(This game sounds familiar. Is it original?)
This is a game for 2 players.
Start with a carefully drawn n-by-n grid.
The players take turns completely filling in a total of n squares of the grid. (So, the first player to move fills in ceiling(n/2) squares, and the second player to move fills in floor(n/2) squares.)
After the squares are filled in, then the second player who filled in the squares is the first player to move in the next phase of the game.
The players take turns. On each turn a player draws a straight line from any empty vertex on the edge of the grid (where a grid-line meets the grid's perimeter) to any other empty vertex on any other edge of the grid.
By "empty" vertex, I mean a vertex that has not yet had a line drawn to it or from it in this phase of the game.
No line may pass through any filled-in square. But a line may touch a filled-in square (along an edge or touching at a corner).
(Also, lines may be vertical or horizontal. For this reason, I suggest that the grid be lightly drawn.)
Every time a line passes through a previously drawn line (previously drawn by either player in the second phase of the game) then the player's OPPONENT gets a point for each line crossed by the player's line.
Players move until there are no more possible lines that can be drawn under the rules.
(If a player claims that he/she cannot move any more, then the player's opponent may challenge this assertion and find, if possible, a path the player's line can indeed follow.)
Highest score wins.
PS: See the post (to my blog "Amorphous Trapezoid") about games-related poetry at: