N-in-a-row game
This is an idea for a game which:
- Is entirely non-random
- Has no hidden information
- Involves strategy
- Is playable by normal humans
- Has an infinite state-space
- Is hopefully fun
- Is generally unsolvable
- Although it may be solvable when restricted to "reasonable" board sizes
The basic idea is:
- The gameboard is an infinite grid
- One player starts by placing a single X anywhere
- The second player must get two Os in a row within f(1) turns (f to be defined)
- Generally, if you get N in a row, then the opponent has f(N) turns to get N+1 in a row or you win. Then it repeats when they have N+1
- You can also get N+1 in a row yourself, in which case the counter resets with you still in the winning position.
Open questions:
- What is f?
- Can you place your symbol anywhere, or only next to the existing game?
Of course, the most vital part is the definition of f, and we're not yet sure what to do with that.