But that is clearly the wrong reduction. Start position will determine the final position every time if we assume a perfect board. Marbles are not wave particles. You get a distribution based on the input distribution.
It's a thought experiment. If we assume a perfect board with perfect marble with all other factors like imperfections/air currents removed and with the same initial position, and let's say the perfectly spherical marble hits the peg dead center every single time, does the marble fall to the left side of the peg or right or does it not fall to the either side?
I can assure you I don't know. That moves the problem from platonic shapes to real interactions of quantum particles. Atoms are not equivalent to perfect spheres.
