The simplest board (basic) is 6x6 for this. Where the player that moves to c1,e4,a3,d5 or f6 wins. Then if you continue, the next winning squares are calculated by applying half the relationship between f6 and the winning squares on 6x6 board to every other square.
I.E. If we take the bottom right half, the winning squares on 6x6 are f6,e4 and c1. If we put this on a 10x10 board so these squares are J10, I8 and G5. The relationship between the first two (J10 and I8) is down two and left one, so if we assume g5 to be the new J10, the next winning square is f3. The relationship between the second two (I8 and g5) is down three and left two. So the next winning square is the theoretical D0.
More taxing: If you have a game where there are two rooks on g8 and h8 and each player can only move one of the rooks left or down each move, and person who cannot move loses, how to win?