General
A tile's number indicates how much influence it exerts over each orthogonally adjacent tile.
The number printed on each tile is its influence value. A tile exerts that amount of influence over each tile orthogonally (up, down, left, right) adjacent to it. Influence is NOT exerted diagonally. The '0' tile and the King tile exert zero influence. Tiles with a control marker on them still exert their influence normally for their original owner — e.g., a blue tile with value 4 that has a white control marker on it still exerts 4 influence for the blue player.
General
A tile or tower is surrounded when all orthogonally adjacent squares are occupied by tiles, board edges, or towers.
A tile or tower is surrounded when every orthogonally adjacent square (up, down, left, right) is occupied by another tile OR is a board edge OR is another tower. Because board edges and towers reduce the number of tiles needed, a tile near the edge or a tower may be surrounded by fewer than four tiles. Diagonal adjacency does not count toward surrounding.
Turn structure
On your turn, you must place exactly one of your tiles on any empty square of the board.
Each turn, you must place exactly one tile from your remaining unplayed tiles onto any empty square on the board. You cannot skip placing a tile. Towers and tower tiles already occupy squares; you cannot place a tile on an occupied square. After placing, you immediately check for surrounded tiles and towers.
Scoring
When a tile is surrounded, sum the influence of all orthogonally adjacent tiles plus the tile itself; the player with the most total influence places a control marker on it.
When a tile becomes surrounded, it is immediately scored. To score it: count the influence exerted by all tiles orthogonally adjacent to that tile, plus the influence value of the tile itself. The player whose tiles contribute the most total influence wins control and places one of their control markers on the tile. If both players are tied for influence, the player who OWNS the tile (i.e., the tile is their color) wins the tie and places their control marker. Control markers do not change a tile's influence: a tile still counts its influence for its original owner regardless of which control marker is on it.
General
A control marker of your color on a tile shows you control it, whether it is your tile or your opponent's.
When you control a tile (by winning the influence count when it is scored), you place one of your colored control markers on that tile. You may control your own tiles or your opponent's tiles. The color of the control marker reflects current control, not tile ownership. Control markers do not affect the tile's influence, which always belongs to the original tile owner.
Special
When a white tower is surrounded, the player with the MOST adjacent influence captures it; ties go to the player who did NOT place the last surrounding tile.
When a white tower is surrounded, count the influence exerted by all tiles orthogonally adjacent to that tower (the tower itself has no influence). The player whose tiles exert the most total influence captures the white tower. If there is a tie, the player who did NOT place the tile that completed the surrounding wins. To capture: remove the white tower from the board and place it in front of you. Leave the white tower tile on its square. Do NOT place a control marker on the white tower tile. For the rest of the game, neither player may place a control marker on that square. Capturing a single white tower provides no immediate benefit beyond progress toward the three-tower win condition.
Special
When the black tower is surrounded, the player with the LEAST adjacent influence captures it; ties go to the player who did NOT place the last surrounding tile.
When the black tower is surrounded, count the influence exerted by all tiles orthogonally adjacent to that tower. The player whose tiles exert the LEAST total influence captures the black tower (opposite of white towers). If there is a tie, the player who did NOT place the tile that completed the surrounding wins. To capture: remove the black tower from the board and place it in front of you. Leave the black tower tile on its square. Then place one of your control markers on the black tower tile. This means capturing the black tower immediately grants a control marker (unlike white towers).
Special
If you control your opponent's King tile when it is scored, you win the game immediately at the end of your turn.
The King tile is a special tile each player has. It exerts zero influence. If your opponent's King tile becomes surrounded and you win the influence contest over it (gaining a control marker on it), you win the game at the end of your turn. This is one of three win conditions.