The second paragraph is a bit handwavey. It’s basically the bit that turns Newcomb into an iterated game. As there’s this causal loop, it can be unlooped by converting into an iterated game, and using your action in the previous round as a proxy for your action in that round. So Omega plays based on your previous action, which is the same as your next one.
I don’t understand the second paragraph.
I buy (what I understand of) this if Omega makes its prediction by simulating you (and not if it makes its prediction by, say, scanning your DNA).
The second paragraph is a bit handwavey. It’s basically the bit that turns Newcomb into an iterated game. As there’s this causal loop, it can be unlooped by converting into an iterated game, and using your action in the previous round as a proxy for your action in that round. So Omega plays based on your previous action, which is the same as your next one.