An ambition to create a game on par with chess.

Continues from my previous short form.
https://yoonwoojeong.github.io/SYZYGY

Personal History

I have played chess since childhood and have long been interested in computer chess. However, developer communities like the one behind Stockfish were highly complex, making it extremely difficult for an individual to make a meaningful contribution. Consequently, I set aside that childhood dream to focus on my university studies. Now, having grown weary of academic work—and with the performance of AI coding tools having improved dramatically—I decided to try my hand at developing a new game. The initial version was 3D, and I experimented with topologies featuring multiple holes; however, these designs proved incompatible with a good user experience. I abandoned those ambitious ideas and adopted standard chess conventions: an n×n square board, a perfect-information turn-based format, and a chess clock. While this is the current result, there is still a long way to go. I am particularly unsure about the implementation of NNUE due to my limited knowledge in that area. I plan to open the project on GitHub for anyone interested in contributing, so feel free to get in touch.

The Game

So, here is a small puzzle. Two players each control one piece on a square grid. On your turn you either take a step, or you knock out one of the squares next to you so nobody can ever use it again. You can't walk over your own footprints, and if you can't move, you lose. Picture an grid of squares. For n=7, white's piece starts on c2 and Black's on e6, and White moves first.

Who wins with with perfect play? Here's the natural trick for the second player. Whatever White does, Black does the half-turn-rotated version of it. On a board with an even side (4×4, 6×6) there is no such square. So Black copies forever, never runs out of moves before White does, and the second player always wins from the symmetric start. On an odd board like 7×7 there is exactly one square the half-turn leaves alone. That one square breaks the copying strategy. A 5×5 board is small enough for a computer to solve.

What about 7×7? Suppose White walks toward the center, c2 → c3 → c4, and Black simply copies, e6 → e5 → e4. Now the position is symmetric, the center is still there, and White is standing right next to it, on their turn. So Black can't just copy on 7×7. Does White win from the real 7×7 starting position?