This page is written by the game's inventor, V. Reinhart.
Trappist-1 (also called "Chess on an Infinite Plane with Huygens Option") is a chess variant played on a chessboard of infinite size. The game includes two huygens for each color. Huygens can jump 5, 7, 11 and other prime numbers of squares in orthogonal directions (i.e. 5, 7, 11, 13, 17,...). Since it jumps in prime numbers, other jumpers such as the knight and hawk, need to make an inefficient maneuver when pursuing a huygens, causing wasted moves.
The huygens are initially located to protect one of the pawns in the rearward flanks (jäger units). 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).
As with the base version of this game, other new pieces are included not just for variety, but to help make enough material available in the endgame so that one player can force a win. Since there are no borders, the king cannot be trapped in a corner. The chancellors (R+N) provide immediate ability to create long distance attacks. There are also additional pawns, including some in rearward formations (jäger units), which can create the threat of additional promoted pieces. A hawk is centered in each jäger unit, initially protecting the rearmost pawns, but can leave its formation and enter into play. Each player also has two guards, which can be used as king defenders or for other strategic play.
(This version uses Fergus Duniho's innovative and abstract piece images).
Black and White each have the following pieces: 1 king, 1 queen, 2 chancellors, 2 rooks, 4 bishops, 4 knights, 2 guards, 2 hawks, 2 huygens, and 26 pawns.
All pieces move as in classical chess, with the "extra" three piece types 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.
Huygens (Hu) - Huygens jump 5, 7, 11 13, and other prime numbers of squares in orthogonal directions.
Pawns play the same and promote at the same rank as in classical chess. (Using the board coordinates shown in the diagram, white pawns promote at rank 16, and black pawns promote at rank 9). 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.
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 (FIDE) chess.
1. Board for OTB Play:
A playing area should be setup with at least 24 ranks and 24 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 separately 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 24 ranks and 24 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 separately from the main diagram.
Ranks are numbered just as in classical chess; ranks 16 and higher are deeper into black's side; ranks 9 and less are deeper into white's side.
Files visible in the initial diagram are labeled a - x. From white's view, they continue to the right y and z, and then aa,ab,ac, and so on. The file immediately to the left of "a" is "phi" ("φ"). Files further to the left are -a,-b,-c, and so on to -z, and then -aa, -ab, -ac, and so on. For convenience, the "φ" file can be written "0". (The zero file = "φ" = "0")
Parenthesis are used around each square identification. Some examples of move notations are as follows (view from white):
1) A rook moving to the left from g9 to a9:
R(g9)-(a9) or R(a9)
(With a classical board, this would be "Ra9")
2) A rook moving to the left one square from a9:
R(a9)-(φ9) or R(φ9) or R(09)
3) A rook moving to the left three squares from the a9 square:
R(a9)-(-b9) or R(-b9)
4) A rook moving vertically three squares from g9 farther back into white:
R(g9)-(g6) or R(g6)
(The game can also be played using numerical coordinates for both files and ranks).
A diagram with the huygen's moves on a 50 x 50 grid can be seen here:
Mathematical note of Interest: It may be mathematically impossible to devise an algorithm to "solve" Trappist-1. The huygens jumps prime numbers of squares, and the complete set of prime numbers is unknown (and no method to compute it), thereby placing Trappist-1 into a category of unsolvable games.
Thanks to Fergus Duniho for making Diagram Designer available, and also the abstract piece collection. Also thanks to Kevin Pacey for helping with Diagram Designer.
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