Marque Cameron Browne (2008) A two-player connection game with capture, played on a special tiling.

Rules

Board: The Marque board is a tessellation of triangles and squares, similar to the semiregular 3.4.6.4 tiling but with the hexagons subdivided into triangles (the seven subdivided hexagons are called bases). This gives a total of 96 cells: 66 triangles and 30 squares.

Figure 1.  The Marque board.

Start: The board is initially empty. White starts by placing a White piece on any triangle.

Play: Players then take turns making one of the following moves:
1) Place a piece at an empty cell, or
2)
Place two pieces on adjacent empty triangles.

Capture: Any groups of same-coloured pieces with no freedoms (adjacent empty cells) are captured and removed from the board. Players may not move at cells without freedom unless that move captures enemy pieces to create freedom.

Players may not repeat the same move they made last turn.

Occupation: Players are deemed to occupy any hexagonal base that contains three or more consecutive pieces of their colour; both players may therefore share the occupation of any base.

Aim: A player wins by forming a connected chain of their pieces that occupies two hexagonal bases on opposite sides of the board. Two pieces are adjacent if they share an edge.

Figure 3.  A game won by White.

For example, Figure 3 shows a game won by White who has made a chain of white pieces that occupies the leftmost and rightmost bases, indicated with red dots. Black also occupies these bases (as well as two others) but has not connected them.

Notes

Single triangles are weaker cells that only have three freedoms. Single triangles on the board edge are even weaker with only two freedoms.

Playing at two adjacent triangles is topologically similar to playing at a single square; both moves have four enclosing edges and hence four freedoms.

The Marque board has 96 cells: 30 squares and 66 triangles (24 isolated and 42 within the seven bases).

History

Marque board design and rules by Cameron Browne and copyright (c) Cyberite Ltd 2008.

Thanks to Stephen Tavener for play testing which resulted in an improvement to the winning condition from "connect three non-adjacent bases" to the more interesting and direct "connect two opposite bases".

Marque can be played on Richard's PBeM server - check out the help file for more details. Please challenge me (camb) to a game any time.

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