Connectin'-It Game

This is a game for 2 or more players.
Start with an n-by-n grid taken from graph paper. (I suggest an n of about 10 to 20 for beginners.)

On a move a player can do one of two things:

He/she can draw a dot at any intersection of the grid that doesn't already have a dot and isn't on a line-segment.

Or she/he can draw a straight line-segment that connects any two dots, provided that the line segment does not pass through any other line segment and doesn't pass over any intermediate dots.

A player gets a point every time she/he connects two dots with a line-segment.

The first player to get a pre-determined score wins.
(I suggest a winning score between n^2/4 and n^2/2, if there are two players.)

Thanks,
Leroy Quet