Dominions

Board and pieces The Dominions board is a base 9 hexagon with 217 cells. The pieces are two identical sets of 63 hexagons, black on one side, white on the other, displaying all the ways that 1 to 6 beams can radiate from the center. A piece, if flipped along its horizontal axis, displays the same pattern in the opposite color. Using the applet, you won't have to worry about that. The 'blank' The blank features in the China Labyrinth as well as in the I Ching Connexion, but plays no role in the game of dominions (other than as move and score indicator in the applet). The numbering of the pieces Pieces are numbered following a simple binary code: the six 'ones' in the diagram are numbered as subsequential powers of two. All other numbers are obtained by simply adding the powers of two concerned. If you move the cursor over a piece, its number will be displayed.

Applet
You can download this MindSports applet, which is tailored to save games played in the Pit, offline.
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download applet play online a word on notation

Rules
The board is initially empty. Dominions' pieces have a fixed orientation. Pieces remain in that orientation throughout the game.

Groups - Liberties - Capture

• A group consists of a single piece or several pieces of the same color that are connected by beams. Adjacent blank sides do not constitute a group connection.
• The liberties of a group are the beams that border on vacant cells. The pieces of a group share the group's liberties. A group lives if it has at least one liberty.
• If a piece, or the group that it is part of, loses its last liberty the piece or group is reversed, uniting its captors in a new group.

The Beam Structure - Sections - Placement

• During the game pieces of both colors get connected by beams. In any position, all beams together (disregarding color) are called the beam structure.
• Pieces may be placed without connecting to the existing beam structure. That way disconnected parts of the beam stucture are created. These parts are called called sections.
  Sections of course may merge by placement of pieces that connect them.
• White starts by placing one piece on the board. Players next move in turn to place one piece. Moving is not compulsory: a player may pass his turn without losing the right to move on his next turn. The game ends if both players pass on successive turns.
  In consequence a player who trails in terms of territory cannot afford to pass, since his opponent would pass also and win the game.
• A piece that is placed must always match adjacent pieces of either color in terms of beams and blanks.
• The piece must be placed adjacent to at least one opponent's piece - this may be a beam-to-beam or a blank-to-blank contact.
  Exception
  A player may freely extend from his own piece or group if this piece or group makes up a complete section of the beam structure. To 'extend' means that the piece must add to this section.
• A piece may not cause oscillation, that is, if it makes a capture, the resulting new group must at least have one liberty.
• Suicide is legal: if a piece by placement takes all its own liberties - or creates a group with no liberties - it commits suicide and (the group) is reversed immediately. This constitutes the end of the turn.

Suicide has many tactical applications: it may be used to reduce the number of liberties of an opponent's group one aims to attack, while preventing extensions. It may also be used to create places to start a new section.
A piece starting a new section makes up a complete section of the beam structure and thus may be extended freely from by its owner! The nearest example is black commiting suicide on his first move: the resulting white group makes up a complete section and may be freely extended from by white.

In the example, white has started with the 'six' and black has put a 'five' on top. White next has sacificed a 'one' by suicide to create space to start a new section. Black follows up with his 'six' at the other end, and white starts up a new section with a 'five'. This piece demands black's immediate attention because it makes up a complete section of the beam structure and thus may be extended freely from by white! A black suicide is no option: the resulting white group would still make up a complete section. So black is forced to engage in local conflict.

The Edge
The outward edges of border-cells are considered neutral blanks. Thus the maximum match for a cell on the side is an 'unbroken four', for a corner an 'unbroken three'.

Object
The game ends if one player resigns or if both pass on successive turns. In the latter case the winner is the player with the most territory. A players territory consists of the number of his pieces on the board minus the number of pieces he didn't place.
This implies that each player would like to end the game with as few pieces as possible 'in hand'. Pieces that in the end can only commit suicide do not affect the outcome: the moving player gains a point by getting rid of the piece, but so does the opponent because of the extra point of territory.

Eyes
Though strategy is largely unknown, creating groups that live unconditionally is a sure part of it. Tactics to achieve this are varied and subtle.
If a group has a liberty at a cell for which the opponent has no longer a matching piece, this cell is called an 'eye'.
A group with an eye lives unconditionally.
An eye of one player's group(s) is not necessarily at the same time an eye of the opponent's group(s) that may have liberties at it: one player may still have matching pieces for a cell, while the other doesn't.

General advise
Adding liberties to a group requires pieces with at least 3 liberties, so be economical with those. Taking liberties from an opponent's group while preventing extensions requires 'suicide pieces', usually 'one's' and 'two's', so be economical with those too. In short: be economical.
Special attention should be given to borderplay: towards the endgame opportunities for creating eyes and starting new live groups increase and the demand for pieces with fewer liberties rises with the possibilities to keep them alive.
Strength hides in the details!

Dominions © MindSports
Java applet © Ed van Zon