There is one great chess variant, which is little known, but is very interesting: Anti-King Chess (invented by Peter Aronson). All rules are the same as in standard chess, except that a new piece is added: Anti-King. The Anti-King is under check when it is not attacked! It is a checkmate, if it can't leave such position. The Anti-King can't capture enemy pieces. At the start white Anti-King is placed on d6, black on d3.

I played this chess variants several times against Zillions-of-Games, but Zillions is not especially strong in it. It would be much more fun to play this chess variant on BrainKing!