Quantum game is one of the important branches in quantum information. Based on the theory of the single-coin-tossing quantum game, quantum game of the same color cards is discussed here, and the theory is also extended for the model which has N states. In classical game, two players shuffle the 13 cards which have the same color in turn, and anyone can not control what the last card is. In quantum game, if one of the players, such as Bob, shuffles the cards using quantum strategies instead of classical ones, while the other player still adopts the usual classical operation, he can always make the last card be what he wants. And then, it is concluded that quantum strategies are more successful than classical ones for the game of the same color cards.