There are various Geeklists that try to seriously characterize games by what type of gameboard the game uses. Innumerable whimsical lists have been avoided.
Gameboards which are a circle, or could easily be rearranged into a circle without affecting play.
N x N Checkerboard
For this series of boards only half, the dark squares, or the NxN checkerboard are used so there are (N^2)/2 spaces on which to play men on an even board, (N^2+1)/2 on an odd board.
N x N Square grid
For this set of games the game should be played in the cell of NxN grid. The overall complexity of the game depends on the number of men, and the overall size of the board which determines the number of playing positions.
While perhaps somewhat confusing at first, games should be considered as if they were played in the cells rather than on the points. This can no doubt be a controversial issue, but the idea is to keep games of the same general complexity together. It doesn’t matter much for large gameboards, but for small gameboards the issue is significant.
(1) The standard Go Board is 18x18 cells, but Go is played on the points of the grid, so it is equivalent to a 19x19 placement grid.
(j*N) x (k*N) Grid
Also Richard Hutnik's personal GeekList of games he designed for half a checkerboard.
- (? future list of games that can be played on a NxN board for any size N.)
Hexagonal Board divided into hexagons
With the edges of the small hexagons at 0º and 60º to the edges of the large hexagon (instead of 30º and 90º), a different series of boards is possible (1, 13, 43, 91, 157, 241, ...):
More general geeklist for other grids made of hexagons:
Also for tiling games that tile the planar to create boards with irregular shapes:
Master Geeklist of Mancala Gameboard Geeklists
This may need to be split by board size if a lot of entries are obtained.
(Note that is does not include games that tile the plane with triangles producing any sort of figure.)
Hexagonal Board divided into Triangles
For this set of games the game should be played in the cell of the triangle and not on the points (which would be equivalent to playing in hexagons).
(For now this list is small and hasn't been subdivided...)
Misc Geeklist about the Gameboard itself
Dot & Boxes Games
These are typically, but not necessarily played on a rectangular grid.
Games with multiple gameboards
Games which only have a vertical gameboard
Gameboards which extend in a vertical direction (eg by stacking...)
Games played on a vertical gameboard
Games which are played in 3 dimensions
Games played by stacking Spheres
Games played by stacking Cubes
Games with Spirals in Gameboard
Abstract games with boards that determine piece movement.
Something in each position on board (beyond just graph lines) that indicates
how a piece can move.