In 11 days, Epic Games will square off against Apple in an Oakland, Calif., courtroom in a trial over whether the iPhone maker violated U.S. antitrust law by forcing the videogame app developer to pay certain fees. A win by Epic would reshape the world’s most valuable company and carve a path for competitors and governments to challenge the dominance of the world’s digital gatekeepers.

But Apple has the advantage. Despite documents and testimony that appear to undermine some of Apple’s defenses, Epic faces long odds because U.S. courts have often ruled against the kind of legal arguments it is making. And U.S. District Court Judge Yvonne Gonzalez Rogers, who will rule on the case following the three-week, juryless trial, has spent years overseeing various antitrust cases against Apple and its App Store and has sometimes appeared skeptical of allegations.