In the coin flip scenario, the intrinsic properties of a coin result in a threshold of 50% which above a certain scale, is very "sharp" or sudden in the transition. Compare this to a hash table or queuing theory, where a certain amount of capacity works well up to a certain point, then it falls apart. If you can design a random test which will display that property, then you can determine it before the fact without having a way to directly calculate that property, like we do for coin tosses.