  Consider the following Maker-Breaker game. Fix a finite subset
$S\subset\mathbb{N}$ of the naturals. The players Maker and Breaker take turns
choosing previously unclaimed natural numbers. Maker wins by eventually
building a copy $aS+b$ of $S$, where $a\in\mathbb{N}\setminus\{0\}$ and
$b\in\mathbb{Z}$. This is a generalization of a game analyzed by Beck. We show
that Maker can win in $|S|$ moves if $|S|\leq 3$. When $|S|=4$, we show that
Maker can always win in $5$ or less moves, and describe all $S$ such that Maker
can win in $4$ moves. If $|S|\geq 5$, Maker has no winning strategy in $|S|$
moves.
