Swinburne spends pages and pages arguing for the existence of God, but most of his discussion boils down to one claim: God is simple. He argues that when the background evidence is taken to be purely trivial logical knowledge, the probability of a hypothesis is determined mainly by its simplicity. It is clear that the universe itself is quite complex. If we have a choice, then, between taking the universe itself as our fundamental postulate and taking God as our fundamental postulate we should (the argument goes) prefer the simpler hypothesis.
The idea that God is simple has a long history in theology. Usually it is taken to mean that God has no moving parts: he is a unity, not something that can be decomposed into sub-units.
Considering how central it is to his whole program, Swinburne spends remarkably little time defending this claim. He only gives one argument to support it, that goes like this: If God had any finite amount of power, then that amount of power would require some sort of explanation. So an infinite amount of power - omnipotence - is a simpler hypothesis than any finite amount of power. He argues similarly for infinite knowledge and infinite freedom for God to do as he wills.
Now, I am tempted to question this argument, but even if we grant it, how does it follow that God is a simple entity? Maybe the God hypothesis is simple in this one (or these three) respects - it need not be true that he is simple in other respects. As an analogy, consider the spatial extent of the universe. It might be true that the hypothesis of an infinite universe is simpler than a finite universe (I'm not convinced that it is, but let's allow it). But the universe itself remains a very complex thing.
On the contrary, we have very good reasons to believe that an intelligent entity must be complex. An electron is simple: it can be described by its mass, spin, charge, and state of motion. But it isn't intelligent. An amoeba has a certain amount of intelligence: it is able to respond in a rudimentary way to external inputs. But it is already a very complicated entity. It has organelles that convert energy, transcribe DNA into RNA, and RNA into proteins, and so forth. An insect is far more complex again, yet has very limited intelligence and often very rigid behavior.
It is only when we get to organisms with highly complex nervous systems - birds and mammals - that we find problem-solving abilities and other aspects of true intelligence.And humans have, pound for pound, more brain than any other animal.
Likewise with non-living things: a crystal is simple, but it is not intelligent. A computer can beat me at chess and perform other "intelligent" tasks - but it requires a very complex internal structure to do so. Computers do not yet have anything like human-level intelligence, but if some day they do, I'm pretty sure they will be still more complex than today's computers.
So we have very good reasons to think that the higher the intelligence, the more complex the entity. It seems logical, then, that infinite intelligence would require infinite complexity.
But if God is highly complex, then, by Swinburne's criterion, God is highly unlikely.