West leads the ♥4 (fourth best). Plan your matchpoint play.
You could lose two spades if East has the K–10–9, K–J–9 or the K–J–10, and you could lose two diamonds as well. If, however, spades are a more friendly 2–2, you can force a diamond lead, and should be part of your plan. Cash the ♥A K and the ♣K, ♣A and ruff a club. Assuming nothing traumatic has happened, play the ♠A and if no king falls, play a second spade. If spades are 2–2, you are in overtrick territory. With hearts and clubs stripped, the opponents will be forced to lead a diamond, better than conceding a ruff and a sluff.
Assuming spades are 2–2 and West wins the second spade and leads a low diamond, play low from dummy. If East plays the 10, win the ace and exit a diamond. Unless East started with the K–Q–10 or West has made a sneaky underlead from K–Q–x–(x), you will lose only one diamond trick. Keep in mind that if either defender started with honor doubleton, that defender will be endplayed upon winning the second lead of the suit. If West leads a diamond honor, take the ace and lead low to the jack. You lose when East has K–10–x or Q–10–x, something you couldn’t do anything about anyway. If, however, West has led a singleton honor, then it is right to duck. Good luck figuring that out.
If East wins the second spade with the king and exits with a diamond honor, the critical holdings that East may have are K–x, Q–x or K–Q–10. In the first two cases, the ace is best. In the other, low is best. Play with the odds, take the trick, and lead up to the jack. You can even afford to lose to K–Q doubleton.
If East exits with a low diamond, play low from dummy. If East started with Q–10–x or K–10–x, you are cooked. If you play the ace, West will (should) unblock with honor doubleton. If, however, East started with Q–10–x–x or K–10–x–x, West will win a singleton honor and be endplayed. If East has led from the Q–x–x or K–x–x, it doesn’t matter what you do because West has Q–10 or K–10 and the defense cannot take two tricks. Playing low also wins when East has both the king and queen.
Finally, if West follows with the ♠K under the ace, run the ♦9. If East wins with an honor and exits a spade to dummy’s queen, try to decide from the carding whether to run the ♦J, hoping to blot out the ♦10 doubleton in West, or play the ♦A. hoping to drop the doubleton K–Q in East.
This problem comes from the U.S. team trials in 2011. As South, you wind up in 7♠ against silent opposition and a low trump lead. East follows. Plan the play.
You have many chances, but 4–1 spades and 4–2 hearts without the queen dropping doubleton would be a bit much. In any case, win the ♠A and play the ♥A K, discarding a club, and ruff a heart high (assuming East follows to the third heart). If the hearts in dummy are now high, you have 13 tricks. All you have to do is draw trumps and you can handle 4–1 spades. Cash two high trumps in dummy, return to the ♦A, discard a diamond on a high spade, cross to dummy with a diamond, etc.
Say that the hearts are not good and the ♥Q remains at large. Cross to dummy with a spade and ruff a second heart high establishing dummy’s two remaining hearts. Dummy remains with a high spade, two good hearts, three diamonds and a club. You remain with a low spade, the ♦A J and four clubs to the ace. You are reduced to finding the ♦Q with West. Cash the ♦A and run the ♦J. If it holds, cross to dummy with a trump and the rest of the tricks are yours.