Criss-cross Grid Game

Here is yet another of my games played on an n-by-n grid drawn on
paper.
For 2 players,each with a different colored pencil.
Players alternate placing an X or an O of their color in the grid's
squares as follows:
*Player 1 places the first O in the upper-left square.
*Each player places their symbol immediately next to the symbol last
drawn
by the other player in the directions of vertically, horizontally, or
diagonally.
*If the square a player draws his symbol in is empty, he/she draws an
O.
*If the square contains an O, he/she writes an X in the square with the
O.
*A player may not draw in (move to) a square already occupied by an X
(and an O).
Play continues until moving is impossible or when one player first gets
a predetermined number of points.
Scoring:
*If a player places an X in the same square as an O, the player who did
*not* draw
the O in that square gets a point.
*If a player places an O in an empty square diagonally adjacent to the
last square
drawn in by the other player, and the other 2 squares in the 2-by-2
bigger square
-- formed by the empty square being drawn in and the last drawn-in
square at opposite
corners of the bigger square -- are both filled, then the player
'completing the (bigger 2-by-2)
square' (the player whose move it is) gets a point.
Example to make above clearer:
+---+---+
!.O.!...!
+---+---+
!OX.!.O.!
+---+---+
Last move put an X in lower left square (getting a point for the player
who
did *not* place the O there earlier).
Player now wants to place an O in upper right square, which would get
him/her
a point (since the upper-left and lower-right squares of the 2-by-2
bigger square are both not empty).
What is a good strategy for this game?
thanks,
Leroy Quet