This is a wonderful idea. It combines two CS-related ideas in a wonderful way:
- People can't do randomness well at all; people confuse "random" and "arbitrary" all the time. If you really want to randomize security patrols, you need to separate the human element from randomness.
- Security is about predictability. If you establish a predictable pattern, an adversary can learn from that pattern and devise countermeasures. On the other hand, an adversary can't compete against a truly random opponent.