Measure the spin of electrons in direction X (that's done with a weirdly shaped magnet). You'll get either +1 or -1 in a conveniently chosen unit system. That's already weird, you'll never measure +0.5 for example. Keep only the +1 electrons. You can measure them again and again, you'll always get +1 in the X direction.
Now measure those electrons in the Y direction, you'll also get either +1 or -1.
But now, if you measure in the X direction again, you'll get +1 or -1 with 50% probability; although before measuring in the Y direction, these electrons always had spin +1 in the X direction.
The math works and the experiments work, but it feels like a broken clock situation. It happens to correlate well, but the understanding and models are missing something in the actual underlying physics that, if understood, would throw the whole randomness part out the window.
My mental model of it is kinda reversed. The maths assign a specific, deterministic state to each electron between each measurement. However, the "left" state is equal to "(up + down) / sqrt(2)". It then follows that when we measure an electron that is in the "left" state along the vertical direction, we get 50% up and 50% down: the probabilistic behavior happens when measuring, which "forces" an electron that was in the "left" state to become either "up" or "down".
I agree though that it would be less frustrating if there was some property of the electrons that would allow to predict in which state it'll collapse.
Unrelated, but I also wish scientists properly used the term "theory".