  We study double-winding Wilson loops in $SU(N)$ lattice Yang-Mills gauge
theory by using both strong coupling expansions and numerical simulations.
First, we examine how the area law falloff of a ``coplanar'' double-winding
Wilson loop average depends on the number of color $N$. Indeed, we find that a
coplanar double-winding Wilson loop average obeys a novel ``max-of-areas law''
for $N=3$ and the sum-of-areas law for $N\geq 4$, although we reconfirm the
difference-of-areas law for $N=2$. Second, we examine a ``shifted''
double-winding Wilson loop, where the two constituent loops are displaced from
one another in a transverse direction. We evaluate its average by changing the
distance of a transverse direction and we find that the long distance behavior
does not depend on the number of color $N$, while the short distance behavior
depends strongly on $N$.
