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The way I implemented it there never is an obligation to move the King out of check. It is just bad strategy to leave it in check, or move it into enemy check, as that would allow the opponent to capture it on the next move. It is only forbidden to move the King into friendly check. (Which would not result in a capture opportunity.) It is allowed to expose the King to a friendly check by moving other pieces, as for the opponent in his following turn this would be an enemy check that he'd better resolve. There is no difference there between a direct check and a discovered check.

So yes, it is legal, but losing. The blue Knight was pinned, and yet it moves away.

I think I understand the game better now, but here is the next rule question:

What about simultaneous double check by red and blue, e.g., Blue moves the Knight to give both check and a discovered check by a red line piece.

Is this a legal move, and if it is, what are its consequences? Can red now take the King and win, or must the red player move the King out of check? If the King is checkmated, who scores the win in this case, or will it be a draw?

I am surprised it plays well. Because even though it appears I implemented the rules correctly, it has absolutely no clue on strategy. The normal strategy, trying to gain material through tactiscs, doesn't work here. The Diagram's AI doesn't evaluate King safety, but even if it would, this would be no help here, with a shared King. Controlling squares around the King helps the opponent to checkmate it just as much as it helps yourself. Centarlization of pieces is also not of much help, as it doesn't bring you in the zone where you can capture yet.

So its strength lies entirely in its ability to see possible checkmates a number of moves in advance.

Plays well. For a game in between!

Works! Great, thank you.

Funny enough this disappearance of pieces had nothing to do with the specific implementation of Borderline, but was due to an existing bug in the Diagram script for a feature that had never been really been used. In particular, there was code to suppress moves that blow up / capture your own royal, and this was tested when the piece doing that was temporarily removed from the board. The code forgot to put it back. And it was also applying this code to non-royals that were counting towards the baring rule (which is the rule Borderline uses, as the normal royalty mechanism doesn't work with a shared King), which was also not intended. A piece that could capture the King (which at that time would be considered an own piece, as you should also be able to move it) during the look-ahead would thus disappear.

This should be fixed now (after you flush the browser cache).

While playing, I noticed the following:

Example 1
1st Rg5 Bf4 2nd Ne3 Bb4 (Rg5 is gone) 3rd Ra5 Nc5 (Ra5 is gone) 4th Qa4 Qd5 5th Nc3 Ne5 6th Nb5 Ne4 (Nb5 is gone) 7th Qc6 Nc4 (Qc6 is gone) 8th Nf5 Ne3 (Nf5 is gone)

Example 2:
1st Bb4 Bf4 2nd Bc5 Qd5 (Bc5 is gone) 3rd Qa4 Bb4 4th Qc6 Nc5 (Qc6 is gone) 5th Ne3 Ne5 6th Nf5 Ne4 (Nf5 is gone) and so on.

Is it that a piece must be located on certain ranks to attack the King? Or is it that crossing the borderline results in a promotion that allows the piece to attack the King from anywhere on the board?

The former is the case. The possibility to attack is only possible beyond the borderline. Crossing the borderline has nothing to do with a promotion, which then applies to the entire board. The possibility to attack corresponds exclusively with the ranks 5-7 or 1-3.

Before the queen can capture the king, the queen must first have put the king in check. And it can only do this when it has crossed the borderline. White queen (here blue) can only do this on ranks 5-7, black queen (here red) analogously on ranks 1-3.

This is along the lines of what I was expecting you would eventually answer, though your rules do not make this explicit, and I could not divine your exact rule from what you wrote. In fact, I'm still uncertain about what this rule means:

The king can only be attacked beyond the borderline, which means that a piece cannot capture the king until the borderline has been crossed.

Is it that a piece must be located on certain ranks to attack the King? Or is it that crossing the borderline results in a promotion that allows the piece to attack the King from anywhere on the board?

could you change the ownership of the membergraphics directory for this page to 'chessvariants'? Currently it is 'apache', which denies me access, and I would want to upload a king image of neutral color there.

Try using the file manager first. As an editor, you have the ability to use the same file manager that is available to the authors of pages. When you're logged in, go to the Edit menu and select Upload or Manage Files.

Does this approximately do what is intended? (After refreshing your browser cache!)

you must move the King into the other camp to be able to give check and checkmate

No, the piece giving check must be beyond the borderline. (The king is restricted to ranks 3-5). Two rooks on rows 5 and 6 could in principle perform the usual mating net. (This is unlikely to work readily, as the opponent can probably intervene other pieces rather than just walk the king to the edge.)

As is evident from the questions here, the rules should be stated more clearly. And the questions around motivation for players to make progress are valid in this very far-from-chess setting; probably the best thing is to throw together a Game Courier settings (no need to enforce rules yet) and invite a few people to play.

Well, you must move the King into the other camp to be able to give check and checkmate. 

Is that so? As soon as white has reached ranks 5-7 or black ranks 1-3, check or checkmate can be given. The king may not have moved until then.

Well, you must move the King into the other camp to be able to give check and checkmate. You also need to occupy the squares on the borderline such that the King cannot escape to that line (this is possible, because the pieces cannot by captured). A defense against this is just to push the King back. A defensive player can always hold a draw by pushing the King back to the borderline whenever the offensive player pushes it into the camp where it can be hurt by check and checkmate.

@Fergus: could you change the ownership of the membergraphics directory for this page to 'chessvariants'? Currently it is 'apache', which denies me access, and I would want to upload a king image of neutral color there.

@Fergus

Before the queen can capture the king, the queen must first have put the king in check. And it can only do this when it has crossed the borderline. White queen (here blue) can only do this on ranks 5-7, black queen (here red) analogously on ranks 1-3.

@Fergus, the third rule means the king isn't under attack from the starting position.

I'll repeat my question, since you didn't answer it.

If the King can be captured, what stops the first player from using his Queen to capture the King and winning right away?

If the situation is not checkmate, it is in the player's interest to move the king out of check (or use another piece to protect it), otherwise it will be captured on the opponent's next move and the game will be lost.

If the opponent can capture the King if it remains in check on the next turn, what stops the first player from moving his Queen to capture the King on his first turn?

True. But I guess moving the King is about the worst thing you could do anyway, and would only be done to move it out of enemy check. In which case the opponent cannot move it back, as this would then put it in 'friendly check'.

This is a bit similar to variants where you are allowed to pass your turn (e.g. Janggi, and Chu Shogi when there still are Lions). If both players decide to pass every turn, the game makes no progress. But usually there is something better to do than passing your turn.

And this again is similar to shuttling your Knight between g1-f3 while the opponent does it between g8 and f6. It is always possible to have no progress, if neither player wants progress. The important thing is how easy it is to make progress in case your opponent doesn't want any.

As far as I can see there is no rule that forbids moving the King back to the place where it came from (at least, when the King move wasn't motivated by escaping check). So a situation can occur where the two players just move the King between two squares in an endless loop and the game makes no progress.

Impressive how the whole thing sounds from your point of view. Chapeau.

I think the crucial part of information that is missing from your description is that a player who captures the King wins the game. Or, consequently, that one must always move the King out of any opponent check (with the additional rule that it should also not be moved into 'friendly check').

I don't think the rule that "pieces move according to FIDE rules" covers this, as it is unclear to who the King belongs, so that the FIDE rule that you cannot expose your own King to check becomes meaningless. As a reader I would only interpret this rule as applying to the pseudo-legal moves of the pieces.

If my interpretation is correct, then an algorithm for playing this variant would be to remove the King from the board when generating the moves for the player currently on move, and mark all board squares to which moves go. (In this variant these are all pseudo-legal moves of pieces beyond the borderline to empty squares, as without Pawns there are no divergent pieces, and capture of non-royals is forbidden anyway.) If the square on which the King should be got marked, the game terminates as a win. Otherwise we can put a King of the color of the side to move there, (which then would not block any of the generated moves), and generate all its moves that do not go to a marked square. That excludes King moves into friendly check. Whether any of the remaining moves runs into enemy check will be discovered by simply trying out the move (which then result in an immediate loss through the mechanism described above if it would expose the King), as the search algorithm of the AI would normally do.

So it seems it only requires keeping track of the King location (which is different from the normal tracking because it should ignore color, but simpler because there can be only a single piece of the type of interest), and a reasonably straightforward modification of the move generator. This is not hopeless.

If the King can be captured, what stops the first player from using his Queen to capture the King and winning right away?

Winning in Borderline is like winning in classical chess. If the king is in check and cannot move away from it or use a piece of its own to protect it, it is checkmate and the game is over. If the situation is not checkmate, it is in the player's interest to move the king out of check (or use another piece to protect it), otherwise it will be captured on the opponent's next move and the game will be lost.

In Borderline, the king can be moved instead of one of your own pieces. It is not possible to move the king into your own check; such a move is not legal. The king can only be moved into check by another piece, not by a move of the king.

If the king is in check and could only be "saved" by a move into its own check - which is not possible/legal - then the player obliged to move has lost.
(here I have adapted my description again).
 

If the King can be captured, what stops the first player from using his Queen to capture the King and winning right away?