The Duke was invented by Eric Greenwood in 1980 for his game RennChess. The Duke is closely
related to the Cavalier -- also
invented for Rennchess -- which has a historical precedent in the Griffon from Grande Acedrex.
Movement
The Duke can move in either of the following ways:
Step one square orthogonally, and then slide any number of squares
diagonally.
Slide any number of squares diagonally, then step one square orthogonally.
In both cases the Duke has the additional restriction that it may
not end its move on a square adjacent to the square on which it
started. It may not jump over other pieces, and captures the same way as
it moves.
The options given for the Duke's movement both produce the same set of
destination sqaures, but give it different paths to those squares.
Movement Diagram
In the diagram below, the Duke can move to any of the squares marked
with a red circle. Note that like the Knight, the Duke always
moves from a light-colored square to a dark-colored square, and
vice-versa.
The diagram to the left below illustrates how the Duke has two
different paths to any destination square. If the Duke wishes to move
from a1 to e6, he can do so by following either the blue circles or
the green circles. As long as one path is open, he can make the
journey, even if the other path is blocked.
The diagram on the right illustrates checkmate by Duke. Black can not
play Rc3 or Rd3 because it would open a path for the Duke from
f1-a5-a6. If black had a knight on b6 instead of a Bishop, however,
he could play Nc4, blocking the Duke.
Remarks
The value of the Duke is difficult to judge, but it is a strong piece,
probably about the same as a Queen on a larger board. Its unique
movement means that it can control a diagonal without actually being
on it, which is often useful when an opponent's Bishop is on that
diagonal as well. The Duke's biggest weakness is that it can't move
to an adjacent square. Like the Bishop, a Duke and a King
can not checkmate a lone King, even if the King cooperates.
Currently, I do not know of any games other RennChess that use the Duke,
but it is a piece worthy of consideration for future games.
