The first player can always win, provided he plays to the centre on his first move. 
But a good variation of the game is to bar the centre for the first move of the first player. 
In that case the second player should take the centre at once. 
This should always end in a draw, but to ensure it the first player must play to two adjoining corners (such as 1 and 3) on his first and second moves. 
The game then requires great care on both sides.