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.