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Here's an amusing possible solution to the problems with this variant:
combine it with <a href='../other.dir/alice.html'>Alice Chess</a>.
<p>
Here's how it might go. You add a second board, like in Alice Chess,
except the 2nd board has reversed checkering: a1 is white, not black.
When a piece's move would otherwise cause it to move to a square of a
different color, it instead lands on the equivalent square of the
other board. Thus Knights always switch boards when they move, and
Bishops never switch boards.
<p>
There are a number of ways to handle switching boards:
<p>
<ul>
<li>Alice Chess-style. The move on the board on which the piece
starts must be legal as in orthochess, and the square on the other
board must be empty.</li>
<p>
<li>The Plunge. A piece moving to another color may only to move to
a square that is empty on their current board, then they plunge through
the board to the equivalent square on the other board, capturing any
opposing pieces they land on, except for Pawns who may not plunge to
occupied squares.</li>
<p>
<li>The Switch-a-roo. A piece makes a normal orthochess move on the board
on which it starts, and then, if the destination square is of a different
color than the piece's starting square, it moves to an equivalent
position on the other board. If the space on the other board is occupied,
then the piece occupying that space is moved to the space just landed on on
the board that the moving piece started on. This version actually allows
Bishops on the 2nd board.</li>
<p>
<li>The Last Square. The piece's move is as normal, except that if the
piece would land on a color of square different from which it started, the
last square of its move is the equivalent space on the other board, and the
move does not pass through what would be the final square of its move in
orthochess. The last square on the board on which the board-changing piece
moved from may be occupied by a friendly or opposing piece -- it doesn't
matter as the moving piece does not pass through it.
</ul>
<p>
I don't know which would be best.
One of your suggested Knight replacements, the Dabbaba+Alfil compound, is also known as the Alibaba. This name is very evocative of where its components have been used historically. The problem of limited Pawn mobility may be best dealt with by substituting a forward-only Ferz, which always moves diagonally. I would be interested to know if there is an established name for this piece. Note that it is different from the array piece in Draughts, which captures by leaping over.
There is a problem with Berolina Pawns being taken en passant: Because their capture has them end on a square of the opposite color, they cannot capture!
Charles: Roger Hare's Dai Shogi page is a cornucopia of weak pieces. These include the Ferz (Myojin = Cat Sword), the forward-only Ferz (Sekisho = Stone General) and the Wazir (Shincho = Angry Bear).
Another subvariant (it's invented not by me, i read about it in another monchromatic chess article): All pieces always must change color! And thus, knights can move freely, bishops are immobile, queens are identical to rooks. By the way, both monchromatic and color-switching chesses have 2 ways of playing (it was noticed by me): 'new game' way and 'agreement' way! 'Agreement' way: legal FIDE game is played: if change color (or move to same color in color-switching game) is only way to remove check, it must be done, and all pieces still checks with FIDE moves. 'New game' way: simple game with different pieces is played (royal ferzes in monochromatic, royal wazirs in color-switching, etc.), and thus, kings may be on adjecent squares, etc. And thus, we have 4 interesting games: new game monochromatic, new game color-switching, agreement monochromatic and agreement color-switching. These 4 games may be interesting mutators (if you are playing Xiang-qi, agreement color-switching is probably best). Alternative bishop in color-switching FIDE chess variant (queen may optionally have it's move): aancas in style of boats from Tamerlane 2: first moves 1 vertically forward, when diagonaly forward, or first vertically backward, when diagonally backward.
This #11 board replica is another chess problem by Raymond Smullyan, author 'Chess Mysteries of Sherlock Holmes': http://www.chessvariants.org/index/displaycomment.php?commentid=23374. And another Smullyan, http://www.chessvariants.org/index/displaycomment.php?commentid=23389 has solution: http://www.chessvariants.org/index/displaycomment.php?commentid=23392.
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