The formulation quoted from Schwarz’s post unnecessarily implicitly disallows unpredictability. The usual more general formulation of Transparent Newcomb is to say that $1M is in the big box iff Omega succeeds in predicting that you one-box in case the big box is full. So if instead you succeed in confusing Omega, the box will be empty. A situation where Omega can’t be confused also makes sense, in which case the two statements of the problem are equivalent.
The formulation quoted from Schwarz’s post unnecessarily implicitly disallows unpredictability. The usual more general formulation of Transparent Newcomb is to say that $1M is in the big box iff Omega succeeds in predicting that you one-box in case the big box is full. So if instead you succeed in confusing Omega, the box will be empty. A situation where Omega can’t be confused also makes sense, in which case the two statements of the problem are equivalent.
Thank you, I edited my post.