Take four black and four white stones in one hand and drop them randomly on the board and adoube them into place. Then continue the game from there.
(not to be confused with Pai Gow)
Black points at two spaces on the board. White then places a white stone in one of those spaces and a black stone in the other. Then white points at two spaces and black places a white stone and a black stone there. Keep alternating. Works best on 9x9.
Instead of alternating b/w/b/w/b/w, alternate using the Thue-Morse sequence. b/w/w/b/w/b/b/w/w/b/b/w/b/w/w/b and so on.
Instead of alternating, both secretly note where they want to go. (For example by covering a pair 20-sided coordinate dice each.) If both choose the same spot, do-over and no-one can choose that spot that round. Keep doing over until you choose different spots. That spot is eligible next turn again.