An imaginary board is a playing surface whose limits are defined by the nature of the game and the placement of the pieces. All freeform games, such as Icehouse, use imaginary boards, but do not enforce placement within a geometric pattern. Games such as Tic Tac Doh! and Martian Backgammon use imaginary boards as well, with pieces adhering to regular patterns (grids).
Any games played on chessboards can also be played on imaginary boards, although the amount of concentration required is so immense that it is not recommended.