Unexpected answer to an expected value problem

Suppose $X$ be Number of flips to reach $+1$ from $0$ as starting point,

$Y$ be Number of flips to reach $0$ from $-1$ as starting point,

$Z$ be Number of flips to reach $+1$ from $0$ as starting point,

and $W$ be Number of flips to reach $+1$ from $-1$ as starting point.

Now if we start from $0$, we have two: $$E(X)= \frac{1}{2}.1 + \frac{1}{2}.E(W)$$ Now obviously for reaching $+1$ from $-1$ we must pass the $0$, So we have: $$E(W)= E(Y+Z)=E(Y)+E(Z)$$ By symmetry we know: $$E(X)= E(Y)= E(Z)$$ So by: $$E(W)= 2E(X)$$ And therefor: $$E(X)= \frac{1}{2}.1 + \frac{1}{2}.2E(x) \Longrightarrow E(X)= \frac{1}{2} +E(X)$$ That has no finite solution!