I am studying the book Probability on Graphs by Grimmett. Let $G = (V,E)$ be an infinite connected graph with finite vertex-degrees. We shall consider a reversible Markov chain $Z = (Z_n : n\geq 0)$ on $V$. With each distinct pair $u,v \in V$ we associate the weight/conductances \begin{align} w_{u,v} = \pi_u p_{u,v}. \end{align} With $w_e$ the conductance of the edge $e \in E$, the dissipated energy of a flow $j$ through graph $G$ is defined as \begin{align} E(j) = \sum_{e = \langle u,v \rangle \in E} \frac{j_{u,v}^2}{w_e} = \frac{1}{2} \sum_{\substack{u,v \in V \\ u \sim v}} \frac{j_{u,v}^2}{w_{\langle u,v \rangle}}. \end{align} Define $J_s = \sum_{v \in V} j_{u,v}$. Then the effective resistance of a network equals \begin{align} R_\text{eff} = \frac{1}{W_\text{eff}} = \frac{E(j)}{J_s^2}. \end{align} Grimmett tells us that the probability of ultimate return by $Z$ to the origin $0$ is given by \begin{align} \mathbb{P}_0(Z_n =0 \text{ for some $n \geq 1$ })= 1 - \frac{1}{W_0 R_\text{eff}}, \end{align} where $W_0 = \sum_{v:v \sim 0}w_{\langle 0,v \rangle} $.
Now, using the above, I want to determine the probability of 'return to $0$' of the infinite binary tree below, with two parallel edges joining to the origin root. Each edge has unit resistance.
For me, it is clear that $W_0 = 2$. However, I do not see why $R_\text{eff} = \frac{3}{2}$. Can we use laws for resistors in series / in parallel to determine $R_\text{eff}$?
