LEARNING CENTER

You have one loser in spades and three club losers. Since you don't have to let your opponents get the lead, you can afford to draw two rounds of trump (keeping the A in dummy) and then ruffing your last spade with the A before coming back to your hand with a diamond to draw the rest of the trump.

Why did they have to lead a heart? If they lead anything else, you draw trump and play diamonds. With a heart led, if you try diamonds, they take the ace and then a heart. As for your other options--you might be a better guesser than I am, but finesses are 50-50 propositions. There's an old saying about how suits divide: "When you are missing an even number of cards, they divide oddly. When you are missing an odd number, they divide evenly." Here you are missing seven spades, so you hope that they are dividing 4-3. If they split worse than that, we hope they do it the right way (with the king falling singleton or doubleton). After winning the first trick, you will play A and ruff a spade with the A. Next play a club (not the 3!) to dummy and  ruff another spade with the K. If both opponents follow or if your LHO shows out, you will make. If LHO shows out, just take a ruffing finesse in spades. What if they split badly? Then you go down. But going down on bad splits is a much better option than a 50-50 guess. 

Here you have five losers: one loser in hearts, one in diamonds and three club losers. It's important that you think of counting from a "master hand" here that master hand is North since North has more trump. Thinking of dummy as the master hand will most frequently happen after a notrump opening, but it can happen other times too--try to be flexible when counting your losers. Just because you only have 5 losers and you will be making your contract doesn't mean that you shouldn't try for more. Overtricks are worthwhile especially if you are playing duplicate. 

You have 1 loser in trump, 1 in clubs, and 2 diamond losers. You might get lucky and find the hearts splitting 3-3, but much better is to ruff your diamonds immediately. If you play any rounds of trump or duck a club, your opponents can draw two rounds of your trump.

You have two losers in hearts, one in diamonds, and one possible loser in clubs. Our plan should be to ruff the hearts in dummy. Since dummy has such small trump, you want to try to draw a little bit of trump first. Here play one round of trump and then ruff a heart (with a low spade). This allows you to return to hand with a trump (drawing two rounds of the opponents' trumps) and now you can ruff high.