  Consider the following Maker-Breaker type game played by Toucher and Isolator
on the edges of a graph $G$ with first move given to Toucher. The aim of
Isolator is to maximise the number of vertices which are not incident to any
edges claimed by Toucher, and the aim of Toucher is to minimise this number.
Let $u\left(G\right)$ be the number of isolated vertices when both players play
optimally. Dowden, Kang, Mikala\v{c}ki and Stojakovi\'{c} proved that
$\left\lceil \frac{n+2}{8}\right\rceil \le u\left(T\right)\leq\left\lfloor
\frac{n-1}{2}\right\rfloor $, where $T$ is a tree with $n$ vertices. The author
also proved that $u\left(P_{n}\right)=\left\lfloor \frac{n+3}{5}\right\rfloor$
for all $n\geq3$, where $P_{n}$ is a path with $n$ vertices.
  The aim of this paper is to improve the lower bound to
$u\left(T\right)\geq\left\lfloor \frac{n+3}{5}\right\rfloor$, which is sharp.
Our result may be viewed as saying that paths are the 'best' for Isolator among
trees with a given number of vertices.
