Variance of first passage time for a biased walk

A particle starts at $0$ on the integers and at each step moves up by $1$ with probability $p=\tfrac23$ and down by $1$ otherwise. Let $T$ be the number of steps until it first reaches $1$. Find $\operatorname{Var}(T)$, or answer $-1$ if it is infinite.

$24$. Conditioning on the first step, $T=1$ or $T=1+T'+T''$ with independent copies of $T$. This gives $E[T]=\tfrac{1}{2p-1}=3$, and the same argument for second moments gives $\operatorname{Var}(T)=\tfrac{4p(1-p)}{(2p-1)^3}=\tfrac{8/9}{1/27}=24$.