Another Dots-Lines Game

Here is another dots and line-segments game (like the
game, Subdivide, I posted earlier).
(I am not sure which game, this one or Subdivide, is
more fun -- probably Subdivide. This game seems to me
to be less original too.)
This game is for two players, and is played using a
pencil/pen and blank pieces of paper.
The game consists of an even number of rounds, each
player playing offense or defense the same number of
rounds.
On a round the players take turn placing a
predetermined number of dots (say, 24, 12 per player)
anywhere on one side of a piece of paper. The same
number of dots are drawn on each round.
After the dots are drawn, players take turns (defensive
player first) connecting pairs of dots with straight
line-segments, connecting one pair of dots with one
line-segment per move.
The line-segments must not cross any other lines or
coincide with any other line-segments or pass over any
other dots other than the two dots at each line-
segment's ends.
The offensive player gets n points whenever a line-
segment drawn by either player connects to a dot with
n line-segments PREVIOUSLY drawn to it. (So, if either
player draws a line-segment from a dot with n line-
segments drawn to it previously by the players, to a
dot with m line-segments drawn to it previously by the
players, then the offensive player has {m+n} added to
his/her score on that move.) There isn't an upper limit
on how many line-segments can be drawn to any dot. (And
there aren't any points awarded on a particular move
for the line-segment drawn on that move.)
It should be noted that, therefore and obviously, the
offensive player probably wants to draw line-segments
to dots with many lines already connecting to them.
While the defensive player may try to draw segments
in such a way so as to block the offensive player from
connecting to the many-line-segment dots so as to
minimize the number of points the offensive player
gets on her/his rounds. The defensive player may also
try to connect to dots with a fewer number of line-
segments already drawn to them, of course.
A round is complete as soon as every dot has at least
two line-segments connected to them.
Highest total score (after all rounds are played) wins.
Thanks,
Leroy Quet