Reason's Greetings

Perhaps the central stance of the critical/skeptical atheist for his or her lack of belief in a god is that there is no evidence for a god. 

So, a major question to consider is, “What counts as evidence for God?”

I think this question to be a tough one, as the individual is forced by the constraints of a worldview to make a subjective judgment, but the very concept of evidence implies objectivity. So, here is the best answer I can personally come up with for now.

Mathematicians have, to my knowledge, a definition of what is considered impossible. Anything that is less likely than one part in 10^50 is considered unlikely enough to happen that it is considered not possible. (For a comparison, that is exactly the number of atoms estimated to be in the earth. It would take hundreds of years just to count the number of atoms one by one on the tip of a needle head.) 

So, I think I would believe in a god if I was able to objectively observe that which is impossible. Such as, if scientists set up an experiment in which a particular result is deemed to be around as unlikely as 1 in every 10^50 runs, and it is recorded and observed by multiple people. That would send a pretty clear message to me I think that perhaps a deistic sort of God exists. 

For any kind of specific God though, he would have to intercede with a message of his own; for example, a very clear message in any interpretable language written within the formation of stars would be a good start. 

What would you consider to be adequate evidence?