  Different versions of percolation games on $\mathbb{Z}^{2}$, with parameters
$p$ and $q$ that indicate, respectively, the probability with which a site in
$\mathbb{Z}^{2}$ is labeled a trap and the probability with which it is labeled
a target, are shown to have probability $0$ of culminating in draws when $p+q >
0$. We show that, for fixed $p$ and $q$, the probability of draw in each of
these games is $0$ if and only if a certain $1$-dimensional probabilistic
cellular automaton (PCA) $F_{p,q}$ with a size-$3$ neighbourhood is ergodic.
This allows us to conclude that $F_{p,q}$ is ergodic whenever $p+q > 0$,
thereby rigorously establishing ergodicity for a considerable class of PCAs.

Probability;Combinatorics