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What's the Flying General in Xiangqi?

All I did to the original diagram was change its formatting to make it easier to read. I got the idea for putting a box around the main board from Pritchard, who did the same, but unlike him, I left all the inner coordinates in.

While on its own the original diagram on this page was a bit obscure, in conjunction with Fergus' circular diagrams it really clarifies the rationale behind Nadvorney's interpretation of the diagonal move; a bit of thought also reveals why Miller's reasoning in keeping the bishop on its own colour is flawed: if the bishop stays on its own colour you would expect a rook stepping over the pole to change colour as it does on a normal square‐cell board, whereas here (or on any spherical/Klein‐bottle‐shaped board with a multiple of four files) it doesn't. On e.g. a 10‐file board, Miller's reasoning would line up with Nadvorney's.

As for Chess on the Dot, the change in the diagonal's handedness at the poles also keeps it on one colour (on a board of this parity), but isn't stirctly necessary for a closed loop: Nadvorney's version (as can be seen on its diagram) does it just as well, and even Miller's manages, albeit via a much more circuitous route.

Fwiw, here's the original diagram as salvaged from the Internet Archive:

c7  d7  e7  f7  g7  h7  a7  b7  c7  d7  e7  f7
c8  d8  e8  f8  g8  h8  a8  b8  c8  d8  e8  f8
g8  h8  a8  b8  c8  d8  e8  f8  g8  h8  a8  b8
g7  h7  a7  b7  c7  d7  e7  f7  g7  h7  a7  b7
g6  h6  a6  b6  c6  d6  e6  f6  g6  h6  a6  b6
g5  h5  a5  b5  c5  d5  e5  f5  g5  h5  a5  b5
g4  h4  a4  b4  c4  d4  e4  f4  g4  h4  a4  b4
g3  h3  a3  b3  c3  d3  e3  f3  g3  h3  a3  b3
g2  h2  a2  b2  c2  d2  e2  f2  g2  h2  a2  b2
g1  h1  a1  b1  c1  d1  e1  f1  g1  h1  a1  b1
c1  d1  e1  f1  g1  h1  a1  b1  c1  d1  e1  f1
c2  d2  e2  f2  g2  h2  a2  b2  c2  d2  e2  f2 

I have a better idea of how this works now. I was describing a torus in my last comment. Unlike a torus, the north and south poles are not adjacent on a sphere. I will write up a better description and provide some more visual diagrams when I have the time.

The description of this game is very confusing. The middle eight rows make sense. These include a regular Chess board with two files from the other side on each side. This much is like Cylindrical Chess.

g8  h8  a8  b8  c8  d8  e8  f8  g8  h8  a8  b8
g7  h7  a7  b7  c7  d7  e7  f7  g7  h7  a7  b7
g6  h6  a6  b6  c6  d6  e6  f6  g6  h6  a6  b6
g5  h5  a5  b5  c5  d5  e5  f5  g5  h5  a5  b5
g4  h4  a4  b4  c4  d4  e4  f4  g4  h4  a4  b4
g3  h3  a3  b3  c3  d3  e3  f3  g3  h3  a3  b3
g2  h2  a2  b2  c2  d2  e2  f2  g2  h2  a2  b2
g1  h1  a1  b1  c1  d1  e1  f1  g1  h1  a1  b1

But the two rows at the top and bottom do not fit the same pattern. Here is the pattern that would make sense to me:

g2  h2  a2  b2  c2  d2  e2  f2  g2  h2  a2  b2
g1  h1  a1  b1  c1  d1  e1  f1  g1  h1  a1  b1
g8  h8  a8  b8  c8  d8  e8  f8  g8  h8  a8  b8
g7  h7  a7  b7  c7  d7  e7  f7  g7  h7  a7  b7
g6  h6  a6  b6  c6  d6  e6  f6  g6  h6  a6  b6
g5  h5  a5  b5  c5  d5  e5  f5  g5  h5  a5  b5
g4  h4  a4  b4  c4  d4  e4  f4  g4  h4  a4  b4
g3  h3  a3  b3  c3  d3  e3  f3  g3  h3  a3  b3
g2  h2  a2  b2  c2  d2  e2  f2  g2  h2  a2  b2
g1  h1  a1  b1  c1  d1  e1  f1  g1  h1  a1  b1
g8  h8  a8  b8  c8  d8  e8  f8  g8  h8  a8  b8
g7  h7  a7  b7  c7  d7  e7  f7  g7  h7  a7  b7

I do not understand why the pattern on the page is not this.

The reason people are calling it a 'Klein bottle' rather than a sphere is because of the weird situation around the poles.

If you draw the eight spaces surrounding each pole as triangles, then the rook shouldn't pass -- it only crosses edges. If you draw them as squares and try to connect opposites, each pole becomes a 'cross-cap' rather than a point. A sphere with two cross-caps is topologically equivalent to a Klein bottle.

(Alternatively each pole could be a double-handle, then you have an orientable surface of genus 4.)

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The rule that a Pawn dropped on 2nd rank regains his double push makes it a case of location-dependent moving, rather than an initial move. Position-dependent moving is not directly supported by the Interactive Diagram, but if can be emulated through automatic promotion: define multiple piece types for the piece with the variable move (all using the same symbol), and automatically 'promote' any of these types to the type that has the move belonging to the square they land on. This can be done by a user-supplied JavaScript function WeirdPromotion(). I did that in the Diagram I recently made for The Consuls.

In this case you would need two Pawn types, where only type 2 has the double push (and only type 1 promotes according to the normal mechanism on reaching the zone). Type 2 would always change into type 1 when it moves; both types would change into type 1 or 2 when they are dropped, depending on where they are dropped.

To make the promotion choice dependent on other pieces present on the board is problematic. The function WeirdPromotion() can also be used to veto promotions that would otherwise be possible. But the Diagram currently doesn't keep track of how many pieces of each type there are on the board. So it would have to scan the entire board to detect whether the proposed promotion piece is already there. This is possible, but would slow down the AI a lot. (But the AI currently cannoot handle games with drops anyway, so perhaps this is not a problem.)

Nelson // Thank you very much !!

(´ ˘ `)

Pawns, unlike other pieces, can be promoted over and over again. The reason is to strengthen the Pawn's advance.

Pawns can be dropped at 1st rank, so they can defend more actively. (For example, like Shogi's Anaguma, you can move the King into a corner and surround it with Pawns.)

However, the Pawn's attack power is relatively weak. Compared to other promoted pieces, Pawn has a lot of limited movement, and I thought it needed appropriate compensation. That's unlimited promotions.

As the saying goes, 'Pawns are the soul of chess', I felt that Pawns needed a unique feature.

H.G. //

Rule to advance 2 squares when moving to 2nd rank after a Pawn is dropped in 1st rank

Rule with restrictions on promotion (e.g., among the promoted pieces, only one piece with the same movement can exist on the board)

etc ?