I think you are missing the point I'm trying to make. You can violate CHSH by giving a non-local distribution (That's what happening with the distribution you

I think you are missing the point I'm trying to make. You can violate CHSH by giving a non-local distribution (That's what happening with the distribution you provide). But there is more than one way to skin a cat. You can also violate them using the mathematical trick as I suggested above. This trick to replicate the result seems a lot more plausible than non-locality. > not obeying the axioms of probabilities. That's exactly what I blame the experimenters for. By ignoring that they are conditioning on the hidden variable, they are treating what is a "conditional probability" exactly the same way as it if was a "standard probability". Which is a big no-no from the math standpoint.