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.
Every time I see this I think, ‘What if you flip a coin?’
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.