Virginia and Massachusetts have banned the games. North Carolina's ban was partly rolled back by a judge, and the law is being challenged in an appeals court. Several cities in Ohio imposed new fees this fall to restrict the games, and the state Legislature is debating statewide curbs. A game room in Rochester, N.Y., that was under investigation by the state attorney general closed. This week, game room operators in Hillsborough County, Fla., challenged that jurisdiction's ban on the games.