It's true in a technical sense for any size board. But the proof that the first winner has a winning strategy can't easily be put into a practical winning strategy. In rough outline, the proof goes as follows: First, note that the game cannot end in a tie. Next, use standard game theory to conclude that one of the players has a winning strategy (proof by labeling the game tree, starting with the leaf nodes, and working up towards the root). Finally, assume for contradiction that the second player has a winning strategy. If so, deduce the absurd result that the first player has a winning strategy: Place your first piece at a random location, then ignore that piece and follow the second player's winning strategy. If that means placing a piece where your initial piece is already, place a piece in a different random location, and continue. This works because having an extra piece on the board can never hurt you.