Counting the Hand

Most “guesses” aren’t guesses at all. By the middle of a hand, a good declarer often knows exactly what each opponent holds, because they’ve been counting.

Counting sounds hard, but it’s just three simple totals:

There are 40 high card points in the pack.
Each player has 13 cards.
There are 13 cards in each suit.

By the end of this module you’ll be able to use the bidding, the opening lead and the play to place the missing cards, and to make the right decision when it matters.

1. Count your tricks first

Before you play to trick one, count:

In a suit contract: your losers in each suit, and how you’ll get rid of the extras.
In no trumps: your sure winners, and where the extra tricks will come from.

Then ask: “What do I need to know to make this contract?” That tells you which opponent’s hand to concentrate on.

2. Counting points from the bidding

Every call an opponent makes, and every call they don’t make, tells you about their points.

What happened	What it tells you
Opponent opened 1 of a suit	About 12–21 points
Opponent opened 1NT	The announced range (for example 15–17)
Opponent passed as dealer	Usually fewer than about 12 points
Opponent passed partner’s opening	Usually fewer than about 6 points
Opponent made a weak two or pre-empt	Usually about 6–10 points
Opponent overcalled at the one level	About 8–16 points

Example: the player who passed

West passed as dealer. You end up in 4♠. During the play, West has shown up with the ♥A K (from the opening lead) and the ♣Q J (when they won a club trick). That’s 10 HCP.

You’re missing the ♦A and need to decide whether to lead towards your ♦K, hoping the ace is with West.

If West also held the ♦A, they’d have 14 HCP, and they’d have opened the bidding. So East holds the ♦A. Play accordingly.

3. Counting shape

Each player holds 13 cards. Once you know the length of three suits in a player’s hand, you know the fourth.

Clues to shape:

The bidding. A weak two shows six cards; a three-level pre-empt usually shows seven; a 1NT opening shows a balanced hand.
The opening lead. The fourth-highest lead from a long suit tells you that suit’s length, and a short-suit lead may suggest a singleton or doubleton.
Showing out. When an opponent can’t follow suit, you know the exact split of that suit.
Count signals. When the defenders give count, they’re telling you too.

Example: a complete count

You’re declarer in 6♥ and need to find the ♣Q. You hold A J 5 in dummy and K 10 4 in your hand: a two-way finesse.

Before touching clubs, you play the other suits and watch:

West opened 1♠ and has shown up with five spades.
West followed to three rounds of hearts (trumps) and then showed out.
West followed to three diamonds and then showed out.

So West has 5 + 3 + 3 = 11 cards in spades, hearts and diamonds, and therefore two clubs. East has four. With East holding twice as many clubs, East is much more likely to hold the queen. Finesse East for it.

Delay your guess. Play the other suits first. Each round gives you more information, and the guess becomes a certainty.

4. Vacant spaces

Without a full count, you can still use vacant spaces: the number of unknown cards in each opponent’s hand.

West opened 3♥ and has seven hearts. East has two hearts. That leaves:

West: 13 − 7 = 6 unknown cards (“vacant spaces”).
East: 13 − 2 = 11 unknown cards.

You’re missing the queen of spades. Without other clues, East is nearly twice as likely to hold it (11 spaces against 6). Play East for the queen.

5. The Rule of 11

When the opening lead is the fourth-highest card of a suit, subtract its value from 11. The answer is the number of higher cards in that suit held by the other three players.

West leads the ♦7 against your 3NT. 11 − 7 = 4. There are four diamonds higher than the 7 in dummy, your hand and East’s hand combined.

Dummy:  ♦ Q 9 3
You:    ♦ K 10 5

You can see four cards higher than the 7 between dummy and your hand (Q, 9, K and 10). So East has no diamond higher than the 7. You can play low from dummy, knowing your ♦10 or ♦9 will win.

The Rule of 11 works for both declarer and the defenders. Module 9 shows how defenders use it.

6. Assume the contract can make

When only one layout of the cards lets you make your contract, assume that layout exists and play for it.

You’re in 4♠ and have three losers already. Your only chance to avoid a fourth is for West to hold the ♥A, so that a lead towards your ♥K wins a trick. If East holds the ace, you’re going down whatever you do. So play West for the ♥A: lead towards the king.

Combine this with counting. If the bidding makes the necessary layout impossible, look for a different line, such as an endplay (Module 7) or a squeeze (Module 8).

Rules worth remembering

40 points, 13 cards per hand, 13 cards per suit.
Count your tricks before playing to trick one.
A pass is information. A passed hand rarely holds 12+ points.
Delay your guess until you’ve played the other suits.
Once you know three suits in a hand, you know the fourth.
Use vacant spaces when one opponent has shown a long suit.
Rule of 11: 11 minus the fourth-highest lead = higher cards in the other three hands.
Assume the contract can make, and place the cards that make it.

Try these

1. East opened 1NT (15–17). West leads. During the play, East has shown up with the ♠A, ♥K Q and ♣A. You need to guess who holds the ♦Q. Who has it?

2. West led the ♠6 (fourth highest) against 3NT. Dummy has ♠ A 9 4 and you hold ♠ K 10 3. How many spades higher than the 6 does East hold?

3. West opened 2♠ (a weak two showing six spades). East has turned up with two spades. Both opponents follow to three rounds of hearts. Who is more likely to hold the missing ♦J?

4. West passed as dealer, then overcalled 1♥ later in the auction. West has shown the ♥A K Q and the ♠J. Where is the ♣A?

Answers

1. East has shown 4 + 5 + 4 = 13 HCP and opened a 15–17 1NT, so East must hold at least 2 more points: the ♦Q is likely to be with East. (Check any other missing honours too. If only the ♦Q is missing, East has it.)

2. 11 − 6 = 5 higher cards in the other three hands. You can see four (A, 9, K, 10). So East has one spade higher than the 6.

3. East. West has six spades and three hearts: 9 known cards, leaving 4 vacant spaces. East has two spades and three hearts: 5 known cards, leaving 8 vacant spaces. East is about twice as likely to hold the ♦J.

4. West has shown 10 HCP (A K Q of hearts = 9, plus the ♠J = 1) and passed as dealer. With the ♣A as well (14 HCP), West would have opened. So East has the ♣A.

Words to know

Term	Meaning
Counting	Keeping track of the points, suit lengths and tricks in all four hands
Showing out	Failing to follow suit, which reveals the split of that suit
Complete count	Knowing the exact length of every suit in an opponent’s hand
Vacant spaces	The number of unknown cards in an opponent’s hand, used to estimate where a missing card is
Rule of 11	Subtract the value of a fourth-highest lead from 11 to find the number of higher cards in the other three hands
Two-way finesse	A suit where you can finesse either opponent for a missing card

What next?

Practise counting one suit per hand at your next session: trumps are the easiest place to start.
Add points as the defenders play their honours, and check them against the bidding.
Move on to Module 7: Endplays, where counting lets you force the opponents to help you.