This is part of a series of Declarer Play articles designed to build on one another. To get the most out of them, it’s recommended to study them in sequence.
You are the declarer in a no-trump contract. The opening lead is made, and Dummy’s hand is revealed.
It’s time to count your winners and make a plan. Effective planning begins with an accurate assessment of potential tricks for both your side and the opponents.
Counting your own tricks is easier than counting defensive tricks.
You can easily identify your high cards and determine which suits may produce additional tricks due to their length.
The way a suit is distributed among the players is crucial. For example, if you hold eight spades, including all the top cards, the number of tricks you can cash depends on how the remaining cards in the suit are divided between your opponents.
| 4-4 split = 4 tricks Dummy ♠ Q T 6 2 |
| You ♠ A K J 8 |
| 5-3 split = 5 tricks Dummy ♠ Q 6 2 |
| You ♠ A K J T 8 |
| 6-2 split = 6 tricks Dummy ♠ 6 2 |
| You ♠ A K Q J T 8 |
| 7-1 split = 7 tricks Dummy ♠ 2 |
| You ♠ A K Q J T 8 6 |
Counting long suits for the defense is not so straightforward
You can’t see how their suits are distributed or how many established tricks they might have. However, with careful analysis, you can estimate the distribution or make an assumption that is more informed than a random guess.
This is where split statistics become valuable. They provide insights into how the opponents’ cards are likely distributed between their hands. Understanding these distributions allows for more effective planning.
You might be worried that I’m about to suggest studying charts full of percentages for all the possible ways a suit could split.
Numbers… calculations… memorization… math!
No need for any of that—it’s completely unnecessary.
Here’s why: statistical percentages only tell you what happens on average across a large number of random deals. For example, “Eight cards will split 6-2 17% of the time.” While true, this isn’t particularly useful.
You’re not planning your declarer play for hundreds of random deals—you’re focused on one specific hand. What you really need to figure out is how the opponents’ cards are split on this deal. A probability chart can’t provide that answer.
However, we do need a starting point. So here’s the one simplified (statistical) guideline to remember:
Suits are most likely to divide as evenly as possible, though not always perfectly.
Which means…
- 10 cards split 6-4 (not 5-5)
- 9 cards split 5-4
- 8 cards split 5-3 (not 4-4)
- 7 cards split 4-3
- 6 cards split 4-2 (not 3-3)
- 5 cards split 3-2
That’s it. It’s a starting point. Not a final answer.
A thoughtful player must also pay attention to the bidding, the opening lead, and other relevant factors. Each new piece of information can help confirm or adjust the initial assumption about the suit distribution.
Split Assumption Practice
Example 1
| Dummy ♠ T 8 2 |
| You ♠ K 6 |
How many spades do they have?
We don’t yet know how they split, but what assumption should we start with?
Example 2
| Dummy ♥ 7 4 2 |
| You ♥ A T 8 6 |
How many hearts do they have?
What split assumption should we start with?
Example 3
| Dummy ♣ A 9 |
| You ♣ Q 4 |
How many clubs do they have?
What is the split assumption?
Example 4
| Dummy ♦ – |
| You ♦ A Q 4 |
How many diamonds do they have?
What is the split assumption?
Example 5
| Dummy ♥ 6 4 2 |
| You ♥ Q T 5 |
How many hearts do they have?
What does the simplified statistical guideline suggest about the suit distribution?
You might say, “Statistics are easier than I thought!”
And the response: “Just keep in mind, our guideline is only a starting point. We need to consider other sources of information as well. Sometimes, we’ll need to refine or even reject the initial assumption based on what we observe.”
Example 6
| ♠ K J 2 ♥ T 8 ♦ A J 2 ♣ A K T 9 6 |
| You ♠ Q T 9 6 ♥ K 6 4 ♦ K 7 4 ♣ Q J 7 |
Contract: 3N – you need 9 tricks.
Opening lead is the ♥3. You play Dummy’s ten. Third hand plays the ♥Q. Obviously you will play your king.
How many winners do you have?
You have two options for more tricks.
If you force out their ♠A, how many new spade winners would you establish?
If you finesse the ♦J and the ♦Q is well-placed, you gain one additional winner.
At first glance, taking three guaranteed tricks in spades might seem better than attempting one uncertain trick in diamonds. However, playing spades will give up the lead, while diamonds might not. To decide, you need to count how many tricks the opponents can win.
Let’s count: they have the ♠A and some heart winners. How many heart winners? Use the assumed heart distribution to estimate how many tricks they can take, keeping in mind that hearts have already been played once.
If they cash all their winners – the ♠A and their 4 hearts, is your contract safe?
So… which is better for you – leading spades or leading diamonds?
Example 7
| Dummy ♠ K J 2 ♥ T 8 ♦ A J 2 ♣ A K T 9 6 |
| You ♠ Q T 9 ♥ K 6 5 4 ♦ K 7 4 ♣ Q J 7 |
Contract: 3NT – you need 9 tricks.
The opening lead is the ♥3. You play the ten from Dummy, and the third hand plays the ♥Q. Naturally, you will cover with your king.
This hand is very similar to example 6. Dummy’s hand remains the same, but I’ve shifted a spot card in your hand from spades to hearts.
How many winners do you currently have?
You still have the same two options for developing the extra winner you need. You can force out the ♠A, or you can finesse the ♦J, hoping the ♦Q is favorably placed.
Playing spades is “slow but reliable.” Slow means you will lose the lead, but reliable means you are guaranteed to develop the winner(s) you need.
Finessing the diamond is “quick but uncertain.” Quick means (if it succeeds) you won’t lose the lead, but uncertain means it could fail, causing you to lose the lead and possibly give the defense an extra trick with the ♦Q.
Now, let’s count the defensive winners using the split assumption to determine whether you can afford to play slowly or need to act quickly.
The opponents have the ♠A and some heart winners. Use the split assumption for hearts to calculate how many tricks they can take. Don’t forget that hearts have already been played once. So, what’s the split assumption?
If they cash all their winners – the ♠A and their 3 hearts, is your contract safe?
So… which is better for you – leading spades or leading diamonds?
Example 8
| Dummy ♠ K J 2 ♥ T 8 ♦ A J 2 ♣ A K T 9 6 |
| You ♠ Q T 9 6 ♥ K 6 4 ♦ K 7 4 ♣ Q J 7 |
Contract: 2N – you need 8 tricks.
This hand is exactly the same as example 6. But I’ve changed the contract from 3N to 2N.
Opening lead is the ♥3. You play Dummy’s ten. Third hand plays the ♥Q. Of course you will play your king.
The count of your winners is the same. You have 8 winners – 5 clubs, 2 diamonds, and 1 heart.
You can establish 3 additional winners using the “slow but reliable” spade play, or you can try for 1 extra winner with the “quick but uncertain” diamond finesse.
In example 6, we determined that the “quick but uncertain” diamond finesse was the better option because the defense already had enough winners to defeat 3NT—the ♠A and 4 hearts (based on the 5-3 split assumption). If you gave them the lead with their ♠A, your contract would fail.
Now consider this: is the diamond finesse still the best choice when your contract is 2NT?
We just concluded that attempting the diamond finesse is a poor choice because it jeopardizes the contract when you already have enough tricks.
But does the “slow but reliable” spade play also put the contract at risk?
There are always 13 tricks won in every bridge hand. No more, no less. That truth can tell you if a plan you’re considering is good or bad.
Add the cashable tricks for both sides.
- If the total is less than 13, you might be able to establish and cash more winners.
- If the total is more than 13, somebody is going to be unhappy – unable to cash all their winners. If you lose the lead, you will be the unhappy one who doesn’t get to cash all your winners. Only risk losing the lead if you need an extra trick to make your contract.
- If the total is exactly 13, be very careful. If you give up the lead while establishing a 14th trick, you won’t get to cash it. You may even wind up with fewer tricks than you had. Consider what happens if you have 9 tricks and they have 4 (9+4=13), and then you take a finesse. Someone will lose one of their “winners”. If they win the finesse, they can cash 5 (five!) tricks (the 4 they had, plus the card that wins the finesse), leaving only an unhappy 8 for you. If you win the finesse, you can cash 10 tricks, leaving only an unhappy 3 for them.
So… Be careful, and don’t be greedy.
Split assumptions when establishing winners
Most hands require you to establish additional winners. However, you must exercise caution with suits where both you and your opponents can create extra winners in the same suit.
Example 9
| Dummy ♠ K J 3 |
| You ♠ Q 2 |
The opponents have one immediate spade winner, while you have none.
You can create two high-card winners by forcing out the ♠A.
However, you must proceed cautiously because the defenders hold more spades than you. Playing your honors could end up establishing additional tricks for the opponents instead of for you.
How many spades do they have?
What is the split assumption?
We have honors to control the suit for three rounds, meaning their extra winners will come on the fourth and fifth rounds. That gives them 2 potential winners, in addition to their ♠A.
Your two high-card winners will be cashable before their extra tricks become available, which is a positive. However, every time you play spades, you bring them closer to being able to cash those two extra tricks.
You should postpone playing this suit until you’ve established your winners in other suits where the opponents cannot create additional tricks.
The spades in this example are from a hand played in a recent duplicate game. Let’s analyze what went wrong when spades were played too early…
A Missed Opportunity for Success
Example 9 (expanded )
| Dummy ♠ K J 3 ♥ Q T 8 ♦ A 6 2 ♣ K T 6 5 |
| You ♠ Q 2 ♥ K J 6 4 ♦ K Q 4 ♣ A Q J 7 |
I don’t want to single anyone out, so let’s pretend you are playing the hand. You don’t mind if I let you “make the mistake,” do you?
Contract: 5NT – Opening lead: ♦5
You need 11 tricks to fulfill your contract.
Currently, you have 7 winners: 4 clubs and 3 diamonds. To make your contract, you’ll need 4 additional tricks from hearts and spades, which means you’ll have to drive out both major-suit aces.
In this scenario, the mistake was starting with spades too early. Let’s imagine you follow the same approach.
Remembering the guideline, “Play the honor from the short hand first,” you lead the ♠Q and play the ♠3 from Dummy. To your surprise, the opponents allow your ♠Q to win.
You then lead the ♠2 and play Dummy’s ♠J. This time, the opponents win with the ♠A. That’s two rounds of spades. You’re now out of spades in your hand, and only the ♠K remains in Dummy.
With the opponents now in the lead, they play a third round of spades, which your ♠K wins. At this point, you’re out of spades in both hands.
Now, using the split assumption, determine how many spade tricks the opponents have ready to cash after the third round of spades.
After driving out the ♠A, you have your two extra spade tricks, so you turn your attention to hearts. What will they do with your first heart lead?
They will play their ♥A to capture the lead, and cash their spade skater(s).
Your contract fails because the opponents were able to establish the decisive trick(s) in spades while still holding the ♥A to regain the lead.
To avoid this outcome, you need to force out the ♥A before playing spades.
How do we determine which suit to play first? We analyze the card distribution and use split assumptions. With 8 spades and only 6 hearts, the opponents are much more likely to have length—and the potential for an extra trick—in spades. Therefore, prioritize playing hearts before spades.
When the defenders might have skaters…
Example 10
| Dummy ♦ A Q 3 |
| You ♦ 5 4 2 |
You have one diamond winner. They have none.
You can attempt a finesse, hoping the ♦K is favorably positioned. If the finesse succeeds, you retain the lead and gain an extra winner, which seems advantageous…
However, the finesse could fail, giving the defense both an additional winner and control of the lead.
Even worse, you know the opponents can capitalize on having the lead. They can continue playing diamonds, forcing out your ♦A and setting up additional diamond winners for themselves.
Now, imagine you’ve just lost the finesse, and they’ve successfully driven out your ♦A. Assuming the split assumption is accurate, diamonds can be played four times. Take into account how many rounds have already been played. With your ♦A and ♦Q out of the picture, their remaining diamonds are now winners. How many unclaimed diamond winners do they have left?
Before attempting the finesse, you had control of the lead. If the finesse fails and the opponents continue diamonds, you’ll eventually regain the lead with your ♦A. However, you won’t be “back where you started”—you’ll have lost significant ground.
- You have lost a trick to the ♦K.
- They now have two more ready-to-cash diamond winners. That’s three new winners they didn’t have before you finessed.
You might say, “I enjoy taking finesses!”
That’s understandable—many beginners enjoy taking finesses after learning how they work. However, experienced players are cautious about the significant risk of losing a finesse in a suit where the opponents can establish additional tricks in the same suit. Instead, they always consider less risky alternatives. You should adopt this approach as well.
When you might have skaters…
Example 11
| Dummy ♦ A Q 3 |
| You ♦ J 7 5 4 2 |
As in example 10, you have one winner, and the defense has none. You also have the same potential finesse, hoping the ♦K is favorably positioned.
However, this time, attempting the finesse doesn’t carry the same risk of a disastrous outcome.
What is the assumed suit distribution?
How does the play unfold? The first diamond trick is a finesse. Let’s assume it loses. After regaining the lead in another suit, you return to diamonds.
You win the second round with your ♦A and continue with a third round, winning it with your ♦J.
At this point, how many rounds of diamonds have been played?
If the 3-2 split assumption is accurate, the opponents will have no diamonds remaining after three rounds. This means that even if you lose the finesse, you could still make four diamond tricks—the ♦A and ♦J as high-card winners, plus two additional tricks from your established diamonds.
The key takeaway from these two diamond examples is…
Finessing is risky when the opponents can win and create additional tricks in the same suit.
However, if you are the one who can establish additional tricks, the risk is minimal. In fact, developing long suits is often a highly effective strategy.
To determine what is risky and what is less risky, you need to count cards, apply a split assumption, and calculate potential tricks.
Which Suit First? Which Suit Last?
Example 12
| ummy ♠ J T 8 7 ♥ A K 5 4 ♦ Q 3 2 ♣ 6 5 |
| You ♠ Q 9 4 ♥ Q 6 3 ♦ A K 5 4 ♣ K Q J |
Contract: 3N. You need 9 tricks to make 3N.
Opening lead: ♥2. The split assumption for their 6 cards is 4-2.
How many winners do you have?
You need 3 more winners to make your contract.
You can drive out the ♣A and promote 2 club winners.
You can drive out the ♠AK and get 2 spade winners.
And, if you’re lucky, you can get one extra winner from diamonds. Why do I say you have to be lucky for a diamond spot card to be a winner?
How many more do they need to set your contract?
The opening lead was a heart. If they persist in hearts, how many extra winners can they develop?
If they manage to develop that one slow heart winner, their total would be 4 tricks—not enough to defeat your 3NT contract.
This means you can afford to develop your extra winners in clubs and spades at a slower pace. The key to making your contract is avoiding plays that help them create a fifth winner. That’s why playing diamonds now is a poor choice. If the diamond suit doesn’t split evenly, it could give the opponents an additional trick.
Now let’s consider spades and clubs. Based on the split assumptions for those suits, you could play all your cards in one of them without allowing your opponents to gain extra tricks.
Which suit is that?
We’ve worked out our plan:
- Win the opening lead in hearts.
- Drive out their spade masters.
- Drive out their club master.
- When your lesser honors are established, cash all your tricks and make your contract.
This plan simplifies the details of losing tricks and regaining the lead. Here’s how it unfolds:
The first time we lead spades, the opponents win and return a second heart. We win that trick and lead a second spade. They win again and return a third heart. We win and switch to clubs. They win the club trick and cash their heart winner. Finally, we regain the lead and cash all our remaining tricks.
With this plan, we establish 10 winners: 2 spades, 3 hearts, 3 diamonds, and 2 clubs. Why, then, will we only be able to cash 9 tricks?
You might ask, “The split assumption for their 6 hearts is 4-2. But what if the assumption is wrong, and the actual split is 5-1? Wouldn’t they have 2 heart winners—enough to defeat our 3NT contract?”
Great question!
You’re right that two heart winners would be enough to defeat 3NT. However, we would identify the 5-1 split when the player with the singleton discards on the second round of hearts. If that happens, we’d need to adjust our plan.
In that case, we could work on developing 2 extra tricks in spades and hope for a favorable 3-3 diamond split. If luck is on our side, we could cash our 9 tricks before the defense can claim their heart winners.
There are also more advanced strategies to reach 9 or 10 tricks before the defenders can cash their hearts, but those are beyond the scope of this discussion.
For now, the key takeaway is recognizing when split assumptions are incorrect. That’s what we’ll be covering next.