Mere theism

One objection that atheists sometimes raise is that a more specific claim has a lower probability than a more general (or simpler) claim. Hence, Christian theism has a lower probability than mere theism. But there are problems with that contention:

i) Mere theism can be just as specific as Christian theism. It's just that Christian theism has already been defined by various Christian traditions. When we think of Christian theism, that denotes a specific concept. That refers to a preexisting position with a particular set of propositions–although that varies according to the theologian or theological tradition.

Taken by itself, mere theism is a cipher. The content needs to be filled in. But once we specify what that amounts do, the claim loses the prima facie appearance of simplicity or generality. 

ii) In addition, even if Christian theism a more specific claim than mere theism, that doesn't make it less probable. To the contrary, there may be specific evidence for Christian theism, corresponding to the specificity of the claims. (Even assuming specific claims are less probable than general claims.)

Conversely, mere theism might well have less evidence. Depends on the version of mere theism. How "mere" is mere?