Count Winners for No Trump

This is one of a series of Declarer Play articles. These articles build upon each other, so I recommend that you study them in order.

Introduction

As soon as the bidding is over, determine the number of tricks you need to make your contract.

Declarer always needs six tricks (sometimes called a 'book') plus the number she has bid. In the following chart, I've used no trump as an example, but the numbers are the same for suit contracts.

1N → 6 + 1 = 7 tricks

2N → 6 + 2 = 8 tricks

3N → 6 + 3 = 9 tricks

4N → 6 + 4 = 10 tricks

5N → 6 + 5 = 11 tricks

6N → 6 + 6 = 12 tricks

7N → 6 + 7 = 13 tricks

You can assess your goal – the number of tricks you need – before the opening lead is made and before you see the dummy. But don't let your opponents rush you. If they lead quickly, count out your goal while they wait.

Bridge is a thinking game. You are allowed to take a few moments to think. You're also allowed to put your hands in your lap and count on your fingers if it helps.

When the dummy comes down, you will count the winners you already have (explained below) and compare it to what you need. Usually you won't have enough winners to make your contract. Don't panic... this is normal.

Fortunately the defense doesn't usually have enough winners to set your contract either.

So both sides will work to develop more.

If you develop and cash enough tricks to make your contract, it won't matter how many tricks the defense later develops. There won't be enough tricks left for them to undo your success.

Similarly, if the defense cashes enough tricks to set your contract, there won't be enough tricks left for you to make your contract, no matter how many winners you later develop.

That's why no trump is often described as a race. You have to develop and cash enough tricks to make your contract before they develop and cash enough to defeat it.

Much of no trump declarer play is about counting. We count to determine our goal. We count the tricks we are certain to win. We count tricks we can develop. We count defensive winners. And we count to see if we will be able to cash enough tricks before the defenders can cash theirs.

The counting we need to do isn't particularly difficult, though there will be a lot of it, including frequent revisions to our counts.

Let's get started.

When the dummy comes down, count winners

What do we mean by winners?

Winners are cards that cannot lose if you lead them. They can be called "master cards," "certain winners," "sure winners," "cashable tricks," "tricks," or various other names. What you call them doesn't matter as long as they cannot lose.

example 1

♠ – 1 winner. If you lead the ♠Q, it can lose to their ♠K. Even if you lead toward the ♠AQ and finesse, it could lose.

♥ – 2 winners

♦ – 0 winners. Any diamond you lead can lose.

♣ – 0 winners

Yes, you can force out the ♦A and develop 3 diamond winners. But you haven't done that yet. So don't count your diamonds as winners. You could view the diamonds as 3 potential winners.

example 2

When counting winners, combine your high cards with Dummy's.

♠ – 0 winners

♥ – 3 winners

♦ – 4 winners (be careful; they're blocked)

♣ – 0 winners

To unblock your four diamond tricks, cash the ♦AQ first. Then cross to the dummy with a heart, so you can lead the ♦KJ.

If Dummy didn't have a winner in another suit, you might have to cash the ♦A, then overtake your ♦Q with Dummy's ♦K. Overtaking would get the lead in Dummy so you could cash the ♦J. If you have to do this, count only 3 diamond winners because you will "crash" two of your honors.

example 3

Master cards are usually winners. But not always.

In this example, you have 12 master cards:

♠AKQJ, ♥AKQJ, ♦AKQJ

But you cannot win 12 tricks with your 12 masters.

How many winners do you have in each suit? Count for yourself before peeking...

♠ ♥ ♦ ♣

example 4

How many winners do you have? show answer

example 5

How many winners do you have in each suit?

♠ ♥ ♦ ♣

Do we ever count skaters as winners?

Yes, sometimes...

Count how many cards the opponents have in your suit. If you have enough top honors, you can make them follow suit to your master cards until they completely run out. Even your smallest cards will then be winners. Counting will tell you if this is guaranteed to work even before you start cashing your top honors.

Like this...

example 6

You have 10 clubs, so they have only 3.

With three top honors, even a 3-0 split doesn't stop you from cashing all 6 clubs.

So you can count 6 winners.

example 7

I've taken away one of Dummy's spot cards. (My wife says that's mean.)

Now they have 4 clubs, including the ♣J.

If you play your ♣AKQ, a 4-0 split would allow them to win the fourth round with their ♣J, stopping you from cashing more clubs. So you can't count your small cards as skaters.

Actually, there's a good chance the clubs will not split 4-0. You could play one round of clubs to see if both opponents follow suit. If they do, you've ruled out a 4-0 split and you could then count 6 winners.

However, there are three reasons not to do this:

1. First, and by far the most important reason, it can become a bad habit if you begin cashing tricks before you plan your declarer play for the entire deal.
2. Second, you may need to preserve your three big clubs for later entries. Again, you must make a plan for your declarer play before you know if you need the big clubs for entries.
3. Third, if you keep your club strength concealed, your opponents may make mistakes placing the honors, and pursue an inferior defense.

A well made plan may indeed begin with testing how the clubs split, but make your plan first.

We'll get to planning soon enough, but for now remember not to assume long cards are winners unless a possible bad split doesn't matter.

example 8

You have 8 diamonds.

How many diamonds do they have? show answer

Whenever you are hoping for skaters, count their cards and consider how they might split between the two defensive hands.

How many diamond winners do you have? 3 5

You could cash two of your masters to see if they both follow suit. If so, there would only be one diamond outstanding and you could then count 5 diamond winners. But again I caution you not to start cashing tricks until after you have made a plan.

Next we'll look at a hand where we count and plan before we play.

After you have counted your winners, compare that number to the contract you are declaring to see how many additional tricks you need to develop.

Then look at each suit to see where you might develop the tricks you need.

example 9

The opening lead is the ♣5.

How many winners do you have? show answer

Your contract is 3N. How many tricks (winners) do you need to develop? show answer

Where might you get more tricks? show answer

Now we're ready to make a plan.

1. Win the club opening lead with your ♣K.
2. Lead spades to establish 3 additional tricks, bringing your total to the 9 tricks you need. If they don't take their ♠A on the first round, persist with spade leads until you have 3 spade winners.
3. When they win their ♠A, they will lead another club. They will be doing the same thing with clubs that you are doing with spades – establishing more tricks. Win this second club lead with your ♣A.
4. Cash your 9 tricks, making your contract. Do not try for overtricks by leading hearts. They would win and have ♠A, ♥AK, and 2+ clubs – enough winners to defeat your makable contract.

The plan for this hand is very straightforward. It could be summarized as:

• win the lead
• establish the tricks you need
• get the lead back
• cash your tricks

Notice that the number of winners changed during the play. You started with 6 winners and quickly improved to 9 winners by playing spades.

Meanwhile, the defense started with 3 winners (♠A, ♥AK) and established more by driving out your two club masters.

They didn't get to cash their newly established clubs because you cashed your tricks first.

That is the essence of a good plan – a logical sequence of plays where you can cash enough tricks to make your contract BEFORE they can cash enough tricks to set it. To make such a plan, you must count winners.

example 9, repeated

Little Bear speaks up, "You said it's not good to play hearts? But if we play both spades and hearts, can't we get 5 more tricks – 3 from spades and 2 from hearts? Then we could make some overtricks. I like overtricks."

You are correct, Little Bear, that all those tricks would add up to overtricks for us. But if you play hearts the opponents will cash their tricks BEFORE you can recapture the lead to cash yours.

After they drive out our ♣AK, they have 2+ club skaters to cash. (The exact number depends on how the clubs split between the two defenders.) Together with their ♠A and ♥AK, that makes enough winners to defeat our 3N contract.

You were just counting your own tricks, Little Bear. You have to count their tricks too.

example 10

This hand is another example of the importance of cashing your tricks before the defense cashes theirs.

Again you are declaring a contract of 3N.

The opening lead is ♣3.

Third hand plays the ♣Q, and you win the trick with your ♣K.

How many winners do you have? show answer

You need two more winners to make your contract.

How many winners do the defenders need to set your contract? Five.

I've peeked at their cards, and I can tell you that (with your ♣K gone) they now have 4 club winners ready to cash. They need just one more defensive winner to set your 3N contract. That means you cannot afford to lose the lead when developing more tricks in the other three suits.

Where can you get the two more winners you need?

1. You can finesse in spades. If the ♠Q is on your left, you can repeat the finesse for two additional winners. However, if the finesse loses, they get a trick with the ♠Q followed by 4 club tricks. That's down one. So sad.
2. You can finesse in hearts. If the ♥K is on your left, you can repeat the finesse 3 times, making an overtrick. That's better than playing spades because of the overtrick. However, if your finesse loses, they get the ♥K followed by 4 club tricks. That's also down one. Ditto sadness.
3. You can play diamonds and hope for two skaters, just enough to make your contract. However, if you try to cash a fourth diamond and the suit doesn't split, you will lose that diamond and 4 clubs. Down one. Hmmm... this is all starting to sound sadly familiar...

Which brings us to a critical point: YOU MUST COUNT their diamonds when you play your diamond masters. Counting allows you to test for skaters without losing the lead. Then you will only plan on cashing diamond skaters when your diamond spot cards actually are skaters.

Little Bear speaks up, "Uncle Smokey uses binoculars to look for bees going in and out of holes in the trees. Then he only climbs the trees that have honey in them. I think Uncle Smokey would be good at bridge."

Me: sigh...

example 10, repeated

After winning the opening lead with your ♣K, what do you think about playing each of these suits next? Decide about each suit first before looking.

♠ ♥ ♦

Summary of the plan:

1. Win the opening lead with your ♣K.
2. Test the diamonds.
   • If the diamonds split 3-2, cash your 9 winners (no finesses).
   • If the diamonds don't split, finesse in hearts.

Actually, if the diamonds don't split 3-2, there are times when you might prefer to take the spade finesse rather than the heart finesse. For example, if RHO (right hand opponent) has promised 5+ hearts in the bidding, you would know the heart finesse would fail, and prefer to take the spade finesse. You would know the heart finesse was going to lose because you COUNTED the hearts, and LHO doesn't have any.

The main skill for good declarer play is counting.

This was a difficult hand for beginners. I suggest you review it before moving on.

Go to the next topic:

Long Suits