I've been talking about games of perfect information and I have another post on the subject coming up so this seems like a good time to mention two of the best known chess variants of imperfect information.
From the nice people at Wikipedia:
Kriegspiel (German for war game) is a chess variant invented by Henry Michael Temple in 1899 and based upon the original Kriegsspiel developed by Georg von Rassewitz in 1812. In this game each player can see their own pieces, but not those of their opponent. For this reason, it is necessary to have a third person (or computer) act as a referee, with full information about the progress of the game. When it is a player's turn he will attempt a move, which the referee will declare to be 'legal' or 'illegal'. If the move is illegal, the player tries again; if it is legal, that move stands. Each player is given information about checks and captures. They may also ask the referee if there are any legal captures with a pawn.and
Dark chess is a chess variant with incomplete information, similar to Kriegspiel. It was invented by Jens Bæk Nielsen and Torben Osted in 1989. A player does not see the entire board, only their own pieces (including pawns), and squares where these pieces could move.I've never actually played either of these games (I have enough trouble with unvaried chess), but they raise all sorts of interesting questions about forming a strategy with incomplete information.