First, shared variables don’t need to be rigorously equal. Values shifts give smooth variations of the global outcome. Randomly different values shifts add only a little noise.
It does not work well when we leave hidden variables of our simulations with binary values. At least 16 values must be statistically distributed uniformly to approach optimal quality. We also observe an almost good calculation when the pseudo angle defined by the hidden variable varies only over a range of 90 °. It’s better at 135 ° and it’s almost perfect at 180 °.
Using floating numbers does not provide a benefit at this time, but this is largely due to the averaging to get out of the ratios per degree.
The variables order does not affect a calculation without memory but it is better that the whole cycle is represented.
Calculations with hidden variables distribution patterns do not provide any new results at this time.
The need to have a lot of hidden variables is relative. Alice and Bob could agree to start with 0 ( or with any universal time dependant constant ), then increment by a common to both arms function of time, sharing time as hidden variable.
Any sequence of circular variables more or less well distributed can do the trick. Temporal synchronisation may produce the simplest one. But all this is physics! In cryptography, only matters the protocol reality !