LEARNING CENTER

Lead the 7 from declarer and play the 9 from dummy if LHO plays low.  

You don't have to memorize the odds, but think about the relevant missing cards: K, Q, and 10. Playing the J will only work if LHO has both the K and Q. Playing the 9 will work if West has the 10 and either the K or Q. Which is more likely? We should have some instinctive sense that needing only 1 specific card and a choice of 2 others is more likely than needing two specific cards, but we can figure out the odds if we need to (25% that both K and Q are with LHO, 38% that 10 and Either K/Q).

K and then low to the ace. You are missing 5 cards. If they split 3-2, then nothing matters. If J9xx is with your RHO (behind the dummy), then you will always lose a trick. If LHO has J9xx, though, you can finesse them for it. You just need to know to do it. Cash an honor from dummy and then lead low to the ace. If RHO shows out, you will finesse LHO after winning your ace. If you play the ace and then the K, you will find out about the bad split, but you are in dummy instead of in your hand. Don't waste entries unnecessarily. 

Lead the 2 from declarer's hand and play the Q if LHO plays low. Leading the Q can't help, if RHO has Kx, they can cover it and you will lose two tricks and if LHO has the K, the finesse loses. If the suit is 3-3, you'll always take exactly 4 tricks. The interesting scenarios happen with a 4-2 split. if LHO has Kx, you can still win four tricks by playing towards the Q and then playing the ace. If RHO has the K, then you will be at the mercy of the split. 

Lead the ace and then low to the Q. Leading the Q is wrong because LHO can cover it and you are missing too many spot cards to promote your 8 (the opponents have the 9 and 10). Your best chance is to play the A and low to the Q. If it wins (and you haven't seen any interesting spots like the 10 or 9, then you can play a third round and hope they were originally 3-3. Here, where we want the most possible tricks, our best hope is that RHO has Kx or Kxx or that either hand has 109 doubleton.

When they are 3-3, you are going to take 4 tricks no matter how you play the suit, but the A and then 4 untangles your suit nicely. 

If you played in a suit contract (not spades), then you would generally lead the Q to try to avoid any losers in the suit (depending on your entries and other needs). 

Lead low to the J and then come back to declarer's hand to lead low to the 10. This is one of the most commonly misplayed combinations. People cash a high honor first. We are missing Q7432. Cashing an honor will pick up singleton Q. It will lose to singleton 7,4,3, and 2. Why? If we play the A first, we can only finesse once. Since there are 4 scenarios where taking a first round finesse is right vs the 1 where it is wrong, you should finesse the first time. Why not the A and then K? With an 8-card fit, we envision a 3-2 or 4-1 split. In either case, the Q is more than 50-50 to be in the hand that has more cards (meaning it won't drop if we play A and K). Since our finesse is 50%, we'll take that chance.