Triangulation Rules

Triangulation

Triangulation is a 3-Person Chess Variant played on a triangular board made up of 64 black and white triangles. Triangulation is a derivative of a variant from the ancient Indian strategy game Chaturanga. Chaturanga is a 2 player game on an uncheckered board made up of 64 squares simulating a battle using the ancient army divisions of infantry, cavalry, elephantry, and chariotry. The original playing pieces were the King, General, Elephant, Cavalry, Chariot (Ruhk in Persian chess), and Infantry which respectively became the King, Queen, Bishop, Knight, Rook, and Pawn in the Middle Ages for the popular game of chess as we know it today.

Triangulation is played on triangles instead of squares to simplify the direction of each player’s movement. There are a total of 27 playing pieces divided into 3 sets, 1 set for each player. Each set has 9 playing pieces consisting of 1 General, 1 Cavalry, 2 Ruhks, and 5 Infantry. Each of the 4 different pieces of each player moves in distinctive ways. Each set is represented by the different colours Green, Red, and Blue. The object of the game is to capture the opponent’s Generals while remaining the last player without having your General captured. The Green player makes the first move, followed by the Red player making the second move, and the Blue player makes the third and final move in a round of play. This sequence of moves continues until only 1 General remains or a Draw is called.

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Initial Setup

Each player picks a corner on the triangular board to start from (Green, Red, or Blue) and places their appropriate coloured pieces as laid out on the board as in Fig.1.

Placement

The Cavalry is placed in the corner.

The General is placed in front of the Cavalry.

The 2 Rukhs are placed on either side of the General.

The 5 Infantry are placed across the 3rd row. 

• Green Infantry placed on Rank C,

• Red Infantry placed on File 3,

• Blue Infantry placed on Column Δ.

Each player is represented by a different colour (Green, Red, Blue) indicated by the coloured line on the bottom side of the white triangles from each player’s corner. Each white triangle has a coloured bar at the bottom of it in the player’s respective colours with the opposite corner of the triangle indicating the forward motion of play for that particular player. Each round of play consists of the Green Player making the first move, followed by the Red Player, and the Blue Player making the last move in the round.

In Triangulation, moves are allowed by travelling across either a side(s) or a corner of a triangle (or both as with the Cavalry) to another triangle. All pieces, except for the Cavalry, cannot move any further than an occupied triangle in its path. A move onto an occupied triangle can only be done by capturing the opponent's piece located there.

Infantry

The Infantry can only move forward over a side of a triangle to an adjacent triangle. On a triangle with the side in front of the Infantry (A1), it may only move forward 1 triangle. On a triangle with a corner in front of the Infantry (A2), it may move either to the left or right side of the triangle to an adjacent triangle. The Infantry cannot move onto an occupied triangle unless attacking. On an Infantry’s initial move, it may move across 1 or 2 sides (B1 & B2).

Infantry Attack:

The Infantry can attack over any corner as long as it is in a forward direction from the attacker’s perspective.

On a triangle where the side is in front of an Infantry (C1), it may attack over either corner to the 2 left or 2 right triangles across the attacker’s-coloured line. If there is a playing piece on the white #1 triangle, Infantry C1 cannot attack either of the black #2 triangles for those triangles are being defended by that piece on the white triangle #1.

On a triangle with the corner in front of the Infantry (C2), it may attack all 3 triangles over the corner across the Attacker’s coloured line. If there is a playing piece on either of the black #1 triangles, Infantry C2 can’t attack either of the white #2 triangles for they are being defended by those pieces on the black #1 triangles respectively.

Once an Infantry reaches the opposite side it may continue to move sideways along the outer edge, or attack across a corner along the outer edge from a black triangle to another black triangle, to an adjacent triangle in either direction.

Rukh

The Rukh can move over any number of sides in a straight path (D1) and can stop on any triangle along this path.

The Rukh cannot move any further than an occupied triangle in its path and must stop on the triangle in front of the triangle (D2) occupied by a playing piece, or land on an occupied triangle (D3) and capture the opponent’s playing piece that is in the path of the current move.

Cavalry

The Cavalry can move either 2 (E1) or 3 (E2) triangles in one direction following either pattern:

1. Start by moving over any of the 3 triangle’s sides, then over the opposite corner,
and/or over the optional opposite side.

or

2. Start by moving over any corner, then over the opposite side, and/or the optional opposite corner.

Other pieces do not obstruct the movement of the Cavalry for it is the only piece that can leap (E3) over any playing piece.

General

The General can move 1 adjacent triangle in any direction over any side (F1) or to any of the 3 adjacent triangles over a corner (F2). The General may not move to an F2 triangle if there is a playing piece on an F3 triangle, for that F2 triangle is blocked by the piece on F3.

The General may never move into a position allowing to be captured (Check) and always must move out of Check, if possible. If a General cannot move out of Check, then that player is Checkmated.  The attacking player that Checkmated the other player must capture the General in their next turn, if possible, to complete the Checkmate. The Checkmated player remains in the game and continues to make moves, even allowing moving their own General into a new Check (if there are no other possible moves), until the General is actually captured. If a Checked attacker has another player in Checkmate, that attacker must execute the capture of the Checkmated opponent’s General before all other moves. A “Double Check” occurs when one player Checks both players at the same time.

All remaining pieces of a defeated General become the assets of the capturing player. Converted Pawns must move forward or attack in relation to their original colour.

Additional Rules

Rescue Captured Playing Piece

An Infantry may rescue a captured piece by moving to the black corner triangle of the other player with that captured piece. Only pieces that have been captured by that other player can be rescued and the recovered piece is placed in the opponent’s corner triangle to resume play. The Infantry that did the rescue is returned to any of the open triangles in the 3rd row (Rank C-Green, File 3-Red, Column Δ-Blue) in their corner to continue play. If the rescue results in only being able to rescue an Infantry then both Infantries retreat to any open 3rd-row triangle of their corner to continue play. One cannot rescue a non-existing piece captured by that opponent. A converted (captured) Infantry may rescue one of its captured pieces from its new colour-designated corner. 

Castling

A General may exchange places with either Rukh. Castling is only possible if neither the General nor the Rukh that is exchanging places has moved and the General is not in, or move, into check.

Ending the Game

The game of Triangulation ends when only 1 General (player) remains. If any of the remaining players cannot resolve in conquering any of the other players the game can be called a Draw. If only 2 players remain in the game then it is a draw between those players for the other player has already lost the game. A Draw is called immediately when either 2 or all 3 remaining players have only a General remaining for a General cannot move into Check to Check another General.

2 Player Gameplay

In a 2-Player game, the 3^rd army is neutral where the 3^rd General can be captured by either player. Once captured the remaining playing pieces of the neutral army become allies of the capturing player. Allies must follow the rules associated with their colour. The setup of the playing pieces is as in regular play, except with the General of the 3^rd (neutral) army being placed in the corner triangle exchanging places with the Calvary. The game ends, as in a 3-player game when only 1 General remains.

Labelling and Designations

Each triangle on a Triangulation board has a specific designation for easy reference to where a playing piece moves from one point to the next and to provide an easy way to keep records of the moves made. Each of the 3 sides on the board is labelled with a unique different notation scale for easy distinction. The Green rows (Ranks) are denoted with capital letters A through H, the Red rows (Files) with numbers 1 to 8 and the Blue rows (Columns) are depicted with Greek letters¹ β through Ω. The 3 scales are read in the order of a Capital Letter, Number, and Greek Character (eg.: F6Σ).  Each triangle on a Triangulation board is identified as in figure 6.