multiplicity positionMultiplicity is an inverted connection game in in which connections often are to be avoided. It uses the one bound - one free opening protocol.

There are two players, White and Red. Each has a sufficient number of stones and both move only with their own color. A 'group' is a number of connected like-colored stones. A single stone is a group by definition.

The game starts on an empty hexhex board. White moves first, after which turns alternate. Moving is compulsory.

The restricted placement phase
White starts by placing one stone on the empty board. From that point on players take turns to:

  • Place a stone on a cell adjacent to the last stone placed by the opponent, and ...
  • ... place a stone on a on a cell that has only vacant cells as neighbors.

Both placements are compulsory. When the player to move can no longer make the second placement, then his turn ends and his opponent may start the free placement phase. The number of white and black stones will always be equal, although the 'density' of the position may vary and either player may end up being the one to start the next phase.

The free placement phase
In this phase players take turns to compulsory place one stone on a vacant cell.

The game ends when the board is full and the player with the highest score wins. A player's score is the product of the sizes of all his groups. The applet keeps track of the score.

Though draws will be very far from common, the game may end with an equal score.

How I invented ... Multiplicity
Using the Multiplicity applet

Multiplicity © MindSports
Java applet © Ed van Zon