Markov Chains & Long-Run Behavior · Medium problem

A player has $\$2$ and bets $\$1$ at a time, winning each bet with probability $2/3$ and losing with probability $1/3$. She stops when she reaches $\$4$ or $\$0$. Model this as an absorbing Markov chain on $\{0, 1, 2, 3, 4\}$. What is the probability that she reaches $\$4$? Express your answer as a common fraction.