# Chess on an Infinite Plane - Huygens Option

Background: The rules for "Chess on an Infinite Plane" were completed January 16.(Link here).

Shortly after, evertVB's "Formation Chess" was blended with the infinite plane. The bishops and  chancellors were disbanded and replaced with an army of knights - fourteen for each color. The knights can cluster into formations, and thereby able to rapidly travel as queen to other areas of the board. (Link here).

Now I am releasing "Chess on an Infinite Plane - Huygens Option". In this variation, two huygens are added to each army.

Huygens can jump 5, 7, 11, or 13 squares in orthogonal directions. These are prime numbers, so when fleeing from another jumper (such as a hawk), the pursuer needs to make an inefficient maneuver to capture the Huygens, causing wasted moves.

The huygens are initially located to protect one of the pawns in the rearward flanks. Thus, it is safer for the hawks to leave their positions and join other battles. (The huygens are named after Christiaan Huygens, a Dutch mathematician who studied the rings of Saturn and invented the pendulum clock).

Rules:

The Pieces:
Black and White each have the following pieces (quantity and name):
1 king
1 queen
2 chancellors
2 rooks
2 bishops
2 knights
2 guards
2 hawks
2 huygens
22 pawns

All pieces move as in classical chess, with the "extra" four pieces moving as follows:

Chancellor (C) - Moves and captures as rook + knight.

Hawk (Ha) - Leaps exactly 2 or 3 squares in any orthogonal or diagonal direction. The leaping move means it can jump over other pieces.

Guard (G) - Moves and captures the same as a king but is not affected by check. Other information on the guard can be found (here). (not particular to this game)

Huygens (Hu) - Leaps 5, 7, 11, or 13 squares in any orthogonal direction.

Pawns play the same and promote at the same rank as in classical chess. White pawns promote at rank 8, and black pawns promote at rank 1. Pawns can promote to chancellor, hawk, huygens, or guard in addition to queen, rook, bishop, or knight. Pawns may capture en passant with the same rules as in classical chess.

Board Setup:

A red bracket indicates the a1 (1,1) square.

There is no castling.

There is no fifty-move rule. Draws can only occur from stalemate, threefold repetition, agreement, or a proven case of insufficient material to force checkmate.
All other rules are the same as in classical chess.

The Chessboard:
1. Board for OTB Play:
A playing area should be setup with at least 22 ranks and 20 files. Ensure provisions are available to expand the board if play requires. If this becomes inconvenient due to far-away pieces, a display board is used to indicate the location of remote pieces. If there is interesting play in small but remote areas, other playing areas can be labeled and used separatelly from the main board.

2. Diagram for Online Play:
A chess diagram is used to indicate the position of pieces either after each move by white, or each move by black. The diagram should include 22 ranks and 20 files. If any pieces are moved outside of this area, the diagram is expanded or notes are shared to indicate the location of far-away pieces.  If there is interesting play in small but remote areas, other diagrams can be used to show piece positions separatelly from the main diagram.

Move Notation:
Numeric coordinates are used to identify piece locations as (file#, rank#). The "a1" square is (1,1) and is marked on the chess diagram with a small red bracket. Increasing files are to the right, and increasing ranks are toward the back.

Parenthesis are used around each coordinate. Three examples of a move notation:
1) A rook moving from (8,4) to (1,4):
R(8,4)-(1,4) or R(1,4)
2) A rook moving from (1,4) and capturing a piece on (0,4):
R(1,4)x(0,4) or Rx(0,4)
3) A pawn advancing from (-1,7) to (-1,6):
(-1,7)-(-1,6) or (-1,6)

There are currently two games of Chess of an infinite Plane in progress, and one game of Formation Chess in Progress. If anyone would like to play either of these games or this new variation, please leave a message!

Or visit (this thread) to look for opponents and other variant game options.

Why not any prime number from 5 on?

Maybe that would be a better rule for the huygens. The only disadvantage is that you would need to think about which numbers are prime before each move (or have a list of them).
Some big prime numbers also have a lot of digits or are expressed with formulas. For example one prime number has more than 9,000,000 digits but can be written as "10,223 × 2^(31,172,165) + 1". But I'm not sure if anyone would want to move a chess-piece that far. I guess normal chess pieces can move really far also. So if a queen is allowed I suppose the huygens should be allowed also!

Btw, I'll consider other variations of this game too. Using one of the musketeer pieces on this board is also possible. I have an icon of the dragon (= Q + N) from musketeer which matches this board style.
Any new or existing players let me know if you wanna play!
OK, great! e4 is the king's pawn which is (5,4). I hope that's what you meant. Also I hope you'll agree to play with the huygens allowed to jump any prime number of squares (5 or more) like EvertVB suggested. So that's 5, 7, 11, 13, 17, 19, 23, 29, 31...etc. All other rules are the same as listed above. I'll play:
1...c5 (3,5)

2...(5,6)

3...N(3,6)

4...(1,6)

5...(2,7)x(3,6)

6...N(5,7)

7...N(7,6)

8...C(2,7)

9...(4,6)

10...(4,6)x(5,5)

11...Nx(5,5)

12...(6,6)

13...B(4,6)

14...(9,6)

15...B(5,5)

If the Huygens can jump any number of squares, can't they take each other immediately? There are 19 squares between them...

The Huygens jump prime numbers of squares (starting 5 or more). And prime numbers are a little weird - they don't have any normal repeating pattern. I have a list of all prime numbers from 5 to 499. Here they are:

5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499.

The pieces 19 squares apart are the Hawks, not the Huygens. Hawks only make jumps of 2 or 3 squares. The Huygens are the pieces that look like they have antenna on their heads. There's nothing they can attack on their first move.