Katarenga
Katarenga is a two-player abstract consisting of a variable board, 16 pawns, and rules of movement derived from Chess. Each pawn’s move is governed by the colour of the square it moves away from (red = rook, yellow = bishop, green = knight, blue = king).
For each game the board is constructed from four double-sided quarterboards, each of which can be placed either way up and any way round, yielding a total of over 24,000 different 8x8 boards. In the basic game your aim is to get two of your pawns to the opposite side without being captured.
The same equipment can be used for playing a variety of other games with the same rules of movement and capture. Can you invent more?