I was surprised that this question by Freudian Slip was voted off-topic. The reason of the vote is that this question is about the optimal classical strategy to win the CHSH game, and needs only logic and no physic to be answered.
However, the CHSH game is a game invented by physicists, to look at physics problems (nonlocality and how quantum physics or other theories could beat it). I have only ever heard about this game in discussion about physics, and I think it is totally boring without physics, whether quantum or post-quantum (with PR-boxes). Such games have become a common tool in quantum information this century, and the optimal classical strategy defines a classical/quantum boundary, which is a physics question.
If this question is off topic because “You could remove all references to QM from this question without changing what it's asking”, then these two questions about differential equations (and many others) is also off-topic.
In other word, I don’t understand why this question is not mathematics in the context of physics, as advised at the help center, since the CHSH-game only make sense “in the context of physics”.