I should tell you that the oral hearing is the last step in the appeal. Before the appeal is heard, you get the written arguments. You get the judgments from the two courts below. You read that material. You read the argument. You know the case pretty well before you go in. In the hour that the lawyer has, he should pick his strongest point and argue it. But the judges don't learn much about the case in the courtroom. They should know about the case before they get in the courtroom. That's usually the way it is: you do know the case before you get in.
Now, cases don't always go the way you think they might, because a lawyer raises a new point, or a judge raises a point, there's an argument around it, and people change their minds, but in 95% of the cases that does not happen.