Counting Tricks
          Creating Winners

There are two complementary approaches to counting: counting winners in a No Trump contract; and counting losers in a suit contract. 
      Counting makes patent the Declarer's overall approach to the hand.  In No Trump contracts count winners off the top. That is, all the tricks which can be taken  without having to give up the lead. If the opponents can win the first trick in a suit, then consider that you have no winners in that suit. If you have enough winners then the contract should be made easily. Say you are in 2 No Trump and you count 8 winners off the top. The contract is readily made. Just execute. 
     But suppose you count the winners and come up short. You are in 2 No Trump but count only 3 winners. When the Declarer discovers that there are not enough winners, then the problem is: how to create winners?
     Three ways of creating winners: LONG SUIT, PROMOTION and FINESSE. see DEC 99.
     This month's hand illustrates creating winners by PROMOTION and FINESSE.

After East  passes, South, with 16 points and a balanced hand opens 1 No Trump.
(The North/South 1 No Trump opening range is 16 - 18.) North with 10 points and a very balanced hand realizes that they are in the Game Zone of 26 High Card Points (16 + 10 = 26) and responds 3 No Trump. All pass.
      Note: a 2 No Trump response by North is invitational. It invites South to either bid 3 No Trump with a maximum (18 points or a good 17); or pass with a minimum (16 points or a bad 17).  In the above hand South would pass a 2 No Trump response by North and a potential game could be missed.  If game is there, bid it.

A No Trump contract is usually a race of the long suits. So West should look to lead his longest suit. In this case Diamonds. It might be possible to promote one of these little Diamonds into a winner. (If partner has a Diamond honor or if the Declarer and Dummy have very few Diamonds.)
     The safest (and most informative) lead against No Trump is from the top of a three (or more) card sequence.  Here West can combine both these conditions by leading the J D.

Dummy comes down. Grab a winner or two? No! Declarer must make a plan and a good time to do it is before playing the first trick. A good plan is based on counting. In a No Trump contract Declarer counts winners. And this is winners off the top; winners that can be taken without giving up the lead. So let's do it: 2 Spades;  0 Hearts; 3 Diamonds; and 0 Clubs.  That is 5 winners; four short of the nine needed to make the hand.  What is Declarer going to do? Take the five winning tricks and call his mother? No! The Declarer must find a way of creating four winners.
      PLAN: A No Trump contract is usually a race of the long suits.  But there are no really long suits in this hand. Try to PROMOTE winners in a short suit by forcing  the Defense to play a high honor in that suit. Declarer considers Hearts. Once the A H is played the other three high Hearts will be PROMOTED  into winners.
     But that gives only eight winners: 2 Spades, 3 Hearts and 3 Diamonds.  Where is the ninth trick coming from? It has to be from Spades. And a way to create a Spade trick is by taking the Spade FINESSE.
      PLAY: Win the opening lead with the A D. Bang down the A S. If there is a singleton Q S in one of the Defenders' hands it will fall under the Ace and there will be no need to take the finesse. But alas, the Queen does not fall. So you will have to eventually take the Spade FINESSE.
     Now however, try to PROMOTE those high Hearts into winners. Play a Heart to the K H. Note: if East has the A H and wins the trick and plays Clubs, Declarer could lose 3 Club tricks for possibly down 1. (If the Spade finesse loses.) 
     But Declarer has no choice; three Hearts are needed to make the contract. So have courage, and hope that West has the A H. (If West has the A H Declarer cannot be hurt in Clubs.) Let's say that on the play of the small Heart from South, 
West plays small and does not win the first Heart trick. (The  play is essentially the same if West wins the first Heart: as soon as Dummy has the lead, take the Spade finesse.) You win in Dummy with the K H.
       Since you are in Dummy, take the Spade FINESSE by playing 8 S. If East plays a small Spade, play the 10 S from the South  hand. (Naturally, if East plays the Q S you win with the King.)
      Win with the 10 S and  continue with a Heart. West wins and returns a Diamond. (As good a defense as any.) You win with the K D in Dummy. It is now cash out time. It is time to take your winners.  Play the 
D followed by a high Heart. Get to your hand by playing a Spade to the King and playing the high Heart for the ninth trick making game. 
       It took nine tricks to make 3 No Trump: 3 Spades, 3 Hearts and 3 Diamonds.

QUESTION: Why not continue playing     Diamonds after the opening lead? 

     There is not much the Defenders can do.  They will just get four tricks: 1 Spade, 1 Heart and 2 Clubs. 
    You may wonder why West never leads the A C.  Without any supporting honors, West's lead of the Ace could actually create winners for South.  With the Ace gone, South could have an honor for a winner.  With the Ace in place, there is always a stopper for any potential lead by South.    Moral of the story:  Save your Aces to take opponents' honors.