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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”.

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    $\begingroup$ For the record: my statement that “you could remove all references to QM from this question without changing what it's asking” is merely a rebuttal to the argument that the question is about quantum mechanics. On its own, it doesn't mean the question is off topic. One needs to consider: if the question is not about quantum mechanics, then what is it about that would make it on topic? $\endgroup$ – David Z Jun 19 '14 at 20:59
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    $\begingroup$ Easy: the boundary between classical and quantum physics. Not a great question, but voted to reopen. $\endgroup$ – Emilio Pisanty Jun 20 '14 at 0:21
  • $\begingroup$ It looks to me that OP is approaching it from an entirely classical perspective, in which case it is a question about game strategies and not physics. $\endgroup$ – Kyle Kanos Jun 20 '14 at 1:47
  • $\begingroup$ OP even says, But it seems to me that the best strategy that doesn't involve QM... This should be clear to everyone that we're not talking about QM here. The fact that OP then goes on about the particular strategy to win 100% of the time should suggest that we're not talking physics either. Voting to leave closed (though I'm open to migration to boardgames.stackexchange.com) $\endgroup$ – Kyle Kanos Jun 20 '14 at 1:49
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    $\begingroup$ @KyleKanos : it’s obviously off topic for boardgames.stackexchange.com : see here. $\endgroup$ – Frédéric Grosshans Jun 20 '14 at 12:51
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    $\begingroup$ @DavidZ It is obviously about QM ! I fail to imagine a scenario were someone would want to find the optimal strategy of the CHSH game if not to define the classic-quantum boundary. $\endgroup$ – Frédéric Grosshans Jun 20 '14 at 12:57
  • $\begingroup$ @FrédéricGrosshans: CHSH could be construed as a card game with human interaction. However, the new beta puzzling.stackexchange.com could be another option. $\endgroup$ – Kyle Kanos Jun 20 '14 at 13:16
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    $\begingroup$ Also, you seem to be willfully ignoring OPs own statement that he is, in fact, ignoring the QM aspect of the game (see my second comment above) and observing it as a purely classical game. $\endgroup$ – Kyle Kanos Jun 20 '14 at 13:18
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    $\begingroup$ @KyleKanos : Yes it could. But no one does this, because it would be a fairly boring game/puzzle. And lots of physics question could be construed as mathematical problems... $\endgroup$ – Frédéric Grosshans Jun 20 '14 at 13:19
  • $\begingroup$ @FrédéricGrosshans: I agree that it would be a boring game. And pure mathematical questions (ones with no physics involved) are migrated to Math.SE, so I'm not sure what your point is there. $\endgroup$ – Kyle Kanos Jun 20 '14 at 13:20
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    $\begingroup$ @KyleKanos : I don’t ignore the fact that they look at it as a purely classical game. It is what physicists working in quantum information do all the time to set the classical-quantum boundary. The motivation of looking at the purely classical side of thing is to be sure there is really something interesting happening on the quantum side of thing. And that is the explicit motivation of the OP. So for me it is all about physics. $\endgroup$ – Frédéric Grosshans Jun 20 '14 at 13:25
  • $\begingroup$ @FrédéricGrosshans: It's one thing to look at the boundary between CM & QM. This, however, is not what OP is doing, he is asking about how his strategy for the classical game is wrong. Outside of stating the game's origin, I see no content about physics whatsoever. $\endgroup$ – Kyle Kanos Jun 20 '14 at 13:29
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    $\begingroup$ @KyleKanos : Full disclosure : I'm probably biased because the question of the OP is very similar as one I’ve often had from students while teaching Bell inequalities. Basically, the classical strategy sets the classical-quantum boundary, and his question about how is strategy is wrong is motivated by understanding this boundary. It is not very different with the many on-topic questions ”what's wrong with this perpetuum mobile/ftaster than light system” : in all these cases, the OP has a simple (but wrong) counter-example to a physics problem and asks where he made a mistake. $\endgroup$ – Frédéric Grosshans Jun 20 '14 at 13:47
  • $\begingroup$ @FrédéricGrosshans: I'd argue that his strategy & question was not motivated by understanding the boundary but by not understanding probable outcomes. At best it's a mathematical question (about probability & statistics) and at worst it's a puzzling/card-game strategy. The only physics is in setting up the background, all else is pure not-physics. $\endgroup$ – Kyle Kanos Jun 20 '14 at 13:53
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    $\begingroup$ @KyleKanos Well, we don’t understand OP’s motivationthe same way from his question and comments. I guess we have to “agree to disagree” on this point, which is crucial on the question here. $\endgroup$ – Frédéric Grosshans Jun 20 '14 at 14:03
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As the author of the original question being argued over, I am probably the last person anybody wants to hear on this subject since I'm severely biased, but here I go anyways.

The purpose of asking any question (in a Q&A site) is to generate an answer. A question must adequately describe the desired response, along with any (and preferably all) information needed to give the desired answer.

In isolation, the context of a question alone should not determine whether it is on- or off-topic. What should determine whether it's on-topic or not should purely depend on whether you need knowledge of the topic in order to correctly answer the question.

So if, as David Z suggests in the comments of my question, "You could remove all references to QM from this question without changing what it's asking", then that would imply that even though the context was QM, the actual content of the question had no dependencies on knowledge of QM, and he would be correct that the topic of the question wasn't QM.

My original question is kind of a perfect storm. I was looking for a reason in the source QM theory about why a non-QM condition was invalid, and the answer ended up having absolutely nothing to do with QM (to an almost embarrassing degree). Add to this the fact that the response I expected did not fully state what I was looking for (at the end I only asked "where am I wrong?"), and it's totally understandable that people would misinterpret my question as being "Look how smart I am, you guys missed this obvious solution to this QM-Inspired card game" instead of what I was hoping for, which was actual QM theory.

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