Game Description: Zuniq

Wow, some good games were suggested by readers two weeks ago! In addition to Nick Bentley donating Y with Shifts, Marcos Donnantuoni commented about his own impartial game, Zuniq. Ernie and I tried this out on Monday, and we immediately liked playing this! Here's how the game works:

The starting board is a grid of dots, similar to dots and boxes. Each turn, a player connects two adjacent (vertical or horizontal; not diagonal) dots, but not exactly like dots and boxes. If a new line segment closes off a region, no future turns can be made inside that region. Also, no two regions can have the same size. Thus, you can't close off a region if a region of that size already exists.

The suggested starting 8x8 board is a bit large, but we gave it a go. (Video: [7:16]) Afterwards we tried with 3x3 boards, to quickly learn that they are not very interesting. (The first player can always win by being just a little bit smart.)

The 4x4 game is definitely more interesting. (Video of lots of little games. [6:08]) After a few of these games, and later with games played against Patrick and my WittSem peer mentor, Alec, I think I can consistently win going first there. Still, my initial guess is that the game is PSPACE-complete in general.

I feel like there are lots of nice theorems that can be shown about this game. At the same time, I'm not familiar with what sort of theorems are "useful" from a CGT perspective (aside from computational complexity results).