  Circular Nim is a two-player impartial combinatorial game consisting of $n$
stacks of tokens placed in a circle. A move consists of choosing $k$
consecutive stacks and taking at least one token from one or more of the
stacks. The last player able to make a move wins. The question of interest is:
Who can win from a given position if both players play optimally? In an
impartial combinatorial game, there are only two types of positions. An
$\mathcal{N}$-position is one from which the next player to move has a winning
strategy. A $\mathcal{P}$-position is one from which the next player is bound
to lose, no matter what moves s/he makes. Therefore, the question who wins is
answered by identifying the $\mathcal{P}$-positions. We will prove results on
the structure of the $\mathcal{P}$-positions for $n = 7$ and $k = 4$, extending
known results for other games in this family. The interesting feature of the
set of $\mathcal{P}$-positions of this game is that it splits into different
subsets, unlike the structure for the known games in this family.
