  The assumption of free will - the ability of an experimentalist to make
random choices - is central to proving the indeterminism of quantum resources,
the primary tool in quantum cryptography. Relaxing the assumption in a Bell
test allows violation of the usual classical threshold by correlating the
random number generators used to select measurements with the devices that
perform them. In this paper, we examine not only these correlations, but those
across multiple runs of the experiment. This enables an explicit exposition of
the optimal cheating strategy and how the correlations manifest themselves
within this strategy. Similar to other recent results, we prove that there
remain Bell violations for a sufficiently high, yet non-maximal degree of free
will which cannot be simulated by a classical attack, regardless of how many
runs of the experiment those choices are correlated over.
