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Ecumenical Chess. Set of Variants incorporating Camels and Camel compound pieces. (8x10, Cells: 80) [All Comments] [Add Comment or Rating]O, what is the Holie Graille of mating potential? Is it the concentration of moves?
H. G. Muller wrote on Mon, Jan 5, 2009 08:49 AM UTC:I think you can only know this by dynamically searching for the move sequence. For pieces that cover only 2 orthogonally contiguous squares it is also necessary that the can get in a single move from a square where they cover (say) c1 to one where they cover BOTH a1 and b1, where the King on b3 should not be in the way. A Gnu cannot do this.
H. G. Muller wrote on Mon, Jan 5, 2009 10:16 AM UTC:Not really, as the King can already do that. In some endings you achieve the same thing (effectively making a null move) by stepping the King in a symmetric way over the diagonal (e.g. b3-c2) while all other pieces are on the diagonal.
Joe Joyce wrote on Mon, Jan 5, 2009 01:30 PM UTC:The 'woody rook' has 5 linearly contiguous squares, counting itself when guarded by the king. I was looking at the pattern of the move: not just linear extension in 1 direction, but in 'both' directions, forward and back, or left and right. The king/guard projects a 3 square linear 'wall' around itself, and is thus invulnerable to a king. [The rook, or any rook analogue, interdicts the king over a range greater than the king can move around, but is still vulnerable to diagonal capture, so must be guarded by the king.] The BN and FAN do not have this property, even though either can mate a king in a corner without any other piece. [Possibly a severe head cold is affecting even my typing as well as higher-level functioning, but I was trying to say that my understanding of what has been discussed is that it requires a rooklike 'walling-off' feature of the piece to mate. It may not be sufficient, as a wazir has that feature, but right now, I'd have trouble mating a lone king with a king and queen, so I don't know whether K + W vs K is a win or draw - seems like it might be a draw, but I don't have the energy to find out...]
I think you're right about the walling off part. That goes hand in hand with orthogonal contiguity. The Gnu draws, I think, because its power is not concentrated enough (there are holes). K + W v. K is of course a draw! ;)
H. G. Muller wrote on Mon, Jan 5, 2009 05:24 PM UTC:It is nonsense to count the square where the piece is standing, as a piece does not defend itself. The fact that a King could defend it is not relevant: to make a checkmate position in the corner the King is already spoken for to cover the squares on the second rank. So the other piece has to attack 2 adjacent first-rank squares. If it cannot do that, there are no checkmate positions.
Joe Joyce wrote on Mon, Jan 5, 2009 08:54 PM UTC:Agree with you, HG, once the king is in the corner. What is required to force the king into the corner? The gnu has 2 contiguous squares attacked, but that is not a piece that can mate, unless the king is already in the corner. What is the minimum requirement in footprint for one piece, X, to force mate in a K+X vs k scenario, when the pieces are scattered but not en prise at start? I think I've got the question down on paper correctly this time; if not, I promise to not say anything more on it until my sinuses stop feeling as if they're filled with cement.
H. G. Muller wrote on Tue, Jan 6, 2009 10:31 PM UTC:What is required to succesfully drive a King into the corner is very difficult to answer. For one, as the 12x12 checkmates thread shows, it is dependent on the size of the board. When you solve the end-games by retrograde analysis, there are several possibilities: Usually you start with very many checkmates, along the edge, none of them enforcible. (Unless you have something like a Queen). Pieces like Bison that cover only 2 orthogonally contiguous squares do not have those, however, and solely rely on a handful of corner checkmates. Usually all longer mates are ancestors of those corner mates. Sometimes the longer mates die out immediately, like in the case of Gnu. There exist mate-in-1 positions, but no mate-in-2 positions, so afterthat, you are done. This is just an unlucky coincidence of the piece not being able to make the critical step between a position needed to force the bare King to step into a corner, and the square where it needs to be for a corner checkmate. More often the number of longer mates increases very slowly with their duration, and then hovers for a long time around a very moderate number. These are the positions where the bare King is already trapped on the edge, and has to be driven into the corner with very precise play. On large boards, the number of longer mates even tends to decrease again, because it becomes easier and easier for the bare King to actually flee towards the corner voluntarily, the attacking pieces not being able to all follow it quickly enough to keep it trapped there, so that it can then escape along the other edge. So you have to confine the bare King more precicely as you are further away from the corner, not only cutting off its way back to the middle of the edges, but also preventing it gets too much of a headstart towards the corner. This leads to a decrease of the number of positions. On boards that are too big the number of mates actually decreases to zero before you retrogradely reached the middle of the edge, and the game is generally drawn: there is no way to drive the bare King towards the edge without it reaching the edge in the middle between corners, and there is no way to drive it over such a large distance to the corner without it escaping in one direction or the other. If you survive (in retrograde time) until the middle of the edges, though, the number of longer mates suddenly starts to explode. It is usually very easy to drive a bare King to the edge, if you don't care where it will hit the edge. Unless the board is really big. But on 8x8, if your own King is in the center, the opponend is already driven onto the second rank. So in the early phase, from very unfavorable position, almost any sequence of moves that step your King plust its lieutenant towards the center (using opposition to drive the opponent out of it) is a direct route towards the checkmate, and there are very many possibilities for this. On all boards I have tried, (upto 16x16) once you reach the point where the number of longer checkmates starts increasing again, it usually fills up the entire space of positions. Either that, or it slowly peters out before it ever got big.
What are the rules for castling, if any, in Simple Ecumenical Chess, where the king doesn't start on the same rank as a rook?
Castling is fully explained. It requires the King and Rook to be onthe same rank at the time, and only to not have moved outside blocks of 2x2 cells. Castling between the King and a Rook starting on the second rank requires that one of the two has moved to the other's rank within the 2x2 block.
Whoops. Interesting. Sorry I just glossed over that section and didn't notice what you were saying. I like it. Thanks.
Dear Mr. Gillman. A N+Q would be a Sherazade? After all... Alfil + Dabbabah= Alibaba...
How would 'Sherazade' be extrapolated? What would Queen+Zemel be? No, I am more than happy with Queen+Camel=Acme, as used in 3 to the 5 from its first posting.
Oh, and note the spelling of my surname!
Anonymous wrote on Thu, Apr 22, 2010 04:44 PM UTC:What about game on 8x8 board, but with pawns (wich can't make duble step)?
Comment added. The commentonitem.php page needed include changed to include_once. That is all.
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