Polar

Strategy between two poles

Material

• Square odd sided board, 9×9 or 11×11 or 13×13
• A sufficient amount of black and white pieces

Connections are orthogonal only. Pieces are placed on empty intersections of the board.

Preparation

The board is initially empty.

One of the players takes two pieces (black and white) and places them on any arbitrary adjacent spaces. The other player may now decide on which color to play.

A setup example.

Black starts, then players take turns placing one of their pieces on an empty space according to the following rules.

Play

Connected pieces form a group and same-colored connected pieces within a group are called a section.

A group may never consist of more than two sections.

Players may only pass if they have no moves left. They must play in a successive turn when moves are available again.

The game ends when both players have to pass.

Score

Groups with one or equally sized sections score zero points.

For any other group, the player holding the majority section gets the triangular number section points:

P(n) = n*(n+1)/2

The player with the higher total score wins. Games can end in a draw.

An example of a finished game on a 13×13 board. White holds the majority in 7 groups, Black in 5 groups. White wins by 124 to 101.