# Difference between Bell's inequality and CHSH

In this section of the Scholarpedia article on Bell's theorem, the first paragraph comments that Bell's original inequality is not ideal for experimental verification because it requires perfect anti-correlation of the variables, and for that reason the CHSH inequality is better. I don't really understand what this means, since as far as I'm aware experiments with e.g. the CHSH game also involve Bell pairs which are perfectly correlated. They allude to some continuity in the correlations, but I don't know what this means. Could anyone elucidate?

• I understand that anti-correlation is required to show $P(Z_a^1 \neq Z_b^2) + P(Z_b^1 \neq Z_c^2) + P(Z_c^1 \neq Z_a^2) \geq 1$. But if they were not perfectly anti-correlated, just nearly so, wouldn't this quantity still be close to 1, and still quite distinct from the $3/4$ of the quantum case? – Pedro Nov 5 '20 at 17:39