The official answer is three formal nights and three smart casual nights but this is not absolutely certain as some changes can and do occur with different cruises. Does one have to dress accordingly.......no but by not conforming you will probably have to eat in the Windjammer or the specialist restaurants. The majority of passengers dress formally, if not by wearing a DJ then by wearing a suit but there are certainly those who do not. I feel that they miss out on part of the fun of the cruise but I would never deride the fact that they do not wish to dress up (unless they consider working clothes like jeans and T shirts suitable to wear to dinner).....Nei.
This chart is a straight lift from RCI's website:
Cruise Length Casual Smart Casual Formal
10-night 6 2 2.