The Mechanics of Counting By Tim Bourke

Source: Countdown to Winning Bridge By Tim Bourke, Marc Smith

How do you count to thirteen?’ This may seem like a silly question, but in this article we shall try to persuade you that there are better ways of doing it than the obvious ‘one, two, three… twelve, thirteen: Keeping track of trumps is a skill novices learn very early. In the beginning, most players figure out if they have drawn trumps by tallying dead cards —cards that have been played. They play a round of trumps and, if everyone follows, count that four have gone. They then add the number of trumps left in their hand and dummy, and if the total is less than thirteen they know some trumps are still outstanding. They repeat the same process after a second round of trumps, and so on.

No one can say that this method does not work, but it is tediously slow and uses a great deal of mental energy. Think of the brain as a fuel tank. When you sit down to play it is full, but every time you make a conscious thought, you burn fuel. As the session wears on, you deplete your reserves of mental energy. To preserve fuel for when you really need to think, you must train yourself to handle routine processes in a way that conserves your mental energy. The first step is to make these basic functions a habit — something you just do without actively thinking about them.

Rather than counting dead cards in a suit, it is more efficient to count live ones. Say, for example, you have seven clubs between your hand and dummy. There is no need to count all thirteen clubs as they are played. It is easier to work out that the opponents started with six clubs, and to reduce that number as clubs are played. You may not need to be Einstein to count to thirteen, but even so, you are even less likely to make a careless error counting to six. This technique works reasonably well for counting a single suit. It is less effective for determining the distribution of the hidden hands. In order to keep track of more than one suit comfortably, or to envision a defender’s hand during the play, you must think in terms of hand patterns and suit distributions.

Let’s change the subject briefly and consider a bidding problem. Your hand is:

 KJ10   Q1032  AQ1086

You open 1 and partner responds 1. Do you rebid your clubs or raise partner’s spades? Some of you will have correctly refused to answer, having seen that you were given only twelve cards. If you didn’t notice that, it is because you are thinking of a hand as thirteen individual cards rather than as a total hand pattern. Once you begin to think in terms of hand shape, you will be able to eliminate actual counting as suits are played.

During the bidding, the distribution of a hand is often as important as its high-card strength. You should, therefore, consider the shape of your hand from the moment you pick up your cards. Hand patterns are commonly expressed in figures such as 4-4-3-2 or 3-5-3-2 with the suits in their ranking order (spades first, then hearts, diamonds and clubs).

Thus, a 4-4-3-2 hand has four spades, four hearts, three diamonds and two clubs. (When a hand pattern is expressed as 4432, without the hyphens, it means you have two four-card suits, a three-card suit and a doubleton, but that the suits are not defined.) Once you are used to thinking in this way, you will know instinctively if the suit lengths do not add up to thirteen (such as the 3-0-4-5 hand above).

When the various hand patterns become familiar, you will also be able to think of individual suits in similar terms. For example, if you are dealt two suits of exactly four cards your only possible shapes are 4432, 4441 and 4450. Similarly, if you have a four-four trump fit, the missing cards can only split 3-2, 4-1 or 5-0. Using this approach, you will find it easier both to keep track of how many cards are outstanding in a suit, and to build up information about the defend-ers’ hands. You are now ready to test your new counting method. The question is, exactly what should you be counting?

Let’s answer this with a straightforward hand on which we can work through the thought processes you should follow:

1 Balanced Raise to 4

2 Roman keycard Blackwood

3 Two keycards no Q

Even on the simplest of hands there is counting to be done, but exactly what should you be counting? At the beginning of each hand, you must count your tricks. This dummy is disappointing as you can only count twelve tricks — five trumps, three diamonds, two clubs, one spade and a club ruff in dummy. However, there are two obvious chances for an extra trick — diamonds might break 3-3 or the spade finesse may work. Your next task is to develop what we shall call an Information Management Strategy (hereafter referred to as IMS).

This may sound complicated and a trifle grandiose, but the name describes exactly what you are trying to do: develop a strategy to gather and manage the information you need. You could try to remember and count every card as they are played, but doing so will almost inevitably lead to errors. Most cards are irrelevant — the trick is to work out, in advance, which ones are not.

The essential ingredient of sound declarer play (and defense) is to recognize the problem; you then adjust your line of play and counting strategy to provide the information needed to solve it. On this hand, the first step is to make sure you can ruff your club loser safely in dummy. You have nine trumps, leaving four for the defenders. As long as the trumps are not 4-0, you can afford to draw all of the defenders trumps before playing clubs.

What other information do you need to keep track of? One of your chances for a thirteenth trick is dummy’s long diamond. It would be pointless to get to trick twelve and then not know if the last diamond is a winner. If the diamond is not good at trick twelve, then you will have to take the spade finesse and hope, so your counting strategy is to make sure trumps break and to count diamonds. Nothing else.

Having come to this conclusion, it’s time to play. East follows with a heart at trick one, so you know trumps are not 4-0 and thus your first problem is solved. You draw as many trumps as are necessary (by watching to see whether the suit breaks 2-2 or 3-1) and then you play three rounds of clubs, ruffing in dummy. While you have been playing these first few tricks, you should have been paying attention to one thing and one thing only — has either defender thrown a diamond?

Assuming the answer is no, then you know there are still six outstanding. If dummy’s long diamond is to be a winner, then you will need the suit to break 3-3. You cash the three top diamonds ending in dummy. If both defenders follow to three rounds of diamonds, you know that dummy’s last diamond is good, and you are home free. If either defender discards on any of these tricks, then diamonds were not 3-3 and you take the spade finesse. Notice that, before playing to trick one, you knew exactly which cards to focus your attention on. It is possible that your initial IMS will suggest you need to watch cards in two suits, but this can be an illusion as the next hand illustrates: 

East wins the spade lead with the king and returns the 9. You cover and West takes the ace, cashes the jack (East following), and leads the thirteenth spade. Fortunately, the defenders haven’t beaten your contract off the top, so it is time to count tricks and develop your IMS. You have eight top tricks — two hearts, three diamonds and three clubs. Your ninth trick can come from a 3-2 break in either minor. In order to ensure that you will make your contract whichever suit breaks, on the fourth spade you discard a diamond from one hand and a club from the other.

It looks as if you have to keep track of the five outstanding cards in both minor suits. While this is not a particularly arduous task on this hand, it is nonetheless unnecessary. Let’s say you ignore diamonds and concentrate on the five missing clubs. East throws a red card on the fourth round of spades and West plays a heart. You win and cash the top clubs, paying attention to whether the suit breaks. If both defenders follow to two rounds of clubs, you are home. If someone discards, then you will have to hope diamonds break. You do not need to count diamonds at all. You plan to cash your winners and lead your last diamond at Trick 13 — you’ll find out then whether it’s good or not! Of course, you could equally well have concentrated on counting the diamonds and ignored the clubs, in which case you would have cashed the top diamonds first. On the next hand it seems at first that you must keep track of three suits, but this, too, is a mirage:

You have ten top tricks, with obvious chances in three suits; you need two of those three suits to divide 3-3 to make twelve tricks. If both diamonds and spades break, you will be home no matter what you do. However, you also want to be able to score an extra club if you need it. Clearly, you cannot play ace, king and a third club, because if clubs are 4-2 the defense will take two club tricks. Nor can you cash your spade and diamond winners before giving up a club, as the defense may be able to cash a second winner when they get their club trick.

The answer is to win the Q lead and play a low club from each hand. East wins and plays a second heart. Now you cash all of your winners while count-ing so that you know which long cards are good. It doesn’t matter which suit you cash first, but it is easiest to start with clubs, as you have already played one round. There are six cards outstanding in both diamonds and spades, and four in clubs. For a long card in a suit to become good, you need an even split.

Let’s say that when you cash the AK everyone follows, so the four missing clubs have broken 2-2 and dummy’s thirteenth club is good. It is tempting to cash it now, but stop! Which of your potential winners are you going to discard on it — the thirteenth spade or the thirteenth diamond? No — much better to leave the club winner in dummy for now.

You will need an entry to dummy to score the long club later, so leave the diamonds intact and start on spades next. Note that you are now in the same position as you were on the last hand. There are two suits to count, diamonds and spades, but you only need to concentrate on one of them — spades, since that is the suit you intend to test first.

There are six spades missing, so you need them to break 3-3. Before you play any spades, fix in your mind that you need both defenders to follow to all three spade winners. If they do, you have twelve tricks. You will take your long spade, cross to dummy in diamonds, cash the long club, and return to the other top diamonds. If someone discards on a top spade, you cross to the K, cash the thirteenth club throwing your spade loser, and hope diamonds break 3-3. There is no need even to count the diamonds. Either they break and your thir-teenth diamond is good, or they don’t and the contract fails.

Let us now go back to the point at which you cashed the AK and say that a defender discards on the third round. Now you need both spades and diamonds to break 3-3. Since the missing spades and diamonds are both still relevant, you must pay attention to the discard on the third round of clubs. If the discard is a heart then you cash the spades as you did above, knowing that you need both defenders to follow three times. But what if someone discards a spade on the third club? As there are now only five spades out, you cash the top spades watching to make sure both defenders follow twice.

Readers who know something about squeezes will know that the order in which you cash your winners can sometimes be important. On the next hand, we shall see how developing a sound IMS allows you to capitalize when an opponent ‘throws the wrong card: Effectively, this will help you to execute a simple squeeze without needing to plan it, or even to know that it is happening!

You see twelve top tricks and if diamonds break, you can claim. Even if diamonds are 4-1, as long as West has Jxxx you will be able to score the 10 via a marked finesse. You take East’s Q with the ace and cash the AK, but West discards a spade on the second diamond. Now you cannot score a fourth diamond trick without first losing to East’s jack. Is there anything you can do? Actually, yes, and it involves a squeeze. But you don’t need to know anything about squeezes except that, if you cash winners, a defender sometimes throws something helpful. Which cards are relevant? There is only one — the K. If anyone throws that card away you will be able to score the J. So, cash your winners and see what happens — does the K appear?

After you have taken a spade, two diamonds, four clubs, and three hearts these cards remain:

When you cash your last heart winner, East will be forced to discard either a diamond or the K. You decided earlier what to do if the K was discarded — cash the jack. If the K hasn’t appeared, then you will just have to hope the diamonds are good after all. So what happened?

You had all of the remaining tricks except one and East was genuinely squeezed because in the two-card ending he needed to keep three cards. You did not have to plan in advance that this was going to happen, you just had to know what to look for so you could take advantage if it did. Managing the available information and knowing what to do with it is vital on many hands. This, coupled with sound technique, sees declarer home on the final hand in this article:

At first glance, the contract seems to depend on one of the major suits dividing evenly. You ruff the diamond lead, draw trumps, and duck a heart. East overtakes West’s J with the king and returns the J to dummy’s queen. You cash the A, knowing that if everyone follows, the suit was originally 2-2 and you are home. West discards a diamond. You have one chance left —spades may break 3-3 so you…

Stop! Unless you have a train to catch, what’s the rush to find out if spades break? As we saw on the last hand, when you have all but one of the remaining tricks it is usually right to cash your winners and see what happens. You don’t need to envision the ending or work out what either defender has. All you must know is what to look for. You do not even need to keep track of two suits. There is only one card you are looking for — the Q. If it is discarded you know to cash the 10. If not, then you will have to hope spades break. So you cross back to hand with the K and cash two more trumps. These are the last three cards:

As it happens, when you cash your last club (throwing dummy’s heart) East has a choice of losing discards — the Q or a spade. One benefit of develop-ing an IMS is that when something unexpected like a squeeze occurs, you are ready to take advantage of it.

There are many types of counting skills in bridge, and you will rarely play a hand on which you do not need at least one of them. In this chapter, we have seen how to keep track of cards efficiently. Using the information you gain by counting to build a picture of the dosed hands, both in terms of high cards and of distribution, will help you solve many problems. Examples of how to do this are given throughout this book.

To get started, practice by concentrating on one of the unseen hands only. Once you have a complete count of one defender’s shape or high cards, always work out what that leaves the other closed hand. This not only cross-checks your arithmetic, but enables you to see solutions and/or problems from two different perspectives.

However, knowing what each defender has will do you no good at all on many hands. So, how do you know when you need to count the defenders’ hands? How often have you reached Trick 9 and thought, ‘Is the 6 good? If only I had counted the diamonds on this hand: Deciding which cards are relevant at the outset by developing an accurate IMS will solve most problems of this nature. However, there is a safety valve if you miss something in your initial analysis.

If we return to our example of the brain as a fuel tank, you will realize that you will quickly exhaust your mental energy if you religiously count the opponents’ hands on every deal. So, how do you know which hands you need to count? The simple answer is that you don’t. You must therefore train your sub-conscious mind to count for you. When you are driving a car, why do you get tired more quickly when it is dark and raining than when it is clear and dry? The answer is that when the weather is poor you have to concentrate harder —it is a strain to see and you must be more aware of stopping distances, and so forth. You know that you must actively pay attention. On a bright and sunny day you do exactly the same things — watch the road and calculate distances and speeds — but you do these things easily and automatically. They are a habit. Under normal conditions, your mind is trained to do all the necessary things without conscious thought.

Similarly, you must train your mind to follow what is happening at the bridge table without having to make an active effort to do so. Then, when you get to Trick 9, if you need to know whether the 6 is good (but didn’t realize it when you devised your initial plan) you can mentally replay the first eight tricks and come up with the correct answer. As a result, on those hands where you have no need to count the defenders’ hands, you won’t have wasted your mental energy doing so.

Training your mind to do this is simpler than you might think. Next time you play in a relaxed game — one where you are not under pressure to play quickly — make a serious effort to count the opponents’ hands on every deal. You will find it hard work, and for a while you’ll probably play worse as you concentrate on counting. However, after you have done this for just two or three sessions, you will find that you are no longer actively thinking about counting, but that, if you need the information, it is there.

At first, you may find you cannot keep track of enough information to count a complete hand. Since knowing the distribution of two suits puts you most of the way there, practice by keeping track of just two suits. Once you are comfortable with that, add a third suit. Remember to start by counting only one of the unseen hands, though.

Eventually, you will come to realize that counting at bridge need not even be as difficult as counting to thirteen.

LESSONS FROM THIS ARTICLE

• Identify which suits are important (i.e. where your extra tricks can come from).
• Decide which suits you must count or which high cards to watch for.
• Fix in your mind how many cards are outstanding in each of the key suits. • Count by keeping track of missing cards.
• Think in terms of how the missing cards might break rather than the total number of outstanding cards.
• Count only one of the unseen hands.
• Once you know the shape of one unseen hand, work out the distrib-ution of the other.

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