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Count Defensive Winners

By Ralph Welton

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.

Counting your own winners is straightforward. What you see is what you get.

But counting defensive winners means counting what you don't see. Actually that's pretty easy too. They always have all the honors you don't have.

example 1

J T 8 7  
A K 6 4
Q 7 2
6 5

Q 9 4
Q 5 3
A K 5 2

How many winners do you have? Remember to look at both hands, and don't count skaters unless you are certain they are winners.

6 winners – AKQ, AKQ. Don't count a skater for either suit because they might not split 3-3.

How many winners do the defenders have?

3 winners – AK and A

example 2

A 9
Q T 5
K J T 7 2  
9 5 2

Q 9 4
J 9 7 6
A 9 6

How many winners do you have?

Just 3 winners – A and AK

How many winners do the defenders have?

They have 4 winners – AK and AK

example 3

K J T 9
Q 8
Q T 7 2  
9 5 2

Q 9
J T 9 7
K J 9 6

How many winners do you have?

None. They have all the aces.

How many winners do the defenders have?

They have 6 winners – A, AK, A, and AK

Why does counting winners matter?

Little Bear looks puzzled. "I understand about counting my own winners," he says, "so I'll know how many more I need to make my contract. But why do I need to count their winners? They have whatever aces and kings they were dealt. There's nothing I can do about it."

That's a good question, Little Bear!

Counting winners can tell you which plays to make, and which plays to avoid.

Let's look at a few examples...

example 4

A Q 6  
4 2

8 6
K Q 7

Suppose you just need one more cashable trick (winner) from these two suits to make your contract.

Which is the better option – driving out the A to establish a heart honor, or finessing the Q, hoping the K is on-sides?

The correct answer is... have to count your opponents' winners before you will know what to do.

If they don't have enough winners to set your contract, driving out the A is certain to give you the one more trick you need.

Certain, but "slow." You'll have to give up the lead and patiently watch them play all the winners they already have before you can recapture the lead and cash your own tricks. It's OK to get your tricks "slowly" like this... IF the defense doesn't have enough winners to set your contract.

example 4, repeated

A Q 6  
4 2

8 6
K Q 7

But if they do have enough winners to set your contract, you must risk the spade finesse.

It only gives you a 50-50 chance to get your one-more-trick. But if it succeeds, you get your extra trick without losing the lead, so you can cash your tricks "faster" and make your contract before the bad guys have the chance to defeat it.

Of course, you won't know how many winners each partnership has unless you count them.

example 5

A K 6 2  
4 2

Q 7 4
K Q 7

This is similar to example 4. Again, you need just one more cashable trick to make your contract.

Is it better to force out the A, or play the top three spades, hoping for a 3-3 split?

Driving out the A is guaranteed to establish the trick you need. But it loses the lead. It's "slow."

You can't tell if that's a good plan until you count the winners for the defense.

If the defense doesn't have enough winners to set your contract...

✓ Play hearts (slow but certain).

If the defense already has enough winners to set your contract...

✓ Your only hope for one more trick would be a "faster" fourth-round spade skater. It's "faster" because it doesn't lose the lead. Faster, but not certain. You won't have a skater if the spades don't split 3-3. Oh well... some contracts do fail, no matter how well you count and plan.

One more point... there's a trap to be avoided:

You might think that if they can't set your contract you could try the spades first. And if spades don't split, then play hearts.

But you must count tricks before you know if that's OK, because...

If the spades don't split 3-3, playing the AKQ establishes a spade trick for the defense (perhaps the J?). Then when you play hearts, the defense has that one-more-trick to cash before you can recapture the lead. Would that J be enough to set your contract?

No surprise... it's a counting question!

You must count tricks.

There's no way around it. All good declarers count tricks.

Every hand.

At the very least you must determine if the defense has enough winners to set your contract.

example 6

Q 7 6
A J T 4 2  
8 4 3

K 8 5 3
J T 9 8
K Q 6
K 6

The opening lead is 7, and third seat plays the J. Of course, you win the trick with your K.

How many winners do you have?

8 – AK, AKQJT, plus the K you just cashed

How many winners does the defense have?

Two hearts and... hmmm... how many clubs? We know they have 8 clubs, but can't tell how many clubs they can cash because we don't know how the clubs split.

You've already won the opening club lead with your K. The opponents have played 7 and J.

A Q T 7 J 9 5 2

If clubs split 4-4, how many cashable clubs do they have?

They have 3 cashable club tricks. They can lead clubs four times, but you've won the first round.
A Q T 7 5 J 9 2

And if they split 5-3?

They have 4 cashable club tricks.
A Q T 7 5 2 J 9

And if they split 6-2?

They have 5 cashable club tricks.

Little Bear says, "Wait a minute! You said I need to count tricks, but you also said I can't tell how many tricks they have because I don't know how their suit splits. What's a bear to do??"

Good pick-up, Little Bear. In fact, figuring out how many skaters they have is so important, we're going to spend the next several pages answering your question!

plush toy bearGo to the next topic:

Split Assumptions

Ralph Welton with BuffyBridge Bears is run by a retired teacher and ACBL life master who has 35 years teaching experience and who's been playing bridge for over 50 years. I don't claim to be one of the top players, but I do understand how slowly beginners need to go when they are trying to learn how to play bridge.