Use dice to determine which pieceor pieces may be moved.
DICE CHESS

Fun as this little idea may be, how many people would want to try this variant out, since it massively restricts the freedom that comes with chess games? (Whether it's FIDE, Xiangqi, Shogi, Makruk, whtat else have you.)
I suppose it might be more fun for those who have hardly played chess (seriously) or not at all, but it doesn't sound like something I would be interested in, in the the forseeable future.
However, in one of my own variants in development (Dragon's Chess II: Game of Conquest), I did propose the dice to be used to determine the Dragonfly piece's promotion to the Dragon piece. In that regard, my Xiangqi variant here would be classified a Dice Chess.
One, two or three dice. What a leveller.