For the actual prizes (that are listed in the sweepstakes rules like the Dream Fastpasses, Dream Ears, Lanyards, trips, etc) your chances are low, but you have as good a chance as everyone else does. The rules state that they are giving away 1,551 prizes (approx) daily. So if you figure that is spread out through MK, AK, MGM, Epcot, Downtown Disney, Typhoon and Blizzard it really is not a large number for any given place in one day (only about 300 I would guess at like MK...when you are talking an attendance over 30,000 on average).