$A,B,C$ are playing backgammon tournament. At first, $A$ plays with $B$. Then the winner plays with $C$. As the tournament goes on, the last winner plays with the player who did not play in the previous game. When a player wins two successive games, he will win the tournament. If each player has equal chance to win a game, what is the probability that $C$ wins the tournament?

$ \textbf{(A)}\ \frac27
\qquad\textbf{(B)}\ \frac13
\qquad\textbf{(C)}\ \frac3{14}
\qquad\textbf{(D)}\ \frac 17
\qquad\textbf{(E)}\ \text{None}
$