In order to prove that p1 wins in "fun" pente (no opening restriction) either on a 13x13 board or 19x19, possibly you could exclude moves N spaces away but it would be tough to prove that different far away moves have no effect on a winning line for one of them. You have to do an exhaustive search -- taking into account every possible move by p2. But you do not have to try every possible move by p1, you can plug in an opening book of good moves by p1 and see if they will lead to a win.