This conversation is a bit confused. Looking back, P and P1 aren't the same at all; P1 corresponds to the case where Omega never asks you for any decision at all! If S must be equal to S1 and S1 is part of the world program, then S must be part of the world program, too, not chosen by the player. If choosing an S such that S!=S1 is allowed, then it corresponds to the case where Omega simulates someone else (not specified).

The root of the confusion seems to be that Wei Dai wrote "def P(i): ...", when he should have written "def P(S): ...", since S is what the player gets to control. I'm not sure where making i a parameter to P came from, since the English description of the problem had i as part of the world-program, not a parameter to it.