One of the tough things about bridge is that the correct line of play for VERY similar card combinations is different.
A General Principle: Do NOT lead a lower honor toward a higher honor (hoping opponent will “cover an honor with an honor”) unless YOU or dummy hold the appropriate lower honors or spot cards to promote.
Second Principle: whether you finesse or play for the drop depends on how many cards you and dummy have in that suit.
Sidebar: Some of these you can work out from first principles like safety plays. With safety plays, you envision what bad break MIGHT happen; figure out if you can guard against it on BOTH sides; or just on one side and take appropriate measures, e.g., KQ9xx opposite A10xxx, cash King (or Queen) first. If either opponent shows out, you still have finessing position again the Jack. However, Kxxx opposite AQ9xx, you canNOT guard against J10xx on either side, so cash King first and then finesse RHO for J10xx if LHO shows out first round.
With finessing combinations, you consider the different lines of play and judge relative frequencies of different distributions, and take the appropriate line of play.
AKJ10x opposite xxx: Proper play is to cash ONE high honor (Ace OR King) first. You are guarding against a singleton Queen. It does not happen often, but is worth protecting against, because you can afford to. You still have two small cards left so you can finesse to the Jack the second round of the suit. So, even if you get a 4-1 break, as long as Queen is onsides, you'll make all five tricks.
AKJ10 opposite xx is different. Now you have only TWO small cards. Taking ONE top honor first to guard against a singleton Queen is wrong. Singleton Queen is even lower odds now that you only have 6 cards between you and dummy. Qxxx is much more likely. If the Queen is onsides, you must finesse to the Jack on first round (and again on second round) in order to get all four tricks.
AQxx opposite Jxxx OR AQxxx opposite Jxx: You are missing the King, 10 and 9. Play low to Queen and cash the Ace, hoping the King is doubleton onsides. DO NOT run the Jack toward the AQ; all you are doing is promoting the 10 or 9 for the opponents. Note that this is exactly the same as AJxx opposite Qxxx or AJxxx opposite Qxx.
If you own the ten, you are in a much stronger position, but even with AQ10x opposite Jxxx, do NOT run the Jack the first round of the suit. Play a low card to the ten. You are guarding against a singleton King onsides.
If you own the nine, it changes things.
AQ9x opposite Jxxx. Now, you'd like to know the distribution of the person sitting in front of the AQ9x. If you can count out that hand as having only two cards in the suit, play low to Queen and cash the Ace. If that person has 3 cards in the suit, run the Jack the first round of the suit. When it is covered, finesse to the 9 the second round of the suit.
If you have 10 cards in the suit, matters change again.
AQ9xxx opposite Jxxx Finessing for the King is correct with 10 cards (unless you strongly suspect or KNOW from the bidding that the person behind the Ace has the King in which case you play the Ace the first round). "Normal" play with fewer cards would be low to Queen and cash the Ace. However, here only 3 cards are out. If they are all behind the Ace, it does not matter how you play the suit. If they are 2-1, your play again is immaterial. However, in order to guard against K10x onsides, you must start with the JACK this time. When jack is covered and RHO shows out of the suit, you get back to your hand and finesse the 10 the next time.
Suppose you are missing the King and Jack, but own the AQ10. If you have from five to 8 cards, you finesse the 10 first; if it loses, then you finesse the Queen the second round of the suit. If, however, you own 9 or 10 cards, you finesse the QUEEN the first round of the suit, e.g., AQ10xxx opposite xxx If you are lucky, the king will be singleton onsides or Kxx onsides with singleton Jack offsides.
You all know that with Axxx opposite Qxxx, you cash Ace and play low toward Queen, hoping King is in front. However, when you own the ten, 9, and 8, your suit is much more robust. Now, you finesse for the King and then the Jack. So, with A1098 opposite Qxx(x), you run the Queen toward the Ace. If it loses to the King, next time you finesse for the Jack. (Occasionally Jack is singleton and the King is onsides and you pick up the whole suit.)
If you have 9 cards in the suit, you get to guess, e.g., A109xx opposite Q8xx. You can run the Queen toward the Ace, hoping RHO has singleton Jack OR you can cash the Ace (hoping for a singleton King) and then lead low to the Queen. Obviously if the bidding gives you any clues, you take those into consideration.
With 10 or 11 cards, play the Ace.
For those of you who need something to put you to sleep at night, there are over 50 pages in the Bridge Encyclopedia on playing different combinations of cards (called "suit combinations").