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I came up with that while trying to think of something else, which might
be called 'Bent Rider Chess'. This would be played on a 11-by-10 board.
Each player would have five different bent rider pieces (two of each)
selected as in Betza's
<a href="../diffmove.dir/augmented.html">Augmented Chess</a>.
<p>
Each piece would have a move consisting of a step or leap followed by a
(optionally) by a rider move. A player would choose from (where X>Y
means moves X, then can move Y):
<pre>
F>R A>R D>R N>R
W>B A>B D>B N>B
F>NN W>NN A>NN D>NN
F>DD W>DD A>DD N>DD
F>AA W>AA D>AA N>AA
</pre>
in such a way that neither the first move component nor the second is
duplicated. That is if you have F>R you cannot have F>NN or A>R.
<p>
Any thoughts?
11 by 11? Shouldn't a game with an asymmetry theme be played on an asymmetrical board? :-) Perhaps the 43-square contest would be perfect for an Asymmetry Chess...
Might be interesting to have a large variant built on the general theme of asymmetry: some pieces would have the asymmetric retreat property but have symetric move patterns, some would also have asymmetric forward and backward moves, some with asymmetric left and right moves, some with divergent captures, etc. Perhaps a 11 by 11 game with strong pieces and a strong, asymmetric King.
Thank you all for your replies.
An even stronger form of asymmetric retreat is the fairy piece the
<a href='../piececlopedia.dir/locust.html'>Locust</a> as used in
<a href='../dpieces.dir/edgehog-chess.html'>Edgehog Chess</a>. It
can only move to capture, and captures by leaping over a piece to
be captured to land on the empty square just past. Thus, while a
Grasshopper can
make a symmetrical retreat after leaping over an adjacent piece,
a Locust could only make a symmetrical retreat if a hostile piece moved
into the square it captured from.
Thanks, Ben. Cannon type pieces of course have asymmetic retreat (though these could be arguably defined as a subtype of multi-movers). Indeed the Grasshopper and the Cannon when capturing have a stronger form of asymettric retreat. Some definitions: 1. High-power Symmetric Retreat--the piece can alway return to its starting square on the next move by reversing its path (unless prohibited by the need to meet check, etc.) Example: Knight. Nb1-c3 can always be followed by Nc3-b1. 2. Low-power Symmetric Retreat--the piece can return to its starting square on the next move by reversing its path unless the opponent has used his turn to block it. Example: Rook. Rc3-h3 can be follewd by Rh3-c3 if opponent has not moved a piece to d3,e3,f3 or g3. 3. Low-power Asymmetric Retreat--the piece cannot reverse its path but may be able to return to its starting square on the next move if the alternate retreat path is not blocked. Example: Gryphon. 4. High-power Asymmetric Retreat--the piece cannot return to its starting square on the next move unless the opponent moves to facilitate it. Example: Grasshopper. Gc3-c7 cannot be followed by Gc7-c3 unless the opponent moves a piece to c4.
well, besides multi-movers, leaping pieces such as grasshoppers have symmetric move patterns but assymetric retreat. and xiangqi cannon has assymetric retreat when capturing but not when moving, which is one of the things that makes it such a neat piece (and difficult to get used to).<P> and incidentally any piece that move differently forwards than backwards (these pieces don't have symmetric move patterns, at least not about the x-axis) is going to have assymetric retreat. this includes lots of betza pieces such as fBbR, fRbB, etc etc (i could go on and on) and shogi pieces (which can of course be easily described in betza notation) such as the gold, silver, copper generals, the white horse and the whale, etc etc.
The bent riders and lame leapers (like the Mao) are part of a larger class that might be called 'multi-movers'. These are pieces that can make two (or more) geometrically different moves in the same turn. The gryphon moves as a Ferz and then (optionally) as a Rook; the Mao moves as a Wazir then (mandatorily) as a Ferz. Any such piece will have the asymmetric retreat property if the order of move types is not reversible. If the gryphon could move Ferz then Rook or Rook then Ferz it would not have the asymetric retreat property (and would be immensely powerful). True leapers such as the Knight in a sense might be said to have the asymmetric retreat property but it is irrelevant as they can jump over occupied squares--I prefer to think of a leaper's move as a direct point-to-point move that does not pass over interventing squares, in which case the Knights retreat is not asymmetic. I believe that multi-movers are the only type of pieces which have symmetric movement patterns but asymmetric retreat. (OK everbody, please prove me wrong if possible!)
My s[w]eeping switchers army for chess with different armies features three pieces with assymetric retreat. All of them are bent riders: The panda (aka slip rook), the erl queen (aka slip queen) and the unicorn. Another one is the mao (xiangi horse) which is not a bent rider. --Jörg Knappen
Check out Ralph Betza's article on <a href='http://www.chessvariants.com/piececlopedia.dir/bent-riders.html'>Bent Riders</a> for more information on this type of piece.
I notice in the page for the Griffon the statement that the Griffon has asymmetrical-retreat properties. This is interesting. I wonder if it might be a nice idea to devise a chess variant where all of the pieces have asymmetrical-retreat properties. Are there any other pieces which have asymmetrical-retreat properties or would some need to be devised in order to produce such a game? There could be a piece which is related to a conventional bishop in much the same manner as a griffon is related to a conventional rook, in that for such a piece there could be a move of one square orthogonally followed by a diagonal move away from the original position for zero or more empty squares, together with the possibility of capturing from a final occupied square of the move. This piece would always move to a square of the opposite colour. It would seem that in order to have asymmetrical-retreat properties that a piece could not be simply a leaper. There could be pieces where one screen piece in the route of movement is a necessity. One such could perhaps be a piece that has movement which changes from orthogonal to diagonal at the screen piece. Any ideas for existing or new pieces which would be suitable for such a game please?
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