The pieces would not exist as solid bodies unless you were observing them. So whenever you were not looking at them, they were more describable by a probability wave function represented by % possibilities of a range of pieces. When you actually observed a given piece, the wave function that describes the distribution of probabilities for that piece would then collapse into a particular piece with a set of rules of movement.
Of course, one of the problems with this is: If you knew exactly where the piece was, you could not be sure how it moves, or, if you were sure of how it moves, you could not know exactly where it was.
1. Ri2-j2