This set I am going to show you in a moment is like unto those of Washington's time, a dating strengthened by its correlation with the chess pieces found from the tragic 1786 wreck of the English Indiaman Halsewell (well written up by Rodney Legg, here: The Loss of the Halsewell). However, it is not clear that Washington played chess: Washington may have been more of a cards and backgammon sort of fellow. Regardless, the form of the bone chess set is a late 17th century one, typified by:

George Washington's chess set: Pictures