Developing counting skills


Ever wonder why good bridge players seem to be able to see through the backs of your cards? Why they are so successful in finding the right lead, locating missing honors, guessing the distribution of their opponents’ cards? The answer is that they are usually not guessing. Whether they’re defending or declaring, good players are constantly gathering clues from the bidding and play and using them to make logical assumptions about the location of the unseen cards.

This exercise – some call it a talent -- is often called card reading, and it’s a skill that even beginners can develop. It involves determining the overall layout – the length and strength (honor holdings) of each suit in each of the two hidden hands. The first and most important step in card reading is counting the hand, which focuses on figuring out how many cards each player holds in each suit.


Counting one suit

At its most basic level, counting involves keeping track of the cards your opponents play as you’re leading one suit. If you're declaring a suit contract, you use this simple count when you’re drawing trumps. If you’re declaring a notrump contract, the first suit you count is the usually one that offers you the greatest number of potential tricks. This is probably your longest fit, and the suit you lead first.

As declarer, there are two main techniques you can use to keep count of the cards remaining in a suit:
    (1)  Count up from the number of cards you and dummy hold in the suit. If you have a total of 8 cards in a suit in your hand and dummy, you would start your count at 8 and then mentally count up to 13 as the opponents play their cards in the suit. If both opponents follow to the first lead of the suit, you would count 9-10, then 11-12 on the next trick. Subtracting the last number from 13 will tell you how many cards the opponents still hold in the suit. 
    (2)  Count down from the number of cards that are missing. With an 8-card fit, you would start your count at 5 and then mentally count down to 0. If both opponents follow to your first lead of the suit, you would count 5-4. The next number in the sequence is the number of cards the opponents still hold.

Most players find #1 the easiest, but it doesn’t really matter which approach you use. Anything you're comfortable with will work fine.

You can use the same counting technique as a defender, with only minor variations. Start your count with the number of cards you and dummy hold in the critical suit. In some cases, you'll already know how many cards partner holds in that suit (from his lead or from the bidding), so you’ll have a full count on the suit before any cards are even played.


Counting two or more suits

Once you master counting one suit, you’ll want to move on to figuring the distribution of two or more suits. To do this successfully, you need:


Collecting information

From the bidding:   
     Whether you're defending or declaring, use what you know from the bidding to come up with an initial picture or one or both opponents' hands. You can start with very simple assumptions, such as the minimum length promised by an opening bid or response. If an opponent opens 1H, for example, you can "see" at least five of his 13 cards. If that opponent makes subsequent bids in the auction, you'll learn more about his other 8 cards and you can often build a fairly accurate -- or sometimes perfect -- picture of his hand pattern.  

You can also use the bidding to determine what a player does not hold in a suit, which will lead you to conclusions about his length in other suits and, in some cases, his partner's length in a suit. For example:

Before you lead or make a critical play during the hand, try to process everything you know from the bidding.  Count one hand at a time, and keep your focus on the number 13. Mentally repeat each fact you've learned about that hand  and ask yourself what logical conclusion you can make from it. Then apply what you know to the other unseen hands. Your thought process may go something like:
     "Declarer opened 1S and then bid clubs twice, so he has 10 cards in those two suits. That gives him 3 cards in the red suits. If he's 2-1 in those suits, that means my partner has ... . If he's 3-0, then my partner has ...".

From the opening lead:
     The opening lead will sometimes pinpoint the leader's exact length in the suit. If it's a notrump contract, for example, and your partner or an opponent leads the 2 of spades (or the lowest spot card), you'll know he has exactly 4 spades (assuming 4th-best leads). The opening lead can also tell you something about the leader's holding in other suits. A defender will usually choose his longer, stronger suit for an opening lead to a notrump contract, so if there are other unbid suits, you can figure that the leader's holdings in those suits are shorter (and/or weaker) than the suit he led. 

Other leads can suggest:
    Shortness in a suit -- a high spot-card lead to a trump contract, for example. 
    A specific honor holding -- the lead of a queen from a QJ holding.
    The lack of an honor combination  -- a lead of a low card (especially to a suit contract) usually suggests that the leader does not hold touching honors (AK, KQ, QJ, J10).

From the play:  
     As each trick is played, look for evidence and clues that will help you refine your picture of the hand (or hands) you're counting. Many of these are obvious, such as when a player shows out of a suit. Others are more subtle and require you to make negative inferences -- why declarer isn't leading hearts, why an opponent didn't return his partner's suit, why he's pitching clubs instead of spades.

Watch the defenders' count and attitude signals. They will be signaling each other about their length and honor holdings in specific suits, and you can use this information to count their hands. 

Discovery plays:  If you're declaring and you have an important guess to make in one suit, you may be able to collect extra information by using a discovery play before you attack the critical suit. A discovery play involves leading another suit (cashing its high cards or trumping its low cards) and keeping track of how many cards each opponent holds in that suit. This will help you complete your picture of the opponents’ length in other suits and lead you to a more informed decision about how to play the problem suit. See "At the Table" below for an example of how to use a discovery play. 


General tips for counting: 

Tips for declarers:

Tips for defenders:

Tips for dummy (yes, dummy):

Your stint as dummy is the perfect time to practice your counting skills. Even though you can see only your own hand, you can work on developing a mental picture of the distribution in the other three hands. Analyze the bidding and opening lead and add up what you know about each player’s suit length. Then watch the played tricks and the defenders' signals and try counting the number of cards each player holds in each suit. This is great practice because there's no pressure; if you make any errors, they're "free", and no one will know.


At the Table

Here's an example of how to use a simple inferential count to make an intelligent guess:

Dummy:   K6
                
J84
                 K1084
                 K653

You:        A643
                K7 
                AJ93 
                A42

 You      Partner 
   1NT      3NT   

Opening lead:  Heart 3

 

RHO wins the heart ace and returns the 9. You win the king and LHO follows with the heart 2. 

Your only hope for 9 tricks is to score 4 diamonds, and that will require you to find the queen. You can finesse either opponent for that card. Is it a pure guess, or do you have a clue that will help you make the decision? 

There's no discovery play available here, since cashing your other tricks first is unlikely to give you any helpful information. All you have to go on is your count in the heart suit, which you've already determined by watching the cards played to the first two tricks.

Here, LHO led the heart 3 and then followed with the 2, so he's shown that he holds 5 hearts (Qxx32). RHO therefore has 3 hearts (A9x). 

When you're in doubt about the location of a specific card, the odds favor it being in the hand that has the most "room" to hold that card. Your count in the heart suit tells you there are 8 chances that LHO has the diamond queen (he had 5 hearts, so has 8 unknown cards) and 10 chances that RHO has the queen (he had 3 hearts, so has 10 unknown cards). So your best play is to cash the diamond king and lead the 10, planning to finesse RHO for the diamond queen.

Here's a defensive quiz where you can use the opening lead and the bidding to come up with the right play:

Dummy (RHO)
  K9765
 
Q7
  J95
  J64 

You:   J1082   
  A65      
     A742    
  A3        

 LHO     RHO 
   1D          1S   
   1NT      Pass

Opening lead:  2 of clubs

Declarer plays low from dummy and you win the club ace. Now is the time to add up all the evidence. It's often right to return the suit partner led, but you'll change your mind if you stop to count out the hand. Try to answer these questions before you make your decision:
     How many clubs does declarer hold?  
     How many diamonds?  
     How many hearts?  
    
How many spades? 
    
How many points does partner have?
     Which card will you lead at trick two?  

Focus your count on declarer's hand.
    How many clubs does he hold?  Exactly 4 (because the lead shows that partner holds exactly 4 clubs).
    How many diamonds?  At least 4 (because he didn't raise spades).
    How many hearts?  Exactly 4. Declarer didn't open 1H, so he has fewer than 5 hearts. It appears that partner also has fewer than 5 hearts, since he surely would have led a 5-card heart suit rather than a 4-card club suit. The 8 hearts that you can't see must therefore be divided 4-4 in partner's and declarer's hands. (Note that you also have a clue that partner doesn't hold a heart honor. Since partner is 4-4 in hearts and clubs and he chose clubs for his opening lead, his clubs are probably stronger than his hearts.)
    
How many spades?  You've counted declarer's hand to be 4-4-4 in the other three suits, so that leaves him with one spade. That means partner has three spades with at least one honor. 
     Note that without a count, you probably wouldn't have expected opener to have a singleton for his 1NT rebid. Many players, however, prefer this approach when they have a 1-4-4-4 pattern. The alternative with this hand is to bid 2C (showing a minor two-suiter), which is also a distortion. 

You can also add up the high-card points here. Declarer's minimum notrump rebid tells you he has 12 to 14 points. (If he had 15 pts., he would have opened a 15-17 1NT.) Add declarer's points to the 20 total points in your hand and dummy, and you can determine that partner holds from 6  to 8 high-card points.

Did you find the killing shift? It's right to lead a low spade at trick two. Partner wins the spade ace and returns a spade for down one. Your side will eventually score seven tricks -- three spades, the AK of clubs and the two red aces. 
   Declarer's hand was:   Q       KJ109   KQ106   Q108
   Partner's hand was:   
  A43    8432    83          K972


Here's a deal where you can use a discovery play to collect extra information:

 Dummy AQ9
                 
765 
                  A432
                  K102  

 You:        K10865
                 842    
                 K7
                 AJ5    

  RHO    You    LHO   Partner 
   1H       1S      Pass       4S

Opening lead:  Jack of hearts

RHO overtakes the heart jack and cashes the AKQ. LHO pitches two small clubs on the second and third hearts. RHO exits with a spade and you cash the AKQ. RHO follows with the J74 of spades. LHO follows with the 32  and pitches a small club on the third spade.

Your contract depends on guessing the location of the club queen. With nothing else to go on, you might finesse RHO for the queen just because he opened the bidding and is therefore more likely to hold the missing high-card points. If you're counting the opponents' cards, though, you might come to a different conclusion. And if you use a simple discovery play, you may be  able to guarantee three club winners.

Your thought process:
    Focus your count on opener (RHO). 
    So far, you know 9 of his 13 cards -- 6 hearts and 3 spades.
    You've seen 10 of his high-card points -- the AKQ of hearts and the jack of spades.
    Did he need the club queen to open the bidding?  No. He could hold the diamond queen or QJ, which would give him 12 or 13 points.

Extra insurance -- the discovery play: 
     Before you make the critical play in the club suit, play on diamonds to gather more information about RHO's distribution. Cash the king and ace and trump one of dummy's small diamonds. RHO will follow to all three diamonds, so you now have all the information you need to take three sure club tricks. You may also see more of RHO's high-card points on the diamond tricks, but the most important information here is his distribution.
     You now know 12 of RHO's 13 cards -- 3 spades, 6 hearts and at least 3 diamonds. That leaves him with a void or singleton in clubs, so you have a "marked" finesse. Cash the club ace, just in case RHO has the singleton queen. If the queen doesn't fall, finesse LHO for his known queen by leading a low club to dummy's 10. 


Additional practice

Read bridge books. One of the best books on this subject is How to Read Your Opponents' Cards by Mike Lawrence. His descriptions of how experts think at the table will give you insights into the "secrets" of counting. Lawrence has also authored Counting at Bridge, an interactive computer program. Another good book on counting is Countdown to Winning Bridge by Tim Bourke and Marc Smith.

For more hands that feature counting by declarer, see Count, count, count  and The one that got away on this site.

Here are some other web sites with counting quizzes and example hands:
    Defensive quiz from the University of Waterloo
    Thomas Andrews' Bridge Fantasia 


Copyright © 2002 -- Karen Walker