Suppose I am declarer, and dummy has a "side" (non-trump) suit with AQx or AQxx, and I have xxx in my hand. I have been told NOT to finesse the Q (a 50-50 chance), except as a last resort, or late in hand. (And to "refuse" the finesse, probably taking the ace, if that suit is led in say, a NT contract).
Change dummy a bit to AQTxx. Now I'm told that I have a COMPOUND finesse, because I am finessing against both the K and J. In such instances, I have been told that I SHOULD finesse (assuming that going twice to my hand to lead doesn't cause problems elsewhere). If the KJ are both with LHO, I win twice, if both with RHO, I lose twice, but most likely, I win one and lose one because the honors are split. If the opponents have a 3-2 split (a 68% chance), I can treat the lost finesse as a "ducking" play, and run the suit for four tricks after I clear it with the ace.
What makes the "double" finesse so much better than the "simple" finesse? Is it because the extra card in dummy might allow me to win a fourth (long) trick? Or is it because I have a second potential stopper in dummy if the first finesse fails? Is it in the compound finesse I PROBABLY win once, whereas in the simple finesse I POSSIBLY win once? Or have I been given the wrong advice about compound finesses?