You are confusing two different concepts. Splitting the coin into two faces amounts to collapse of the wave function into physical observables. The two halves have been determined.
The idea with Bell Inequalities is that if Alice and Bob are given entangled particles and some predetermined information (local hidden variables) then when Alice and Bob make specific measurements:
1. For local hidden variables, Alice should see results predicted by the whatever she already knows and won't see Bob's actions having any effect on her results.
2. Without local hidden variables, Alice will find (after the fact) that her results are skewed by (correlated to) the measurements Bob made.
Exhaustive experimentation has been consistent with #2.
The idea with Bell Inequalities is that if Alice and Bob are given entangled particles and some predetermined information (local hidden variables) then when Alice and Bob make specific measurements: 1. For local hidden variables, Alice should see results predicted by the whatever she already knows and won't see Bob's actions having any effect on her results. 2. Without local hidden variables, Alice will find (after the fact) that her results are skewed by (correlated to) the measurements Bob made.
Exhaustive experimentation has been consistent with #2.