Today's combination is from Hand #13 at Soledad Club, August 6, 2018. You and your partner arrive at 3NT and you want to play J75 opposite A10642 for four tricks. Forget about 5-0 and 4-1 breaks. There is no way you'll get four tricks in those cases. So, you simply assume that clubs divide 3-2.
The general rule is: Do not lead an honor toward a higher honor unless you have lower touching honors to promote. When you lead a lower honor toward a higher one (such as Jack toward Ace), when your honor is covered, you have to spend TWO of your honors to capture ONE of the opponent's honors. If you do not have the lower cards, you are just promoting 10's or 9's for the opposition. If you lead the Jack in this case, any decent opponent who holds either the King or the Queen will cover. [An opponent can see—with the length in Dummy—that ducking your Jack is hopeless because next round the A10xx will be behind their honor.] So, the only time playing the Jack toward the A10xxx works, is when LHO has BOTH the King and the Queen. That, however, is against the odds.
Both honors on your left is only 25%. Either the King OR the Queen on your left is 50%. So, the legitimate play for four tricks is to hope for a doubleton honor on your left. You play low to the ten. In this case, it loses to the King. When you regain the lead, you cash the Ace. Since the Queen was doubleton on your left, it falls and you take four club tricks. [If you lead Jack first round, LHO will cover with Queen. Whether you cover this time or not, opponents will get two club tricks—either Queen and King OR King and 9 (which you promoted). Running the Jack also loses big time when there is a singleton honor on your left.] Actually laying out these combinations with cards may help you visualize it all!
Just to make your head spin, let's look at J10x opposite Axxx. You want TWO tricks from this combination—and cannot afford to lose two tricks to gets your two (e.g., a 3-3 break). Please note that if EITHER hand held the nine, you would be in great shape. Here, again, you make the assumption that the “royal marriage” (King and Queen) are divided between your two opponents. [Obviously if the bidding tells you differently, you change your play.] If the opponent's cards are divided 3-3, you will lose two tricks. If, however, they are 4-2, you have a shot to get two tricks while only losing one trick. This is one of those combinations you'd like to play other suits first to get a partial or, ideally, a complete count on the hand. If you believe that LHO has only two cards in the suit, you start with the Jack. MOST people with a doubleton honor will cover. If LHO covers the Jack, you play the Ace, then lead a low card from Dummy. If RHO has other honor, RHO will usually take the trick. If RHO ducks, you play 10. If LHO ducks the Jack, it loses to an honor on your right. When you regain the lead, you cash the Ace—again playing for a doubleton honor to fall from your left.
Suppose, however, your inferential count leads you to believe that RHO has the doubleton honor? Now, you must start the suit from Dummy. You play a LOW card (away from the Ace) toward your J10x. If the doubleton King is on your right, that person will almost always rise with it. Doubleton Queen will duck most of the time. If the King (or Queen) wins on your right, after you regain the lead, you run your Jack—finessing LHO for the other honor. If, when you play a low card from Dummy on the first round of the suit, your RHO ducks, you will play the Jack (losing to an honor on your left). When you regain the lead, you will cash the Ace—hoping for an honor to fall from your right.
Astute readers will note that if you were SURE that there was a doubleton honor on your RIGHT with the very first combination (Jxx opposite A10xxx), you could play this combination the same way: start with a low card AWAY from the Ace. If RHO hops with an honor (very likely if it is the King that is doubleton), you can run your Jack to finesse LHO for the Queen (or other honor) the second time around. If RHO ducks when you play a low card away from the Ace, then your Jack loses to an honor. You cash the Ace the next time, hoping to kill a (now bare) honor on your right. However, low to the 10 originally is still the best overall way to play that combination. It wins whenever a singleton honor pops on the left; whenever both honors are on the left; and whenever a doubleton honor is on the left.