The Rule of 11: The Math That Reads Your Opponent’s Hand

The Rule of 11 in bridge sounds complicated but becomes second nature once you use it a few times. It’s a simple calculation that tells you exactly how many cards higher than the opening lead are distributed among three hands: dummy, your hand, and the leader’s partner.

As declarer, it tells you whether to play high or low from dummy on the opening lead. As third-hand defender, it tells you which card to play to give your side the best chance. Unlike most bridge “rules,” this one is actual mathematics. It works every time—as long as the opening lead is fourth-best from longest and strongest.

The rule of 11 bridge technique is essential for both declarer play and defense, turning uncertainty into information you can count on. Here’s how it works and how to use it to improve your game.

The Mathematical Principle

When your opponent leads fourth-best, subtract that card’s value from 11. The answer tells you how many cards higher than the one led are in the other three hands (dummy, your hand, and leader’s partner).

Formula: 11 - (card led) = cards higher in the other three hands

Why 11? When you lead fourth-best, you have 3 cards higher in your hand. That leaves 11 cards higher distributed among the other three players. It’s mathematical certainty, not a guideline.

How to Apply It

Let’s say partner leads the ♠6. You’re sitting in third seat (or you’re declarer looking at dummy).

Step 1: Subtract the 6 from 11.
11 - 6 = 5

This tells you that 5 cards higher than the 6 exist in the other three hands (dummy, your hand, and one hidden hand).

Step 2: Look at how many cards higher than the 6 you can see in dummy and your hand combined.

Count carefully. The ♠7 is higher. The ♠5 is not. Don’t count cards lower than the one led—they don’t matter for this calculation.

Step 3: The difference tells you how many cards higher than the 6 are in the leader’s partner’s hand (or declarer’s hand, if you’re on defense).

If you can see 3 cards higher between dummy and your hand, then the fourth player has 5 - 3 = 2 cards higher than the 6. That’s precise information you can use immediately.

Example 1: Third Hand Defender

Partner leads the ♥5 against 3NT. Dummy has ♥J83, you hold ♥AQ2.

Apply the Rule of 11:
11 - 5 = 6 cards higher than the 5.

Count visible cards:
Dummy: J, 8 (2 higher)
Your hand: A, Q (2 higher)
Total: 4 higher

Declarer has 6 - 4 = 2 cards higher than the 5.

The play: Declarer has two cards higher than the 5. If declarer plays low from dummy, play the queen, not the ace. The queen forces declarer’s king (or wins), and partner’s suit is still alive.

Using It as Declarer

The Rule of 11 is just as powerful when you’re declarer. It tells you whether third hand can beat dummy’s card, helping you preserve stoppers and make the right play from dummy.

This is particularly crucial in notrump contracts where you’re racing to establish your tricks before the defense cashes theirs. Knowing exactly what East holds over dummy can mean the difference between making your contract and going down.

Example 2: Declarer Play

West leads the ♠4 against your 3NT contract.

Dummy: ♠Q73
You: ♠AJ2

Apply the Rule of 11:
11 - 4 = 7 cards higher than the 4.

Count visible cards:
Dummy: Q, 7 (2 higher)
Your hand: A, J (2 higher)
Total: 4 higher

East has 7 - 4 = 3 cards higher than the 4.

The play: East can beat dummy’s 7 with any of three cards. Playing the 7 is pointless. You must decide between the queen (hoping East has the king) or low (planning to finesse the jack, hoping West has the king). Combine the Rule of 11 with other clues: bidding, tricks needed, defensive signals.

Example 3: Declarer Knows to Duck

West leads the ♥6 against 3NT.

Dummy: ♥1073
You: ♥AJ4

11 - 6 = 5. Dummy has 10, 7 (2 higher). You have A, J (2 higher). Total: 4.

East has 5 - 4 = 1 card higher than the 6.

The play: East has only one card higher. Play the 10 from dummy. It likely forces East’s honor or wins outright. If it loses to the queen, you have AJ4 sitting behind West’s king, limiting losses to two tricks.

Using It as Third Hand Defender

The most common use of the Rule of 11 is when you’re sitting in third seat and partner leads fourth-best. The rule tells you whether you need to play your high card or can save it for later.

This is where the Rule of 11 really shines in defensive play. Partner has led the suit, you’re looking at dummy and your hand, and you need to make an instant decision. Play too low and declarer wins cheap. Play too high and you waste an honor you’ll need later. The Rule of 11 gives you the answer every time.

The key insight: if declarer can’t beat a lower card from your hand, there’s no reason to play a higher one. Save your honors for when they’re actually needed.

Example 4: Saving Your Honor

Partner leads the ♠7 against 3NT.

Dummy: ♠J32
You (East): ♠KQ5

11 - 7 = 4. Dummy: J (1 higher). You: K, Q (2 higher). Total: 3.

Declarer has 4 - 3 = 1 card higher than the 7.

The play: Declarer has only one higher card. If declarer plays low from dummy, your queen wins. Save the king to cover dummy’s jack later. When declarer plays the 2, you play the 5 and it wins!

Example 5: You Must Play High

Partner leads the ♦4 against 4♠.

Dummy: ♦1096
You (East): ♦AJ2

11 - 4 = 7. Dummy: 10, 9, 6 (3 higher). You: A, J (2 higher). Total: 5.

Declarer has 7 - 5 = 2 cards higher than the 4.

The play: Declarer can beat dummy’s 6 with either of two cards. Playing the 2 is useless. Play the jack to force declarer’s honor.

When the Rule of 11 Doesn’t Apply

The Rule of 11 only works when the opening lead is fourth-best. If your opponent leads differently, the math breaks.

It Doesn’t Work Against:

Top of nothing (9 from 983) - Not fourth-best.
Third or fifth-best leads - Use the Rule of 12 for third-best (see below).
Attitude leads - Common against suit contracts. High = honor, low = nothing.
MUD leads (Middle-Up-Down from three small) - The 8 from 983 isn’t fourth-best.
Honor leads - King from AK or KQ isn’t fourth-best.
Short suits - Can’t lead fourth-best from three cards.

How to Tell if It’s Fourth-Best

Most partnerships lead fourth-best against notrump. Against suit contracts, it varies. Check partnership agreements.

Clues:

If the card is a 7 or higher, probably not fourth-best (unless partner has a strong suit).
If you see three cards lower in dummy and your hand, it can’t be fourth-best.

The Rule of 12 (Third-Best Leads)

Some partnerships lead third-best, particularly against notrump. Use the Rule of 12 instead.

Formula: 12 - (card led) = cards higher in the other three hands

Example: Third-Best Lead

Partner leads the ♥7 (third-best agreement).

Dummy: ♥J94
You (East): ♥Q103

12 - 7 = 5. Dummy: J, 9 (2). You: Q, 10 (2). Declarer has 1 higher than the 7.

The play: If dummy plays low, your 10 might win. Save the queen to cover dummy’s jack later.

Worked Examples in Full Deals

Deal 1: Declarer Uses Rule of 11 to Make Contract

Contract: 3NT
Dummy: ♠K73
You: ♠AJ4
Opening Lead: ♠6

11 - 6 = 5. Dummy: K, 7 (2). You: A, J (2). East has 1 higher card than the 6.

The play: Play low from dummy. East plays the queen (their one higher card), you win the ace. Now you have J4 behind West’s presumed 1098x, preserving your stopper. You make 3NT because the Rule of 11 told you East couldn’t hurt you.

Deal 2: Defender Uses Rule of 11 to Beat Contract

Contract: 3NT
Dummy: ♠1096
You (East): ♠AJ3
Partner’s Lead: ♠5

11 - 5 = 6. Dummy: 10, 9 (2). You: A, J (2). Declarer has 2 higher than the 5.

The play: Dummy plays the 6. Play the jack to force declarer’s king. Later, when you get in with a club, cash the ace and continue spades. Partner wins the queen and runs the suit to beat 3NT. If you’d played low on trick one, declarer would have two stoppers.

Deal 3: Declarer Avoids a Trap

Contract: 3NT
Dummy: ♠Q85
You: ♠A103
Opening Lead: ♠4

11 - 4 = 7. Dummy: Q, 8 (2). You: A, 10 (2). East has 3 higher than the 4.

The play: East can beat the queen with any of three cards. Play low from dummy. East plays the jack, you win the ace, preserving Q10 as a second stopper. The Rule of 11 told you playing the queen was dangerous.

Common Mistakes

Mistake 1: Applying It to Non-Fourth-Best Leads

The biggest mistake is using the Rule of 11 when the lead isn’t fourth-best. Know your partnership agreements.

Mistake 2: Miscounting

Count carefully. Dummy’s higher cards, your higher cards, do the subtraction. Take your time—nobody can see you doing mental math.

Mistake 3: Forgetting It’s About Three Hands

The Rule of 11 tells you about three hands: dummy, your hand, and one other. It doesn’t tell you about the opening leader’s hand (they have three cards higher than fourth-best).

Mistake 4: Ignoring Other Information

The Rule of 11 is a tool, not magic. Combine it with the bidding, defensive signals, and distribution clues. Sometimes the bidding overrides the math.

Why It Matters

The Rule of 11 turns guesswork into certainty. Without it, you’re playing third hand hoping your card is high enough, or you’re declarer hoping dummy’s card will hold. With it, you know.

That knowledge adds up over hundreds of hands. You make better decisions as third-hand defender. You preserve stoppers as declarer. You avoid wasteful plays and find the winning line.

Consider the difference: without the Rule of 11, you might play your king as third hand “just to be safe,” wasting a crucial honor. With it, you know exactly when the queen will suffice. As declarer, you might blow a stopper playing the wrong card from dummy. With the Rule of 11, you know which card East can beat and which will hold.

And unlike most bridge conventions, which require partnership agreement and memory, the Rule of 11 is pure math. You can use it even if your partner has never heard of it. The card they lead tells you everything you need to know. It works at any level of play, from club games to world championships.

The Deep Principle

Bridge is a game of inference. The Rule of 11 is one of the cleanest inferences available. When your opponent leads fourth-best, they’re giving you a mathematical constraint: exactly 11 cards higher than the one led are distributed among three hands.

Use that constraint. Count what you can see. Figure out what you can’t see. Make the play that wins based on the math, not the hope.

That’s the difference between guessing and knowing. The Rule of 11 lets you know.