Partitions 2024

Partitions is a two-player abstract strategy game, a type of territorial game in which players control groups to score.

Components

Hexagonal board of any size (size 5 or larger, odd number of cells) A sufficient number of black and white pieces

Terminology Group 　When pieces of the same color are adjacent and connected to each other, they form a group. Division 　A group is said to be divided or a dividing group if the board is disconnected when all the cells it occupies are removed from the board. 　A group that does not divide the board is called a fragment group.

Setup Each player decides which color he or she is responsible for. The game begins with the board empty.

Game Play Starting with the white player, the players take turns placing one piece of their color on any empty cell.

Game End The game ends when the board is completely filled. Each player scores the number of pieces of the opponent's color belonging to the fragment group. The player with the higher score wins.

If there is a tie, all pieces belonging to the fragment group are removed from the board, and pieces of the opposite color are placed in the empty cells, and the same evaluation is made. No draws occur.

If both players have enough experience, it may be possible to end the game earlier.

Note The way the game is scored is much like Brian Whitman's Loops, and the author noticed this similarity after creating the rules; the only difference from Loops is that in Partitions, if all of the cells that a group divides are occupied by allies, it is no longer a dividing group. This makes for some interesting differences in properties.