The Crossbishop slides like a rook. But to capture it must jump over any piece and then slide like a bishop in the prolonged movement direction. The square immediately behind the jumped piece must be empty (this is "weak" Crossbishop). The "weak" Crossbishop's value is 3, that is, the same as a bishop or knight. Otherwise the rules are the same as in standard chess, except for the possible promotion to Crossbishop.
Although the Crossbishop loses 'screens' to jump over when the pieces become fewer, it becomes more mobile when the orthogonals are cleared from pieces. Thus it often retains its value in the endgame. Note that the Crossbishop can have a big influence from behind the friendly pawn chain, especially if it can slide along the first rank.
The 68-squared Gustavian board makes it possible to place additional pieces on the board without substantially increasing the board size. This often means that a strategical and tactical intensity is maintained. It also brings the advantage that bishops and knights remain equal in value. Crossbishop Chess, and the new Crossbishop piece, were invented by undersigned, August 2006.
The Crossbishop slides like a rook, but captures by a jump followed
by a bishop's slide.