News that Iran's and Turkey's governments reached an accord on Idlib, a Syrian town now the focus of American interests, brings relations between two of the largest and most influential states in the Mideast momentarily out of the shadows. Their rivalry goes back a half-millennium, included eleven wars, and now remains, in the words of the Washington Institute's Soner Cagaptay, the region's "oldest power game." What does the recent accord signify and how will their competition influence the region's future? Iranian and Turkish parallels are noteworthy. Both countries have populations of 80 million. (Egypt, the region's third large country, has...