I can't speak for the Sovereign as I have never sailed her, but from the deck plan on the RCI website, I'd say the casino is large enough to have the normal assortment of table games. They normally have at least one $5 Black Jack game and that table can sometimes be hard to get a chair at, but for the most part the casino is not that crowded and its open most of the day on "sea days", so the crowd is spread out through the day. You should not have a problem.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013