Comments/Ratings for a Single Item

A possible rule to add that when castling normally the king moves two
squares, when castling over the edge the king move three squares.

The notation to this can simply be O-G , O-H , O-C and O-B . It depends on
where the king lands. For discriptive notation : O-KN , O-R , O-B and O-QN
.

[Do you say that the knights in cylindrical chess are also equal to rooks?]

Knights are spooky! - is the best evaluation I have at the moment.

Nightriders are very strong on the 12x8 Courier Chess board, due to their ability to make long moves sideways, for example, from (b1) to (j5). They should even more powerful in Cylindrical Chess.

Can you tackle my question about the relative value of a non-cylindrical queen on a cylindrical board?

Ah, you're right. Knights are certainly not equal to Rooks in this game. But they do gain value from their ability to jump, AND Betza's leveling effect. If all the pieces were equal in value it would be a dull game, where people would exchange pieces and reach a pawn endgame.

Incidentally, I think the bishop, on a semi-open position, is stronger than the Rook on this board.

This is a diagram for the Nightrider's movement. The squares marked with & are can be reached by more than one path.

   +---+---+---+---+---+---+---+---+  
8  |   |:::| * |:::| & |:::| * |:::|  
   +---+---+---+---+---+---+---+---+  
7  |:::|   |:*:|   |:::|   |:*:|   |  
   +---+---+---+---+---+---+---+---+  
6  | & |:::|   |:*:|   |:*:|   |:::|  
   +---+---+---+---+---+---+---+---+  
5  |:::|   |:*:|   |:::|   |:*:|   |  
   +---+---+---+---+---+---+---+---+  
4  |   |:::|   |:::| N |:::|   |:::|  
   +---+---+---+---+---+---+---+---+  
3  |:::|   |:*:|   |:::|   |:*:|   |  
   +---+---+---+---+---+---+---+---+  
2  | & |:::|   |:*:|   |:*:|   |:::|  
   +---+---+---+---+---+---+---+---+  
1  |:::|   |:*:|   |:::|   |:*:|   |  
   +---+---+---+---+---+---+---+---+  
     a   b   c   d   e   f   g   h

'If all the pieces were equal in value it would be a dull game, where people would exchange pieces and reach a pawn endgame.'

Pieces only start out with theoretical equality. At the start of FIDE Chess, the bishop and knight are said to be equal. But that doesn't mean one arbitrarily exchanges off all ones bishops and knights and then the real struggle takes place. The relative value throughout the game of each piece becomes all the more difficult to determine and these relative values are largely contingent on placement and pawn structure. [That helps make the game exciting: How can you maneuver in such a way as to make one piece take on greater value than another of theoretically equal value?] A knight is more powerful than a stopped up bishop in a closed position, to take an obvious example.

At any rate, my question is itself only theoretical. It isn't meant to be a value judgment about how to improve the aesthetic quality of Cylinder Chess. However: Would a game like the one I mention be worth playing and enjoyable? I think so!

Jeremy asks: 'Maybe nightriders that can travel no more than two knight jumps away?'

2-step nightriders are useful pieces, which I value equal to Bishops on a 16x16 board. Certainly an interesting idea to try out in this game. Note: nightrider on (e4) can reach squares on the a-file by more than one path, as Abdul-Rahman Sibahi just pointed out.

Rooks can be deadly - suppose WHITE has King(g1), Bishop(g2), Pawns(f2, h2). Moving a BLACK Rook to the first rank gives double check and mate, as the Bishop can block either attack, but not both at once. A non-cylindrical queen on a cylindrical board might give the players headaches. A cylindrical queen with maximum move two squares can be very effective at hunting the king once the queen gets close enough. Probably similar in value to a cylindrical rook. Suspect the colorbound cylindrical bishop is still worth a pawn less than the cylindrical rook.

Hey, there is very interesting point:
Cylindrical Xiang-qi. There is cannon on one of ranks. And there one of opponent's pieces on same rank. There are no other piece on that rank. Can cannon capture this piece? Hehe...

Yes, a Cannon in Cylindrical XQ can indeed capture a piece by hopping the same piece first and wrapping round, as long as there is no third piece on the rank. Likewise a Cannon in Billiards XQ can capture a piece by hopping the same piece and bouncing off the edge of the board.
	Another feature of Cylindrical XQ is the unbinding of Elephants.

Oh, yes, it was mistake, just like king or general may move directly away from cannon without puttting itself in check.
But such game, where position, wich was before making move is more important than position after making move, would be interesting...

I've heard of non-edge variants of chess, but I hadn't read this specific page until just recently.  The game seems interesting and might eliminate the usual "going for the center in the opening" strategy.  Still, I can't help but wonder if the king might be tough to mate if there are no right and left edges.  Can a knight, bishop and king mate the lone opponent king?

Maybe they should make a restriction on the king - he is restricted to the usual board edges perhaps?

A beautiful spherical board for cylindrical chess:
http://makezine.com/2017/04/13/playing-chess-on-a-globe/

(Test edit; I can't edit this using the ordinary user edit script, but can using the editor script. An error in the new Session scripts?)

In interesting variant that has a board geometry somewhat like that of Circular Chess.

Jeffrey T. Kubach wrote on 2017-04-23 UTC:

Maybe they should make a restriction on the king - he is restricted to the usual board edges perhaps?

I was thinking the same thing.  King + Rook vs. King can't force a mate.  I'm not even sure King + Queen can force a mate.

Ok, it seems King + Queen can mate.  Which is good.  If they couldn't, that would also mean that King + Pawn would be a draw.

I have now added support for this to ChessV 2.  Silly me, I thought this would be pretty simple.  All directional movement is handled by lookup from a big multi-dimensional array indexed by direction number and square number that gives the number of the next square in that direction or -1 if it leads off-board.  I thought I could just update that lookup table to accomodate the board wrap and I'd be set.  But, of course, there were several additional challenges:

First, I had infinite loop problems since a Rook on an open rank can just zoom around and around.  Needed to add a check to internal move generator to stop generating whenever a piece returns to its starting square.  (And not generate that move, since null move is not allowed.)  This check will slow down, at least microscopically, move generation in all games, most of which don't have this problem, but that's life.  ChessV is not built for efficiency.  And Circular Chess is another example of a game with this problem.

Next, I had an issue with the move generator generating duplicate moves.  If a Rook is on a rank that is empty except for one enemy piece, that piece can be captured by two different paths.  So the generator adds the capture twice.  This is not good.  So I had to build deduplication capability into the move generator.  This is slightly expensive, so it is controlled by a Game flag and only enabled for games that need it.  (This could be an issue for more than games with funky boards - for example Switching Chess - a1 switches with b1 is really no different than b1 switching with a1.)

Then, a related problem with having multiple paths between squares, is that this could totally screw up the Static Exchange Evaluator (SEE).  A fix for that would be complex and I wouldn't want to complicate the regular SEE engine so it would require building a special one just for this game. And I'm not doing that.  So I switch it off.  There was already a game flag for disabling SEE since other games I've implemented are not compatible - most notably, anything with a Chinese Chess Cannon (or similar piece.)  I've tried to think about how SEE should be reprogrammed to support cannon-type pieces, and it is a fascinating problem, but it makes my head hurt.  Quite frankly, I don't think I'm smart enough to ever get that right.  Fortunately, SEE is a nice trick but not really necessary.  Quiescent search solves the same problem, and more accurately, just far more slowly ...

Ok, at this point, we have a functioning, accurate program.  But there are still problems with the positional evaluation functions.

Piece-Square-Tables (PST) encourage pieces to move into the center, but this game has a radically different concept of "center."  Instead of a square, the center is a stripe accross the center of the board.  Fortunately, I could adjust which squares were considered part of "small center" and "large center" and that fixed the PSTs intelligently.  It also fixed the consideration of which squares are elligible for knight outposts. This change was clean and worked out well.

Then there is pawn structure evaluation, and this is important.  There are a number of issues, for exmaple ... We penalize isolated pawns. But in this game, an A-pawn is not isolated, even if there is no B-pawn, if there is an H-pawn.  I was able to fix pawn structure issues pretty cleanly.

Then there is end-game evaluation.  King+Rook is no longer a win, it is now a draw.  So I fixed that, although in a cheesy way. (I also fixed this issue in Omega Chess while I was at it.)  But this "fix" was not good, and there are probably other changes required ... can KBB or KBN mate?  Probably not.  But that's enough for now. I expect I've already reached the point where this will be the world's strongest Cylindrical Chess engine (not that I've looked) and this is a lot more time than I had planned to invest in this.

The page for this game was very old and the content wasn't really appropriate as a formal description of this historic game, so I have completely rewritten it.  The original version can still be found here.

I have added a few more things to this page that I found in Variant Chess magazine, issues 22 and 48.  There is more information about the history, a note that the Bishop attacks the (4, 4) space by two different paths allowing it to issue double check by itself, and more information about endgames.  I was thinking that a Bishop pair probably won't be able to mate but that is not correct.  In fact, even if the orther side has a Knight, according to Variant Chess issue 48, the Bishop pair will still mate in at most 18 motes.  I have not verified that move count, but I have verified that KBB forces mate against KN. The outcome of KBN vs. K is still unknown.