Markov Chains & Long-Run Behavior · Superchallenge problem

A board game has squares $0, 1, 2, \ldots, 7$. A player starts on square $0$ and each turn flips a fair coin, moving forward $1$ square on tails and $2$ squares on heads; the player finishes as soon as a move reaches square $8$ or beyond. Square $2$ has a ladder: landing on it moves the player straight to square $4$. Square $6$ has a snake: landing on it sends the player back to square $0$. What is the expected number of turns needed to finish? Express your answer as a common fraction.