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:

• The ability to count to 13 at least twice (4 times, if possible).
• Memory skills, which can be developed with practice. (See Developing your Card Sense for tips on developing your bridge memory.)
• A basic knowledge of the meanings of bids, leads and defensive signals.
• Technical skills – knowing how to use “discovery plays” and other techniques that help you collect clues about each player’s distribution.
• Concentration. You have to put some energy into counting. Pay attention to every trick and modify your picture of the unseen hands as you collect new clues. 

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:

• If an opponent opens 1D and then does not support his partner's major-suit response, it's guaranteed that opener has 4+ diamonds (because the only time he would open 1D with a 3-card diamond suit is when his distribution is exactly 4-4-3-2).     
• If the opponents' auction goes 1H-1S-1NT, you'll be able to narrow down your picture of opener's hand to one of three patterns: 2-5-3-3 or 3-5-3-2 or 3-5-2-3. This conclusion is based on three logical assumptions:
      (1)  Opener showed a balanced hand with his 1NT rebid, but he did not raise his partner's 1S response (so he has exactly 2 or 3 spades);
      (2)  He did not rebid his heart suit (so he holds exactly 5 hearts); and
      (3)  He did not show a second 4+-card suit (so he has at most 3 cards in each minor). 

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: 

• Memorize the common patterns of the 13 cards in a suit -- 4432,  4333,  4441,  5332,  5431,  6322,  7321, etc. (Note that all the patterns of four numbers fall into one of two even-odd combinations: three even numbers and one odd, or three odds and one even.) Drill yourself on the patterns and become so familiar with them that you won't even have to think once you get a partial count. If you discover that each opponent has 4 cards in a suit and you hold 2 cards, you won't need to do any arithmetic to know that partner holds 3. The 4432 pattern will instantly pop into your head. 
• Concentrate on how the unseen cards divide. Once you become adept at recognizing the common patterns, start thinking not just about the number of outstanding cards in a suit, but about how they might break. If your hand and dummy have 8 total cards in a suit, try to focus on the possible divisions of the 5 missing cards. With practice, it will become second nature for you to go beyond thinking "5" and start thinking "3-2,  4-1,  5-0".
• Memorize the original layout.  Whether you're declaring or defending, study the dummy at trick one and create a mental picture of its distribution. Commit it to memory by repeating the pattern in your head (for example: 3-5-3-2, or 35-32). Do the same with your own hand. Later in the play, if you can't remember how many cards have been played in a suit, you can often reconstruct the play -- and figure out how many times the suit has been led -- by recalling your mental picture of the number of cards you and dummy originally held in the suit. 
• Mentally review the bidding before you play to the first trick. If possible, come up with a picture of each player's general hand pattern and high-card strength. Consider not just what the hidden hands actually bid, but what they did not bid.
• Focus your count on just one unseen hand.  The easiest hand to count will usually be the player who made the most bids during the auction, or who made the opening lead. Use what you know about that hand to figure the distribution of the other hidden hand. 
• Consider the skill of your opponents. The more experienced they are, the more reliable their bidding and carding will be ... and the easier it will be for you to make accurate assumptions about their hands. Popular bridge author Eddie Kantar observed, "A madman's hand is particularly hard to count, but he's usually in the wrong contract, which evens things out."
• Practice, practice, practice.  It will take time and lots of practice before you can process all the information available and make the right conclusions. You can speed your progress by making a concentrated effort to count at least one or two suits on every deal you play, even on those where it appears you can't affect the result. The more hands you play and the more suits you count, the more adept your brain will become at remembering the cards.
• But ... don't overload your neurons.  Early in the play, try to decide which suits are critical and concentrate on counting just those suits. If you're declarer, your count will usually be focused on your longer fits -- the one or two suits where you and dummy have the most cards. If you're a defender, try to start your count with the suit you or partner led, then move on to figuring the distribution of one of the declaring side's longer fits.

Tips for declarers:

• Study the opening lead.  Try to make some conclusions about the opening lead. Does the card led suggest length or shortness in the suit?  Does it pinpoint the leader’s exact length  (and therefore his partner's length)?  Does it show an honor combination or the lack of one?  What does it tell you about the leader’s possible length or honor holdings in other suits? 
• Play on one suit at a time. Once you begin drawing trumps or establishing a suit, stick with that suit. If you have to lose a trick, resume leading and counting the critical suit as soon as soon as you regain the lead. Resist the temptation to cash high cards in other suits unless you have a clear purpose in doing so (you need them for entries, for example). When you're done cashing tricks in the first suit you’re counting, move on to the next suit and start a new count. 
• Watch the defenders’ count and attitude signals. Be aware, however, that you can’t trust these implicitly. If an opponent thinks a signal will be of more help to you than to his partner, he may not give an accurate signal, especially late in the play.
• If possible, delay your important decisions. Collect all the information you can about the defenders' distributions before you decide how to attack a critical suit. Run your long suit or cash a few extra trumps (if you can do so safely) and see what you can learn from the opponents' discards. Use discovery plays to get a count on side suits. If you have tricks to lose, consider giving the defenders the lead to see if they'll provide you with a discovery play. 
• Play the odds.  If, for example, you have a two-way guess for the location of a queen, use your count in the suit to decide which way to finesse. If you determine from the bidding or play that one opponent is likely to have more length in the suit, finesse that opponent for the missing queen. (See "At the Table" below for an example of this situation.)

Tips for defenders:

• Watch partner's signals. They tell you about his length and possible high-card holdings in key suits.
• Give partner good signals so he can count out the hand, too. Use your judgment here, though. Some signals help declarer more than they help your partner, so it’s sometimes right to withhold a count signal if you think it will tell declarer how to play a suit.
• Find a time to add up what you know. Think while declarer or partner is thinking or when it's your lead. If possible, avoid long thought when it’s your turn to follow suit. Make your decisions early and be ready to follow smoothly when declarer or dummy leads.
• Beware of falsecards -- especially those that won't fool declarer, but will fool partner. If you hold QJ2 of a suit and play the 2 and then the queen when declarer cashes the ace-king, you’ll lead partner to believe that your original holding was Q2. If he’s trying to count the hand, this clue will lead him astray.

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:

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   Q1085 
   Partner's hand was:      A43    8432    83          K972

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

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

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

Read bridge books. One of the best 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.

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

Copyright © 2002 -- Karen Walker