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my last post trying to help you - pls try to think
Maybe you should follow your own advice?
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The real simple case:
If you lead the J and AQ108 is on your left, you will lose 4 tricks.
If you lead toward the J and the AQxx is in either hand you cannot lose 4 tricks.
In the problem, declarer has the 9 in dummy & 8 in hand, which are quite significant cards. As long as you don't do something completely irrational, you can never lose 4 tricks. The question is whether you lose 3 tricks or 2 tricks.
If LHO has AQTx, you will lose 3 tricks either way. If RHO has AQT7, same thing. But if RHO has AQT3, leading the J gains over leading toward the J. Leading toward the J, you lose the first trick to the Q. Then when you lead toward hand, RHO ducks or plays the ace, sooner or later you lose a trick to the T and the ace. In contrast, if you lead the J, pinning the singleton 7, you will hold your losses to 2 tricks. If RHO plays ace first round, you later go to dummy & run the 9 if not covered. If covered, you win K, and your 8 drives out defender's 2nd and last trick. If RHO ducks, you duck & lead toward the K later. If RHO covers with the Q, you win the K, and your 9 & 8 will drive out defender's remaining A/T.
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Let me repeat - There is NO arrangement of outstanding cards where leading the jack gains over leading toward the J - NONE
It doesn't matter how many times you repeat a false assertion, it won't become true.
Besides the singleton 7, you also gain when LHO has ATx, and either Tx or Ax depending if you are leading toward the K or running the 9 after losing to RHO's Q. Try it! Running the J, if LHO has ATx, you lose to just LHO's A & T whether RHO covers first round or not. Leading toward the J, you lose first trick to RHO's Q, then the next two to the A & T. If LHO has Tx, running the J loses only 2 tricks, as RHO has to play ace or Q 1st round. Leading toward the J, you lose to the Q, then when you lead back to the K you have to guess. If you duck, you lose to the doubleton T on the left and the third trick to the ace. If you go up, you pick up that case, but instead you lose a third trick when RHO started with QTx. Leading the J picks up all these cases for 2 losers only.
Leading toward the J does pick up some cases leading the J does not, but only AQT on the left and one of QT/AQ on the left (depending if K is played 2nd round or not by people who run the J 1st round), which is fewer cases.
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