Make a note of this, I'm *NOT* going to let go of the arm I had first if the arm bar is working. That would be stupid. However, the fact is that I often don't get the first arm bar attempt. Once I have rolled the person over and I have their arm trapped, they're suspicious, trying to pull in that arm. They aren't thinking so much about the arm that I don't have.
That's why it's called the sneaky arm bar entry.