Objective: Claim dots on an $8 \times 8$ grid to form squares and score the most points before the board fills up.
Turns: Players alternate placing one dot per turn (Blue for Player 1, Red for Player 2/AI).
Game End: The game ends when all 64 grid points are occupied. The player with the highest total score wins.
Square Formation: A square is scored whenever 4 dots of the same color form the 4 vertices (corners) of a square.
Orthogonal Squares: Squares whose sides align vertically and horizontally (e.g., $1 \times 1$, $2 \times 2$, $3 \times 3$).
Tilted / Rotated Squares: Squares whose sides are tilted at an angle. These are formed by vertex offsets $(a, b)$ relative to the horizontal and vertical grid axes.
Shared Vertices: A single placed dot can simultaneously complete multiple squares. Every unique square formed yields full point value.