Nigiri as tie breaker
Nigiri is normally used to decide which player gets which colour.
But it can also be used as tiebreaker by itself. In that case one player (White) grabs a handful of white stones and the other player (Black) guesses if the amount is odd (by placing one black stone on the board) or even (by placing two black stones on the board).
After this the white stones get counted and if Black player guessed right he wins the tie and when he is wrong White wins the tie.
This has the same randomness as any random tie breaker.