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Strilanc comments on [LINK] Counterfactual Strategies - Less Wrong Discussion
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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.)
If I recall correctly, the recommendation was to fold on average hands, and play aggressively on strong and weak hands. You don't need to flip a coin, because your cards can already be viewed as a kind of coin that your opponent can't see.