Birds of a Feather is a single player, perfect information card game. The game can have multiple board sizes with larger boards introducing larger search spaces that grow exponentially. In this paper, we investigate the solvability of the game, aiming at building a machine learning method to automatically classify whether a given board state has a solution path or not. We propose a method based on image-based features of the board state and deep neural network. Experimental results show that the proposed method can make reasonable predictions of the solvability of a game at an arbitrary stage of the game.