Richard Dawkins, perhaps the most prominent of the "new atheists," presented an argument for why God almost certainly doesn't exist. He dubbed it "The Ultimate Boeing 747 Gambit." It's an argument that educated theists love to hate, poo poo on, or generally despise as beneath them.
I'm a theist myself, but I don't think the argument can be poo pooed so easily, and I'll tell you why. But first a short summary of the argument. As when a chess player sacrifices a piece to gain an advantage (this is called a gambit), Dawkins makes a similar sacrifice when he concedes the point theists often make. They claim that life, due to its complexity, has about the same chance of occurring randomly as a hurricane blowing through a junkyard and producing a Boeing 747 jetliner. Theists then quickly add that God's designing activity must then be responsible for the life. Dawkins, however argues that God, if He is capable of such a design, must be at least as complex as what He's supposed to explain. If that's true, then the probability of God existing would be even less than that of a Boeing 747 arising out of a hurricane blowing through a junkyard.
What then is the solution to the origin of the complexity of life? Evolution by natural selection. The complexity of life can be explained by a long series of very simple steps, simple enough to occur by chance, in which complexity increases. These increases are preserved due to natural selection if they provide a survival/reproductive advantage. Thus we have a very simple algorithm for, as he puts it, "climbing mount improbable," that is, accounting for apparent improbability of life arising by blind natural forces. Not so with God; either you have Him with all his powers and intelligence, or you don't! There is no step-by-step simple algorithm for God's existence; and if there were, He wouldn't be much of a God!
Why is this argument poo-pooed? I've seen a few reasons. One is the stupid (I don't like to use this word in connection with the many otherwise brilliant Christians who say this, but it is stupid) and arrogant objection that Dawkins isn't a philosopher but a biologist and doesn't know what he's talking about when he comes to theistic arguments, theology, etc. So what? An argument is an argument is an argument. Who cares about his credentials? If we were just taking his testimony as reason to believe something, then his credentials would be important. But when someone offers an argument, to shift attention to the arguer instead of refuting the argument is to commit an ad hominem. I've noticed this sort of thing coming from people I otherwise respect, people like William Lane Craig, or Paul Copan.
But they have other responses, fortunately. One is simply to reply that God is simple. Theologians have always said this. So Dawkins is wrong. Supporting this response is to say that God is a non-physical entity, and thus doesn't admit of division. I also heard Craig saying that Dawkins is assuming materialism, that minds are the result of very complex brains. Theists, of course, deny this; they believe that minds without bodies are possible -- God is one of them. Thus God doesn't need a very complex brain; He can be a simple being.
Another reply: God is a necessary being. What "necessary" means is that God couldn't not exist. He's not the sort of being that comes into existence or goes out of existence. God is, in this sense, like the number 2; 2 exists necessarily. If God is a necessary being, then His probablity is 1. So any probablisitic argument becomes irrelevant. However, defining God as an existing thing is very question-begging for the theist; it's better to say that if God exists, then he exists necessarily. But even with this concession probablistic arguments are irrelevant.
Two quick replies on Dawkins's behalf. The first is that "simple" may have more than one meaning. One is regarding divisibility -- something is complex if it can be divided into simpler parts. Another is regarding description -- something is complex if a lot of information is needed to describe it. I think Dawkins is talking about the second meaning, but the divisibility argument only addresses the first. If God is both simple in that it He is indivisible yet complex in that a lot of information is required to describe Him completely, then Dawkins still wins, for it's the second sort of complexity that's linked to low probability.
The second is all of the examples of intelligent beings in our experience are complex. To posit a special being that is both intelligent and simple is completely ad hoc; there is no independent reason to think that there could be a simple yet intelligent being. Theists bring this in just to save themselves from Dawkins's argument.
Third, Dawkins could argue that necessary beings are impossible; there are no such thing as things that could not not exist. This might be a hard case to make, however.
Also, the ad hoc charge isn't really true, for theologians have been saying that God is simple for thousands of years, supporting the claim with a variety of arguments (see Divine Simplicity from the Stanford Encyclopedia of Philosophy for some of these). Perhaps they mean in both or all senses of simple. And it may be that simplicity of the first kind implies simplicity of the second kind. Thus I don't think any of the above replies are the best way to press the the Gambit.
This brings me to the makeover idea. Let's not construe the Gambit as a probabilistic argument, for if it is, it's addressing a God that no one believes in. The Gambit does establish that the probability of a being with complexity greater than that of life arising out of chance is just as improbable as life arising out of chance. But this isn't what, Christians at least*, worship.
Instead, let's construe the argument as a conceptual, deductive, incompatible properties argument. These kinds of arguments mean to establish that God is not merely improbable, but impossible. How so? They try to show that the concept of God is like that of a square circle, self-contradictory. You could argue that, for instance, God is impossible because He's supposed to be free and know the future; if He knows the future, then He knows what He's going to do, and hence His actions are determined and not free.
How about this then; God is supposed to be both intelligent and simple. These two properties are not compatible, for intelligence requires complexity. Thus God, inasmuch as these traits are part of His definition, cannot exist. He is like a square circle. And God's alleged necessity just adds to the problem. The only way for a being that that is such that, if it exists, it cannot not exist to not exist is for it to be impossible** (apologies for the convoluted sentence). But then Dawkins has a card to play here -- God is impossible, not because necessary beings are impossible, but becaue God is impossible due to other incompatible properties.
This all rests on the claim that intelligence requires complexity. Is this so? I see no reason to think it would have to, though examples in everyday life support a connection. But everyday life might not be a good rule for understanding the nature of a being like God.
The theist, I think, should, as Craig does, try to argue that some intelligent personal being must be responsible for the existence of the universe, fine-tuning, and the rest. If this argument is strong enough, then one can justifiably appeal to mystery regarding how God is both simple and intelligent. For all we know, mysteries might (and I think do, look at the mysteriousness of phenomenal consciousness) exist. If we have good independent reasons for thinking that there are such mysteries (like God), then, well, we just need to accept it.
*The theist philosopher Richard Swinburne doesn't say that God exists in every possible world. He offers probablistic arguments for God's existence. Perhaps Dawkins could follow Swinburne (use his arguments) for God's not being logically necessary and reply with a probablisitic argument against God's existence. But Dawkins's attack would only apply to the sort of God Swinburne accepts and to the approach Swinburne makes.
** This claim depends on the following: a being that is such that if it exists it cannot not exist must be such that if it's possible for the being to exists it must exist. I think this can be proven using modal logic, for if God exists in one possible world, then His existence is necessary for all possible worlds. There still is room for doubt (the claim isn't question-begging), for we don't know whether or not God is possible. God is either necessary or impossible.