My game theory textbook had a simple explanation of this in terms of poker. If you play aggressively on strong hands, but don't bluff on weak hands, then everyone will fold whenever you try to play aggressively, and you never win any money. The Nash equlibrium recommends that you bluff a lot, so your behavior on strong and weak hands is indistinguishable.
Yes, the advantage comes from being hard to predict. I just wanted to find a game where the information denial benefits were counterfactual (unlike poker).
(Note that the goal is not perfect indistinguishability. If it was, then you could play optimally by just flipping a coin when deciding to bet or call.)
Link:
Counterintuitive Counterfactual Strategies
Overview:
Over the weekend, I was thinking about the variant of Newcomb's Paradox where both boxes are transparent. The one where, unless you precommit to taking a visibly empty box instead of both boxes, omega can self-consistently give you less money.
I was wondering if I could make this kind of "sacrifice yourself for yourself" situation happen without involving a predictor guessing your choice before you made it. Turns out you can.