Experimentally we observe quite frequently value above 2. However, please be aware that there are a lot of loopholes in our test. The most obvious ones are:
  1. Position of the polarizers is not random.
  2. The detectors are not well separated.
Other loopholes exist, but all realistically known loopholes have been closed over the course of the last three decades. \cite{Giustina_2015,Shalm_2015,Hensen_2015}.