  We consider excited random walk (ERW) on $\mathbb{Z}$ in environments with
identical stacks of infinitely many cookies at each site, subject to the
constraint that the total drift per site $\delta = \sum (2p_j - 1)$ is finite.
Building on the methods of Kozma, Orenshtein, and Shinkar (arXiv:1311.7439), we
show that ERW in finite-drift environments is recurrent when $|\delta|<1$ and
transient when $|\delta|>1$. In the case $|\delta|=1$ we prove that ERW is
recurrent under mild assumptions on the environment. In addition, we show that
ERW may be transient when $|\delta|=1$, an interesting new behavior that was
not present in previously studied models.
