Who throws the dice for you?

[FallentoReason]

I honestly don't see where he begged the question.

One could rephrase the syllogism as:

1. If God exists, there will be unexplained behavior.
2. If God does not exist, there will not be unexplained behavior.
3. There is unexplained behavior.
C. Therefore God exists.

This seems an equivalent formulation with no question begging. Am I missing something?

If by "unexplained" you mean "random" (because that's the only way I can relate your post to the OP) then I think there is question begging: premise 3. What's to say that there isn't a deeper explanation for the apparent randomness of quantum physics?

It's still a god-of-the-gaps argument.