> The actual measurements work differently. It's been experimentally proven many times that at the moment you look at your marble, the other marble's 50/50 probability of being red and blue shifts substantially to, for example 75/25. And that's without it having any way of knowing that you've seen your marble. So there are hidden variables that we don't understand, but they're not local. They somehow affect both marbles.

This is completely incorrect, to the point where what you were trying to correct was actually more accurate, though incomplete.

The usual setup is that for any given axis, each person always measures 50:50. Measuring your own doesn't change the odds of the other.

Knowing the _results_ of your own does. For the same axis, the correlation is exact. For axes with an angle theta between them, we get a correlation of R ~ cos(theta/2).

The upshot is that there is no underlying (classical) probability distribution that can give rise to this that can explain things for all measurement axes. This is sometimes glossed as "correlation without correlata".