Given a board game of N x M size. A domino is of size 1 x 2 and can be rotated to make it 2 x 1. A player can place a domino in any of the available position. When a player is not able to place a domino, he loses. An AI is created to play against the user. The AI selects a random position in the board and places the domino there. Improve this AI. What solution will be the best when board size is small and what if the board size is large.

Anyone has any idea how to solve this problem?