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).
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.
- 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.)
- 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.
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 Lead: 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 |
1 | 1 |
1NT | Pass |