[zwvwluuf] Hook

Large board shogi variants have pieces that hook move: first moving one direction then another in the same move.

On larger and larger chess boards, the proportion of squares reachable in a single move (from say, an otherwise empty board) by a normal ranging piece (e.g., queen) asymptotically decreases to zero.  However, that proportion can remain nonnegligible, often 50% or 100% for a hook mover.

The two simplest hook movers move one direction orthogonally or diagonally, then turn exactly 90 degrees.  More complicated hook movers could sequentially meld any pair of pieces.