Sliders control how many things are on each side of the balance. Each object has a certain mass, with a slider to control that. The final slider is the mass of the beam itself.

When the beam of the balance is heavy, especially compared to the ratio of objects, the balance will never get to maximum tilt.

Some Math:

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A = object count
B = other object count
C = (A+B)/2, which is half of total objects.  This provides a reference for where balance or 0 is.
a = A/C, ratio of objects on the A side vs the balance of the objects.
b = B/C, ratio of objects on the B side vs the balance of the objects.

a+b=2  or  A/C+B/C=2  represent the total weight to be divided;
this is more of a given, along the lines of 1(A)+1(B)=2((A+B)/2)

The ratio of the weights are; in the below expressions, the C term is mostly meaningless
other than a+b=2 part for the normalized versions, since A/C / B/C = A/B  similarly with the inverse.

(A-B)/A or (A-B)/B  depending on whether A or B is heavier.
1-B/A  or A/B-1  are equivalent to the above expressions.

the result of the above expressions is the fraction of 0 to 90 degrees that is the tilt of the scale.

--- When also considering the mass of the beam... ---

M = beam mass
m = M/(A+B) which is beam mass per object.

1-(B+m)/(A+m) and (A+m)/(B+m)-1  are the expressions including beam weight per object.

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The red line is `cos( A/(A+B) )`(or `-cos( B/(A+B) )`) and is the classical physics prediction; at least if the cos(theta) term in QM polarizer predictions is equated to weight. The overall error in degrees is shown; this is probably the fraction of 90 degrees they differ, and is nearly an error percentage itself.