I created a perfect (for 4n balls, single pile) Nim player that has more automation, i.e. it’s exclusively lever pressing with no manual turning of gears.
To take a ball use the blue lever. To end your turn use the red lever. The “computer” will automatically begin when the human ends his/her turn, and it will depress the red lever when it is again the human’s turn.
https://www.lodev.org/jstumble/?board=0l0lrebrelergebleebrglfrbfexiflrfrerflerf_0_16
I’ve tried building this on my physical board, but its correctness is very inconsistent (keeps dropping marbles). Let me know if you have any suggestions for how to make it more reliable!