Subsume Board Game: Rules

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Subsume is an ancient board game that had been lost in the sands of time. If you've ever wondered why so many other board games are based on exactly an 8x8 board or are otherwise derived from grids, you can probably trace their roots back to the game of Subsume. Yet Subsume is a very modern game that parallels much of the development of computer technology. The paradox behind Subsume's anachronistic creation is quite simple: in the future it fell through a time hole to the past and smacked a proto-human on the head. That's almost certainly not true, but you should be here to learn how to play Subsume, and not researching its future history.

Board

Subsume is most often played on a square board divided into a grid of any number of smaller square areas. The nature of the game favors boards with a size that is a power of 2. Commonly, an 8x8 board like the one used for playing chess or checkers is used to play Subsume. Play begins with an empty board.

Players

Subsume, on a sufficiently sized board, can be played by any number of players. An 8x8 board typically supports 2 players, and these instructions will mainly cover the basic 2 player game.

Board DimensionsTotal SquaresPlayers
8 x 826 = 6421 = 2
16 x 1628 = 25623 = 8
32 x 32210 = 102425 = 32
65536 x 65536232 = 4294967296227 = 134217728

Territory

The object of Subsume is to control the most territory on the board. The base territory is the single unit, or 1u, of area covered by the smallest squares that make up the board. The next higher territory is a 2u (covering 4 1u areas), followed by a 4u (= 4 2u = 16 1u). The progression of doublings continues up to the size of the entire board.

1u2u4u

Tokens

Colored tokens are used by each player to mark their territory. The smallest token is 1u, naturally, and larger tokens are used to mark larger territories. Commonly, black and white tokens are used for a 2 player game. Commonly, a 134 million player game will make your eyes bleed.

If a territory has multiple tokens, they get stacked like a deck of cards. Tokens can only be added and removed from the top of the stack.

Fractal

It is useful to note that different boards at different scales are self-similar. That is to say, given the same layout, a 16x16 board with only 2u tokens on it is identical to a corresponding 8x8 board with 1u tokens on it, which is identical to a 32x32 board with 4u tokens on it.

1u @ 1x1u @ 2x1u @ 4x