Game of two players on table 20X20:
Player one is starting the game. Each turn he can put red stone on any point $(i,j)$ such that there isn't another stone on $(i,j)$ and there isn't another red stone place on the table in distance of $\sqrt{5}$ (Euclidean distance) from $(i,j)$.
Player two in his turn place blue stone everywhere he want, as long as there isn't another stone placed there already. The goal of player one is to put as many red stones as he can, and for player two the goal is to reduce as much as he can the amount of red stones placed by player one.
The question:
How many red stones Player one can assure he will be able to place in the end of the game? what is the invariant condition and Player one's strategy?
What I've tried so far:
I'v noticed that distance $\sqrt{5}$ are equivalent to the distance that horseman can play in chess. Also, if I didn't make any mistake, I found out that if the game is on table $3 \times 3$ or $4 \times 4$, then Player one can put at least $4$ red stones, and can't assure better result.