JHostler wrote: a genuinely viable candidate of the name Andrews - one making no diligent effort to remain anonymous - would almost certainly have been nailed long ago.
I'm not sure this conclusion is as certain as is implied. It is very difficult to find out much about the vast majority of people who lived in 1902. We are biased to think otherwise because the people we do know about -- Edwin S. Andrews, W. E. Sanders, Gallaway, etc., are people that have left a wide trail in the archives that are searchable today. The more we can find out about them, the more likely we are to find something that looks like a connection to Erdnase.
But if someone doesn't have much written down about them (in formats or locations that we can search today), then we won't be able to build a case that they were Erdnase. It doesn't mean that they didn't exist, or that their lives weren't similar to what we think Erdnase's life was like; it just means we don't have evidence in hand to demonstrate it.Here
is a man named "E. S. Andrews" who was active in show business in 1906. This is all I know about him. He could have been Erdnase; it is impossible to know at this point.Here
is another man named E. S. Andrews, who worked in the circus in 1906. Is he the same guy as the previous? Is either of them skilled with a deck of cards? There's no way to know.
Out of maybe a dozen or so people named "E. S. Andrews" about whom I've found reference between 1890 and 1910, most of them are only a name that exists in the censuses or in newspapers. There isn't enough other information available to find about them that can indicate similarity between them and Erdnase to draw any conclusions about them.