Single Comment

This might be a good place to point out that the Mao, Moa and Moo do not
exhaust the possibilities of lame Knight moves. They are the only
possibilities as you lay out the Knight's leap on the board as an
orthogonal + diagonal step (in either order). But there are other paths
that lead to a (1,2) leap as well.

Super Chess, for instance, makes use in some pieces (Archer, Ambassador)
of a three-step Knight move, reaching (1,2) through the unique path
(0,1)-(1,1)-(1,2) (i.e. a zig-zag path of orthogonal steps, first and last
one in the same direction, and the middle one perpendicular to that). The rationalization in Super Chess is that an Archer needs a clear line of fire, and thus both 'intervening' squares must be empty. This introduces an even larger degree of lameness to the moves, which can now be blocked on two squares. (Note that a path (1,1)-(0,1)-(1,2) effectively would be the same.)

Other posibilities would be to lay out the path as (1,0)-(1,1)-(1,2) or
(0,1)-(0,2)-(1,2), the L-shaped moves. These would also be 'double
lame'. In practice lameness is a very strong handicap, especially in a
piece like Mao, where two moves in different directions can be blocked on
a single square, due to overlapping paths. A Mao in normal Chess would be
worth only half a Knight , almost exactly. With doubly lame moves almost
no value would remain, unless the lameness is partly ameliorated by mking
the piece multi-path, like the Moo.

If we would combine the two L-shaped and the zig-zag doubly-lame move in a
multi-path piece, it would have exactly the same degree of lameness
(topologically equivalent) as George Duke's Falcon!