Not so fast," says Omega, "to get that possible million dollars you have to be in the right frame of mind. If you are at least 99% confident that there's a million dollars in the box, there will be. If you're less confident than that, it will be empty. I'm not predicting the state of your mind in advance this time, I'm reading it directly and teleporting the money in only if you have enough faith that it will be there. Take as long as you like."
Assume you believe Omega. Can you believe the million dollars will be there, strongly enough that it will be?