Pah Tum is a bit unbalanced (white wins 55%, black 31% of the games). Maybe it would be better if the players alternate in blocking squares, instead of blocking them randomly.
The number of blocked squares is determined randomly (3, 5, 7 or 9). Black starts to block a square, and black also blocks the last square. Then the game goes on as usual.
Alternatively use a swap rule: one player blocks the squares, then the other chooses a side. And equal points might count as a black win, to make the game draw-free.
Thom27: I agree with you that white has a big advantage. My suggestion would be that black starts with 1 point. Something similar happens with go variations. This would mean a draw would count as a win for black and would make the % 54 to 46. A draw will be possible still but unlikely.