I briefly explained my justification when I first suggested it, but I have no idea what page that is on, so I'll reiterate and elaborate. When first creating Ito Shogi, I came up with interpretations of orthogonally forward/backward, and diagonal moves on a 1D board. However, the knight move fits neither of these, as the move is basically a move in between orthogonal and diagonal. For the forward/backward, I interpreted this based on one explanation of the 2D move: one orthogonal followed by one diagonal. If I had interpreted it based on the more common interpretation, it would have been different: two squares orthogonally followed by one orthogonal perpendicular step. This would be interpreted as simply two squares jumping forward or backward instead of three, as it currently is in my game.
Why bother with this detail, as it seems irrelevant to the single orthogonal step of the cavalryman? Well, it shows that interpreting the knight move is difficult compared to all other moves. On a 1D board, I simple disregard sideways moves. But the sideways knight moves aren't truly sideways. Again, they are between an orthogonal and a diagonal. Since there is still some progress forward in the forward or backward directions when making a sideways knight move, I figured this aspect of the move could still be used on a 1D board. Let me make some crude illustrations:
- - -
- - N
- - -
If I move my Western chess knight to the left, the following two squares are available:
x - -
- - N
x - -
If I squash this 2D board back into a 1D board, it looks like this
(squish)
x -
- N
x -
(squish some more)
x
N
x
Make sense? Another plus is that every knight move makes it land on a square of the opposite "color" (even though shogi doesn't use colored squares, the principles is the same). This remains true with this interpretation of the sideways move.
As for our present game, S-7b