Atheist guru Richard Dawkins Makes the argument that God would have to be more complex than the universe he creates, and the more complex something is the less probable it is. “The whole argument turns on the familiar question ‘Who made God?’ which most thinking people discover for themselves. A designer God cannot be used to explain organized complexity because any God capable of designing anything would have to be complex enough to demand the same kind of explanation in his own right. God presents an infinite regress from which he cannot help us escape. This argument…demonstrates that God, though not technically disprovable, is very improbable indeed.”  Of course that assumes the contradictory notion that God is subject to a higher power and is the product a set of laws such the laws of physics. It's treating God like a great biologicals organism The Christian tradition asserts that God is not complex. Of course Christian tradition asserts that God is spirit, thus is unlike any sort of thing in creation, no subject to natural law and not complex but simple. This latter dictum will be the focus here.
According to the classical theism of Augustine, Anselm, Aquinas and their adherents, God is radically unlike creatures in that he is devoid of any complexity or composition, whether physical or metaphysical. Besides lacking spatial and temporal parts, God is free of matter-form composition, potency-act composition, and existence-essence composition. There is also no real distinction between God as subject of his attributes and his attributes. God is thus in a sense requiring clarification identical to each of his attributes, which implies that each attribute is identical to every other one. God is omniscient, then, not in virtue of instantiating or exemplifying omniscience — which would imply a real distinction between God and the property of omniscience — but by being omniscience. And the same holds for each of the divine omni-attributes: God is what he has as Augustine puts it in The City of God, XI, 10. As identical to each of his attributes, God is identical to his nature. And since his nature or essence is identical to his existence, God is identical to his existence. This is the doctrine of divine simplicity (DDS). It is represented not only in classical Christian theology, but also in Jewish, Greek, and Islamic thought. It is to be understood as an affirmation of God's absolute transcendence of creatures. God is not only radically non-anthropomorphic, but radically non-creaturomorphic, not only in respect of the properties he possesses, but in his manner of possessing them. The simple God, we could say, differs in his very ontology from any and all created beings. 
Long time readers of this blog have seen me talk about theologians such as Paul Tillich who say God is "being itself." This is the core of the concept. The scholastic philosophers defined it in saying God's existence is his essence, For contingent or temporal things in creation existence is distinct from essence. That a thing is not the same as what it is. There can be potential things that exist only in potential and not in reality. Since God is the basis of all reality he is being itself. To be is to be either God or a creature of God. period. Those are the only forms of being there can be. These ideas sound very odd to modern people especially when they never studied theology, Thus atheists are often left to attack such notions,.
Clearly God is not complex in the way that Dawkins means. Dawkings deals with thye idea ofa big man, an organism something that grows and has parts. This is totally unlike God and God is simple in that sense.
So first, according to classical theology, God is simple, not complex. More remarkable, perhaps, is that according to Dawkins's own definition of complexity, God is not complex. According to his definition (set out in The Blind Watchmaker), something is complex if it has parts that are "arranged in a way that is unlikely to have arisen by chance alone." But of course God is a spirit, not a material object at all, and hence has no parts. A fortiori (as philosophers like to say) God doesn't have parts arranged in ways unlikely to have arisen by chance. Therefore, given the definition of complexity Dawkins himself proposes, God is not complex.In that sense God is Simple.
Skeptics usually open their attack on DDS with the notion of Trinity. "Of course, we have all heard that the doctrine of the trinity is incompatible with divine simplicity. How can God manifest himself in these different ways and still be simple? The standard answer to this question is that the three persons of the trinity are not "parts" of God. They are a unity in three persons, distinguished by their relationships with each other. One skeptic says "Well, that settles it, then. We just play a little game of word salad, and pretend that we have made a cogent response to the question."  I will save a full discussion on persons in Trinity for another time. The skeptic has to stop calling he doesn't understand "word salad" and start thinking about critical distinctions. There is a critical distinction to be made between God being more than a super symmetrical point with no diverse aspects and not having parts. This is especially crucial since not having parts is the definition of complex. God can be Triune and still simple because the three persona are not parts but aspects of one thing: divine essence. Analogy: three shafts of sunlight shining through the clouds aspects of one light without being "parts" of the sun. God is not the product of a development, he didn't grow and thus has no parts.
Skeptics might also the notion of God as a person, having knowledge, will, volition and ,man being made in God's image.  The notion of God as a person is part of Orthodox understanding, but is more of a modern idea.
Brian Davies observes that the formula ‘God is a person’ “is by no means a traditional one. It does not occur in the Bible. It is foreign to the Fathers and to writers up to and beyond the Middle Ages. Not does it occur in the creeds”... The Christian Trinity speaks of three persons of one substance (ousia or substantia). It does not say the Godhead itself is a person, or that God is three persons in one person. Stanley Rudman argues that thinking of the Godhead itself as a person is a relatively recent development (1998, ch. 8). It is mostly absent from Western theology before the eighteenth century. William Paley (1741–1805) and Friedrich Schleiermacher (1768–1834) provide early examples of trying out the idea. The nineteenth century sees an emphasis on God as a person or personality gain considerable momentum. ...
Granted God would have to possess these attributes of knowledge, will, volition, on terms other than human consciousness, but we know that's the case anyway, God is spirit, not a biological organism. we can't draw conclusions about God based upon our own natures. The concept of being in God's image doesn't mean personhood just as it doesn't mean body. It probably refers to consciousness but that is not the same as personhood. Consciousness refers to the state of knowing. Being a person entails personality and that means hang ups so God can't be said to have one. Personhood is social and genetic. God is a product of neither,
Now we come to the most crucial problem, the coherence issue. Because the super essential Godhead (God as being itself) is based upon God's simplicity we have to accept the notion of God's attributes or properties being identical with God in order to be simple. Yet that's incoherent. As Plantinga points out if God is identical with his properties then he is a property and thus an abstract entity and thus inert. Moreover all the different properties would be identical and that makes no sense., But Nicholas Wolterstorff points out that adherents of the Augustinian and Thomisitic tradition do not see properties of individuals as added abstractions external to them, but being ontologically constitutive of the person. Being material human beings have relatively varied degrees of constitutive properties. Not so with God. Since God is immaterial thus there is no individuating between God and his nature. If God is just he is justice. The divine nature is not a abstract object
Material beings are individuated and diversified by their signate matter. Thus Socrates and Plato, though the same in nature, differ numerically in virtue of their different portions of materia signata. Matter makes them individuals, and matter makes them numerically diverse individuals. God, however, being immaterial, is not individuated by anything distinct from his nature, and so can be said to be a self-individuating nature. As self-individuating, there is no real distinction between God and his nature. In Thomist terms, in God nature and suppositum are identical.(ST I, q. 3, art. 3) The divine nature is not an abstract object related across an ontological chasm to a concrete individual;the divine nature is a self-individuating concrete unitary nature. 
Even though divine simplicity appeals to me, I am not a Thomist and I'm not stuck with Thomism alone for answers. That is not to say that I don't have great sympathy and respect from them, especially Gilson. Nevertheless, as an answer to Dawkins I would say to things: (1) The kind of complexity he's looking for is not characteristic of God. (2) Simple and complex are relative terms. They lose their meaning when used of God. A printed circuit is complex but not compared to the human brain. What meaning does it have to speak of the basis of reality as complex?
 Richard Dawkins, The God Delusion, London: Black Swan, 2007, 136.
This is what he refers to as the "747" gambit.
 William F. Vallicella, , "Divine Simplicity", The Stanford Encyclopedia of Philosophy (Spring 2015 Edition), Edward N. Zalta (ed.), URL = http://plato.stanford.edu/archives/spr2015/entries/divine-simplicity/. accessed 5/7/16
 Etienne Gilson, God and Philosophy, New Haven: Yale University Press; 2nd edition, 2002, 50.
 Alvin Plantinga, "The Dawkins Confession," Books and Culture a Christian Review: Christianity Today, URL http://www.booksandculture.com/articles/2007/marapr/1.21.html aacessed 5/7//16
Even though Plantimnga argues against Dawkin's concept of complexity he does not support the Thomisitc notion of DDS.
 I Am Skeptic
 I Am Skeptoc, op cit
 Peter Weigel, "Divine Simplicity," Internet Encyclopedia of philosophy, online resource URL:
http://www.iep.utm.edu/div-simp/#SH5b access 5/7/16/
Peter Weigel is at Washinton college