Just one other aspect of this that no-one's touched on.

Sometimes reels are written in such a way that when you get to the end of a section, it is obviously intended that you go on to the next section rather than repeat.

An example of this is the reel "Man of the House". Strictly speaking, this is single reel, although more often than not the sheet music will call it just a reel, and you're left to depend on the presence or absence of repeat signs (though music publishers sometimes get these wrong too).

Reels can still be single reels, even when the sections lend themselves to repeats - for instance, the Ash Plant. Why some are, and some are not, is lost in obscurity, or lost to me anyway, and the distinction is hardly ever drawn in session playing, where AA BB AA BB is almost always the format, except sometimes in medleys.

As far as I can recall, double reels are never described as such. They're just reels, and again you most hope you can rely on the presence/absence of repeat marks. On the other hand, I've often seen double jigs so described - even though there are no single jigs, as far as I know.

Where a tune is in three parts - eg Dingle Regatta - the norm would be to play AA BB CC twice over. For dancing, and especially in competitions, the usual assumption for jigs and reels is that tunes will be in eight-bar sections played AA BB AA BB, though there can be exceptions (eg all competitors dancing to the same three-section tune).

Hornpipes, set dances, polkas etc don't seem to be subject to these vagaries. Just be sure to play each section twice before moving on, and you'll usually be safe, almost regardless of whether repeats are indicated.

So in the end, I guess it just comes down to Irish common sense. And whoever said check with the dance master, hit the nail on the head. Interesting though. Or maybe it isn't....