The Laws of Cheops
Nine-level pyramid chess.
Article 1: The nature and objectives of the game
1.1Cheops is played between two opponents who move pieces on a triangular board of 81 cells. The two sides are Green and Orange.
1.2The players move alternately, one piece to each turn. A player may not decline to move.
1.3The objective is the Ascension: to have your Queen standing on the Apex with the opponent’s King in check at the end of your own move (8.1).
1.4A game may also be won by resignation, and may end in a draw (8.2, 8.4).
Article 2: The board
2.1The board is one large triangle divided into 81 smaller triangles, called cells, arranged in nine levels.
2.2Levels are numbered from the base upward, 1 at the base to 9 at the apex. The seventeen columns are lettered a to q, left to right. A cell is named by its column and then its level, as printed along the edges of the board:
a1 and q1 are the base corners, i9 the single cell at the top.2.3Level 1 spans columns a to q. Each level up loses one column from each side: level 2 spans b to p, level 3 spans c to o, and so on to level 9, which is the single cell i9.
2.4Cells alternate in orientation along every level. A cell that points up is light; a cell that points down is dark. The cell a1 is light, and colour alternates along every level and along every column. There are 45 light cells and 36 dark.
2.5i9 is the Apex. i8, the only cell with which the Apex shares a side, is the Gate. h8 and j8, which touch the Apex at a point only, are the flanks.
Article 3: The lines of the board
3.1 Step
3.1.1Every cell is a triangle with three sides. A step crosses one of those sides into the cell beyond it.
3.1.2A light cell has its flat side at the bottom. Its three neighbours are the cells to its left and right on the same level, and the cell directly below it in the same column. It has no neighbour above it.
3.1.3A dark cell has its flat side at the top. Its three neighbours are left, right, and the cell directly above it in the same column. It has no neighbour below it.
A step therefore always changes colour, and a piece moving one cell at a time can climb only from a dark cell.
3.2 Band
3.2.1A band is a straight strip of cells running across the board. Three bands cross every cell, giving six rays. One runs along the level; the other two gain a level every two cells. Cells alternate colour along a band.
3.2.2To trace a diagonal band, alternate one column sideways and one level up, always going the same way sideways:
i3 · j3 · j4 · k4 · k5, or a1 · b1 · b2 · c2 · c3.3.3 Corner
3.3.1A corner line joins cells of the same colour that meet at a single point. Three cross every cell, giving six rays: along the level, two columns at a time (
i3 · k3 · m3 · o3); and diagonally, one column and one level at a time (i3 · j4 · k5 · l6 and i3 · h4 · g5 · f6). The reverses run downward.3.3.2Every cell on a corner line is the colour of the cell the line was traced from.
3.3.3A corner move passes over one of the moving cell’s three side-neighbours. That cell is not on the line and does not block the move.
3.4 Column
3.4.1A column is a single letter: the column through e1 is
e1 · e2 · e3 · e4 · e5. Two rays, up and down. Cells alternate colour.3.4.2The longest column is the spine,
i1 to i9, which ends at the Apex. The outermost columns hold a single cell each.3.5 Leap
3.5.1A leap reaches any cell whose shortest route is exactly three steps, ignoring everything between. Up to nine cells qualify, fewer near the edges, and all are the opposite colour to the leaper’s own.
3.5.2The cells touching the leaper, by side or by point, are all barred. It jumps to the ring beyond them.
3.6 Capture, attack and blocking
3.6.1A cell holds at most one piece.
3.6.2Moving onto a cell held by an enemy piece captures it: the captured piece is removed from the board as part of the same move and the moving piece takes its place. A piece may not move onto a cell held by a piece of its own side.
3.6.3A band, a corner line and a column are each blocked by the first piece standing on the line. That piece may be captured; it may not be passed. A leap cannot be blocked.
3.6.4A corner line holds cells of one colour only, so only a piece standing on that colour can block it.
3.6.5A piece attacks the cells on which it could capture, whether or not that capture would leave its own King attacked. A Pawn attacks only where it threatens (4.7.2), and the Apex is governed by Article 5.
Article 4: The pieces and their moves
4.1Each side has sixteen pieces: nine officers and seven Pawns.
| Mark | Piece | Letter | Count | Moves |
|---|---|---|---|---|
| King | K | 1 | One cell, by step or corner. Up to nine cells. | |
| Queen | Q | 1 | Band, any distance. Six rays. | |
| Swordmaster | M | 2 | Level and column, any distance. Four rays. | |
| Sister | S | 2 | Corner, any distance. Six rays. Dark-bound. | |
| Assassin | A | 3 | Leap. Cannot be blocked. | |
| Pawn | - | 7 | See 4.7. |
The marks are how the pieces are drawn on a board; the letters are how they are written in a record (Appendix A). Neither is a rule. Two of the six carry one: the Swordmaster's four rays are the level and the column of 4.4.1, and the Sister's cut-out is a dark cell, the only colour 4.5.1's note lets a Sister stand on.
4.2 The King
4.2.1The King is never captured and never leaves the board. It moves one cell, by step or by corner. A King attacked by an enemy piece is in check.
4.2.2No move may be played that exposes your own King to check, or that leaves it in check.
4.2.3A King may never move onto a cell that would leave it attacked.
4.2.4If you have no legal move and your King is not in check, the game is drawn (8.4.1).
4.2.5If you have no legal move and your King is in check, it is in checklock. Article 4.2.2 then ceases to apply to you and you play under 4.2.6. If you still have no legal move, the game is drawn.
4.2.6While your King is in checklock: it may not move; no Queen or Pawn of yours may move onto the Apex; and you may not put the opponent’s King in check.
4.2.7Checklock does not end the game. The King is entombed, and the rest of your army plays on. The checklock breaks the moment a legal move exists under 4.2.2.
Two consequences need no rule of their own. Since a King may never step into danger, two Kings can never come next to each other. And since 4.2.2 is suspended only in checklock, a player can end their own turn in check only while entombed.
4.3 The Queen
4.3.1The Queen moves along a band, any distance.
Bands change colour along their length, so the Queen is bound to neither colour.
4.3.2The Queen and a Pawn are the only pieces that may end a move on the Apex.
4.4 The Swordmaster
4.4.1A Swordmaster moves along its level or along its column, any distance.
Colour alternates along every level and along every column (2.4), so the Swordmaster is bound to neither.
4.5 The Sister
4.5.1A Sister moves along a corner line, any distance.
Corner lines do not change colour (3.3.2) and every Sister begins on a dark cell (6.1), so all four are bound to the dark cells for the whole game. A Sister can never stand on a light cell, and so can never stand on the Apex.
4.6 The Assassin
4.6.1An Assassin leaps. It cannot be blocked, and nothing it passes over is affected.
4.7 The Pawn
4.7.1Movement. A Pawn moves like a King - one cell, by step or by corner - to an empty cell, and never to a lower level. A Pawn never captures by moving. Article 5 restricts where a Pawn may enter the Apex (5.3, 5.4).
4.7.2Capture. A Pawn threatens three cells, all of its own colour: the two one level above it, and the one on its own level toward the opponent’s corner. It captures only there. At the edge of a level it threatens fewer; on the Gate it threatens none.
The third cell lies two columns away, not one, because a level alternates colour cell by cell - the nearest cell of a Pawn’s own colour on its own level is two along, and it is a corner neighbour. The direction belongs to the side, not to where the Pawn stands: a Pawn of the a corner always threatens toward q, and one of the q corner always toward a, wherever it has got to.
4.7.3Promotion. A Pawn reaching the Apex becomes a Queen.
Article 5: The Apex
5.1Only a Queen or a Pawn may end a move on the Apex. A Pawn promotes on arrival, so only Queens ever stand there.
5.2Collapse. Any other piece may move onto the Apex to take a Queen standing there, but the two pieces collapse together: both are removed and the Apex is left empty. The King may neither collapse nor enter the Apex.
A Sister can never collapse. Corner lines do not change colour (3.3.2), every Sister is dark-bound (4.5.1 and its note), and the Apex is light, so no line a Sister can move along reaches it. Only a Swordmaster or an Assassin can.
5.3A Pawn enters the Apex by moving only from the Gate, and only when the Apex is empty. A Pawn on the Gate threatens nothing, level 9 holding no cell of its colour.
5.4A Pawn on a flank threatens the Apex and may capture a Queen standing there, promoting on arrival. It may not move onto an empty Apex: from a flank the only way in is by capture.
5.5A player in checklock may move neither a Queen nor a Pawn onto the Apex (4.2.6).
Article 6: The initial position
6.1Each side fills a sixteen-cell wedge in one base corner. Levels 5 to 9 start empty. The Queen stands on d2, not on the corner cell; the corner is an Assassin's.
| a corner | q corner |
|---|---|
| d2 Queen | n2 Queen |
| b1 King | p1 King |
| c1 Swordmaster · b2 Swordmaster | o1 Swordmaster · p2 Swordmaster |
| d1 Sister · c2 Sister | n1 Sister · o2 Sister |
| a1 Assassin · e1 Assassin · c3 Assassin | q1 Assassin · m1 Assassin · o3 Assassin |
| Pawns d3 d4 e2 e3 f1 f2 g1 | Pawns n3 n4 m2 m3 l1 l2 k1 |
6.2Either colour may take either wedge. The board is symmetrical about the spine - the mirror leaves i1 to i9 exactly where they are and changes no cell’s colour - so the choice of corner decides nothing.
6.3The player to move first is decided by lot, or by agreement.
Article 7: The act of moving
7.1Each move is made with one hand.
7.2If a player deliberately touches one of their own pieces, they must move it if it has a legal move. If a player deliberately touches an opponent’s piece, they must capture it if it can be legally captured.
7.3A player who wishes to adjust a piece on its cell must first say I adjust, and may do so only when it is their own move.
7.4A move is complete when the piece has been released on its destination cell; a capture, when the captured piece has been removed from the board; a collapse, when both pieces have been removed.
7.5If an illegal move is completed, the position immediately before it shall be restored and a legal move played instead. If that position cannot be established, the game continues from the last position that can.
Article 8: The completion of the game
8.1The Ascension. The game is won by the player who, at the end of their own move, has a Queen standing on the Apex while the opponent’s King is in check. Both conditions must hold at the end of that move. The check need not have been given on that turn, and may come from the Queen on the Apex or from any other piece.
8.2Resignation. The game is won by the player whose opponent declares that they resign.
8.3There is no other way to win. A King that cannot escape check is in checklock (4.2.5), and the game continues.
8.4The drawn game. The game is drawn in the following cases.
8.4.1Immediately, without any claim: when both players have been reduced to no Queen and no Pawns; or when the player to move has no legal move.
8.4.2Upon a correct claim by the player to move: when the same position has appeared for the third time with the same player to move; or when the last fifty moves by each player have been made with no capture, no collapse and no Pawn move to a higher level.
8.4.3Automatically, without any claim: when the same position has appeared for the fifth time; or when the last seventy-five moves by each player have been made with no capture, no collapse and no Pawn move to a higher level.
8.4.4Upon agreement between the players, at any time.
8.5Two positions are the same only if the pieces of each side stand on the same cells and the same player has the move.
8.6A player with no Queen and no Pawns can no longer achieve an Ascension, but does not lose.
Appendix A: Notation
A.1A cell is written column then level, in lower case:
a1, i9, q1. Pieces take an upper-case letter - K Q M S A - and Pawns take none.| Written | Means |
|---|---|
Mf5 | Swordmaster to f5 |
e4 | Pawn to e4 |
Mxf5 | Swordmaster captures on f5 |
dxe5 | Pawn from column d captures on e5 |
Axxi9 | Assassin collapses with the Queen on the Apex |
i9=Q | Pawn to the Apex, promoting |
Mf5+ | … giving check |
Mf5++ | … giving checklock |
Qi9# | … an Ascension, and the game |
A.3Where two pieces of the same kind could reach a cell, add the column of the one that moves; if that does not distinguish them, the level; if neither, both.
A.4A record should state which corner moved first, since
i1 is reachable by either side on the opening move.