Richard,
"Alice receives from me the instruction to press the button marked "90" on her perspex box. Remember, the box has two buttons and two lights. ..What happens inside the box? (in terms of cards and disks)"
We've dropped the cards. It's now even simpler. What arrived was the spectral disc (representing a spinning sphere) either 'heads' or 'tails' first.
That side of the disc sits behind, and facing, the dial. When Alice presses the 90 button the slot ('pointer') moves to the 90^o position, half way between red and green. A colour appears in the slot. It is half way between red and green in the spectrum. We call it "Sand".
Now a queue of students one by one get to see the colour. Each has to decide; "Is it closer to Green?(+1)or to Red? (-1)" and push the Red or Green button to light the red or green lights.
It's that simple. It's subjective, and fine tuning may be needed, but the overall statistical result somewhere in that part of the spectrum will be 50%.
There are two other versions of the innards, both work just as well; A low res spectroscope detects wavelengths between green(1) and red (+1) and throws the light switch one way or the other depending on which side of the median. At half way between red and green it can only find 50:50.
(What'll be important to bear in mind here is that the output is not necessarily some 'spin state' but effectively reflects an energy level, with 'zero' half way between +1 and -1.)
That should have been tautological. The more interesting bit comes next.
Best wishes
Peter
