The Culbertson Law on symmetry was based upon his alleged experience that more often than not the distribution pattern in one hand tended to repeate itself around the table. For instance if you had a void, and in particular if you found another void in Dummy you should expect voids (or “near voids” i.e. singletons) in each of the two remaining hands as well.
There may have been some basis for his theory in the days of manual shuffling and dealing of cards, but with todays random based card dealing procedures the theory is at best questionable.
