Wow, thanks for taking the time to reply to that! I've been wondering about that for years. I love the simplicity of your symmetrical strategy.

It puts me in mind of a simple strategy I used to play in the game of Nim. Creating two mirrored sets of piles worked well enough to get you to a place where some simple exceptions would apply. No need for any arithmetic, just simple symmetry and memorization of a few other winning patterns such as a three piles with 1, 2, and 3 respectively.

(This is for the misère version of Nim, where you want your opponent to pick last, but is easily turned around for regular Nim).

This strategy worked particularly well with large numbers if piles, where I could quickly establish a winning pattern against a novice player.