Black has sure win if he plays his second move the closest possible to the center. This is serious flaw and this game on higher level is not competitive at all.
Enlarging forbidden zone to the 7x7 central square, replacing 19x19 by 15x15 board and not counting overlines (that is 6 or more stones in a row) as a win would reduce black advantage considerably, although black would still have an edge.
