if you visit the east coast known as Punta Cana, in the areas Punta Cana, Cabeza de Toro, Bavaro, Cortecito and Macao a lot of hotels have their own casino, from all others you'll get transportation, mostly free, just check for info in the lobby area of your hotel or with the guest service, there's casino promotion all over. i just don't know about the hotels in the area named Uvero Alto (mostly sold as Punta Cana too), that area is 1 hr drive north of the real punta cana/bavaro area, hotels named Secrets excellence, Sirenis and Ivory.
good luck
Mike