Expected Rolls to Reach Position 10 in a Symmetric Random Walk

You start at position $0$ on the number line. Each turn, you roll a fair six-sided die and get a result $X$. - If $X \in \{1, 2, 3\}$, you move $X$ steps to the right. - If $X \in \{4, 5, 6\}$, you move $X - 3$ steps to the left (i.e., 1, 2, or 3 steps left). The process ends when you first reach position

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