  When it comes to random walk on the integers $\mathbb{Z}$, the arguably first
step of generalization beyond simple random walk is the class of one-sidedly
continuous random walk, where the stepsize in only one direction is bounded by
1. Moreover, the time until state 0 is hit by left-continuous random walk on
$\mathbb{Z}$ has a direct connection to the total progeny in branching
processes. In this article, the probability of left-continuous random walk to
be negative at an even (resp.\ odd) time is derived and used to determine the
probability of nearly left-continuous random walk to eventually become
negative.
