No corkscrew, though, am I right?

(I'm not kidding about the usefulness of the Flair's corkscrew. It works well enough that it isn't only for emergency use: at crowded parties it's often quite a lot easier for me to dig out my Flair than to wander around several rooms looking for the house's official corkscrew. The official one would generally be a bit easier to use if I could find it, but not easier enough to warrant going and looking.)

Mine definitely has a corkscrew (that lives with the extra bits, IYSWIM, and attaches to the main bit).