Lines-From-Lines Game

Sorry if this is unoriginal.

Here is a game for two players. It is played on an n-by-n grid drawn (practically perfectly) on paper. I suggest that n be at least 8.

Note: (The lines of the grid do not come into play here. Only the "grid-vertices" {where the lines of THE GRID intersect} are important as far as the grid is concerned.)
By "lines" below, I am referring to straight line-segments drawn by players during play. I suggest these lines be drawn with a straight-edge.

The first player to move draws a line from any grid-vertex to any other grid-vertex.

The players thereafter take turns drawing lines, one line per move, such that:
* each line starts at a grid-vertex intersected by any previously drawn line (drawn by either player).
* each line ends at any grid-vertex not yet touched by a line.
* no line crosses another line or coincides with another line.
* no line starts/ends at or crosses another line's end/start-point (whether or not yet another line passes completely through that vertex).


If you can move, you must. (The other player can help you find allowable moves.)

The LAST player to be able to move LOSES.

And let me clarify things, in case I am a bad writer.
A line may PASS THROUGH a vertex at most once.
A line may START OR END at a vertex at most once.

The same vertex may have one line passing through it and another
single line terminating (ending or starting) there.



There must be an easy strategy to always win. Anyone know of one?


Thanks,
Leroy Quet