In 2010 Steve Hassenplug lead a team that created the robochess you see in the video above. Using LEGO MINDSTORMS for each piece they used, in fact, around 100 000 LEGO pieces to create the whole thing in a year (the board, the robot bases, bodies, mosaics ).
On a board that is 156ft2 (14.5m2) you can play against a human or computer or you can see computer vs computer. The robots can move around based on a recursive square-by-square tree search. Nice part is that you can use a tablet to direct pieces on the board and then see the magic happen.