Hmm, i just discovered of this board's existence and there was a really interesting discussion about what is the Pahtum-3to9* game? A white, a draw or a black wins game?
One answer can be given but not so clear.

Definitelly Nothingness was wrong! Pahtum is a white wins game OR a draw game! That means if white plays a perfect game then black can't win and can only achieve a draw.......Easy to prove**. AbigailII already did.......
The really interesting problem comes when you try to restrict this and to convert this to a stronger statement like if it is a white wins game or a draw.
I have not yet an answer, but i want to say that i have the impression that white's extra tempo is crucial! Since the directions that a 3-stone point can be build are 2, black can't force white not to create at least a 3-stone point at the end......It's easy to prove this also. But this doesn't prove that Pahtum-3to9* is a white wins game since we didn't prove that at the end black can't build a 3-stone point too.........

*Pahtum-3to9 = Pahtum game with 3 or 5 or 7 or 9 holes placed randomly at the first turn.

About this randomly: While the placement of holes should be randomly is it really in the Brainking's variation?
What i mean: I have never see a placement where a single playable square is surrounded by 4 holes or 3 holes while the playable square be at the edge of the board. Like this:
OXXXXXX
XOXXXXX
OXXXXXX
where the X=playable squares and O=holes
Can this position occur in Brainking's Pahtum?

**In a game that:
1)Is played between 2 players that execute alternating turns of moves
2)Is played by placing something(ex. stones) and staying there for the rest of the game unchanged, into any empty(meaning that no one has already played there) position of a specific finite number of positions that doesn't move or change during the game
3)It's true for every possible position, that if we make a move-1 for the side to move and we will have with perfect play a win or a draw with that move-1, then by making a random move-2, after playing move-1 (that means to play 2 times in our turn), then the result will not become worse by making this move-2. A win will remain a win and a draw will not become a loss

then in this game that has 1) and 2) and 3) valid
it is true that player that plays second CAN'T win!