Trying to understand when to take a deep finesse?
AQ8
JT9x    Kxx
    xxx


If you play small towards AQ8 in dummy, LHO should play one of the J, T, or 9. Then you can only score one trick in the suit. If the position is

    AQ9
JTxx    Kxx
    xxx


then splitting honors does not prevent you scoring the 9 (after J, Q, K, you can come to hand and repeat the finesse).

So the general answer is: only take a deep finesse if it can promote a trick.