The model of special divine action based on quantum randomness tends to get more attention than the rest. In the standard interpretation of quantum mechanics, some events are not merely unpredictable but also truly indeterministic. This would allow God to work within such ontologically random events without violating any laws of nature. An unappreciated weakness of the model is that quantum fluctuations are not readily amplified into the macroscopic realm. Dynamical systems theory, continuum mechanics, and condensed matter physics show that such fluctuations are prevented from bubbling up within macroscopic systems. While some look to chaos theory for help, chaotic systems are not nearly as prevalent as the popular literature indicates. Once all the relevant physics is considered, models of divine action based on quantum randomness and chaos are far more limited than they are generally assumed to be. Unless some sort of new physical mechanism is discovered, the amplification problem cannot be solved. This means that there is little that God can accomplish by way of quantum randomness.