Two players White and Black alternately put dominos into a rectangle. Between these moves, a red square is thrown in randomly, but obeying the polyomino rule. This polyomino rule says that at each state the dominos and random squares together must form a polyomino---a connected shape.
Again, as in the nonrandom version, the player who cannot move loses, the other one wins.
You make your move by clicking into an empty square adjacent to a square already taken (except for the first move, of course). Clicking the square again deletes this tentative move, clicking on a square adjacent to it confirms your move and completes the domino.
Erich Prisner, 2012