I gotta toss my two cents in here.
1. I once watched a Japanese bantam hen fly 30 feet straight up to a beam on top of a barn. It was at a bird club auction and two guys spent a couple of hours tossing stuff at it to get it back. Darn thing flew like a pigeon!
2. If you want to use a 4 ft fence, put a one or two foot strip angled in to the yard. Birds likely won't fly up and then back. Don't underestimate a motivated chicken.
3. Chickens can learn and be taught. If one gets out, expect copycats to quickly follow.
4. Clipping wings work. All you need to clip is the primary wing feathers (the big ones at the end of the wings). This puts them off balance. I've had to clip wings with a 6 foot fence.
5. Dogs work partly because they leave a scent around the yard. I took this to the next level by leaving MY scent around the yard. (Yep, my wife married a redneck.) (In the following 15 years lost 1 bird to a falcon and two chicks to crows. I did manage to shoot one of the crows. Fine for the farm but I wouldn't recommend shooting things in the city.)
6. In the city, night critters are probably worse than day critters. One night I had a racoon kill ALL my birds in the shed. 25 dead, one eaten, all heads removed. After that it was war. Live trap cages, dog, the works.