  There are increasingly suggestions for computer simulations of quantum
statistics which try to violate Bell type inequalities via classical, common
cause correlations. The Clauser-Horne-Shimony-Holt (CHSH) inequality is very
robust. However, we argue that with the Einstein-Podolsky-Rosen setup, the CHSH
is inferior to the Bell inequality, although and because the latter must assume
anti-correlation of entangled photon singlet states. We simulate how often
quantum behavior violates both inequalities, depending on the number of
photons. Violating Bell 99% of the time is argued to be an ideal benchmark. We
present hidden variables that violate the Bell and CHSH inequalities with 50%
probability, and ones which violate Bell 85% of the time when missing 13%
anti-correlation. We discuss how to present the quantum correlations to a wide
audience and conclude that, when defending against claims of hidden
classicality, one should demand numerical simulations and insist on
anti-correlation and the full amount of Bell violation. This preprint version
adds a section on realisms and shows the actual programs with output.
