Phutball (pronounced as football) is a two player strategy game described in this book.
It has a host of interesting properties including
- Determining whether a player has a winning strategy with the ball centered is PSPACE hard.
- Answering the question "Can I win this turn?" is NP-Complete.
- John Conway (RIP) created the game alongside Elwyn Berlekamp and Richard K. Guy.
Gil Kalai recounts a lovely story about learning Phutball from Conway.
Conway set a special rule for me: Everytime I am convinced that I loose, we can switch sides. Needless to say that we switched sides several times; I was sure that my position is desperate beyond repair, we switched sides, and shortly afterward I was again sure that my position in the game is beyond repair.
While online mode is not finished yet, you can play around with the phutball board simply by opening src/index.html in a browser of your choice.