Avoiding Colinear Points(Puzzle, Sequence, Game)

I will start this post describing an unoriginal game, then describe a puzzle and a sequence based on the idea.

2 or more players.

Start with an n-by-n grid drawn on paper. (I suggest an n of at least 10.)

Players take turns drawing dots at the lattice points of the grid, one dot per each player's move.

Whenever a player makes a dot which is colinear (in any direction) with any other 2 dots, that player is eliminated. (And 'colinearity' here is as if the grid were drawn perfectly and uniformly, and as if the dots were drawn at exactly the intersections of the grid's perpendicular lines.)

With only 2 players, the game is dumb

Wouldn't this strategy lose immediately, rather than force a win?

On an 11-by-11 grid, for example, the center dot would be f6. If the second player played, for example, d5, and the first player played the symmetric move, h7, there would already be three collinear points.

Or perhaps by 'reflected about the grid's center' you meant 'center line' rather than 'center point', i.e. d7 rather than h7 in the above example. In that case, all bets are off

For n=6 you can place 12 dots, for n=7 14, and for n=8 at least 15, as shown here in some examples:

Duh!...You are right, obviously. (What was I thinking?)

Regarding Richard Mathar's post: I guess the new challenge is to find a 16-dot solution for n = 8.

thanks, Leroy Quet