The Rule of 11

The rule of 11 in bridge is a piece of arithmetic for the defender in third seat. Whenever partner's lead is fourth best, it tells you how many cards higher than the one led are in declarer's hand. Partner leads a small card, dummy comes down, and instead of guessing what to play at trick one, you count.

Subtract the rank of the card led from 11. The result is the number of cards higher than the card led held by dummy, third hand and declarer together. You can see dummy and your own hand, so whatever is left over belongs to declarer.

The 11 comes from simple counting. Rank the jack as 11, the queen as 12, the king as 13 and the ace as 14. If the card led is a 7, there are seven cards higher than it in the suit, namely the 8, 9, 10, jack, queen, king and ace. A fourth-best lead means the leader holds exactly three of those, so the other four are in the remaining hands. Seven minus three is 4, the same as 11 minus 7. For any fourth-best card the same calculation gives 11 minus the rank.

Eleven minus seven is four, so four spades higher than the 7 are in dummy, your hand and declarer's hand together. Dummy has one (the queen). You have three (the ace, jack and nine). That accounts for all four, so declarer has no spade higher than the 7.

Now trick one is easy. Play the ♠9, which wins because nobody else can beat it. Playing the ace would leave dummy's queen as a stopper, and playing the jack would waste a useful card for nothing. You also know exactly which high spades partner holds. Of the seven cards above the 7, dummy has the queen and you have the ace, jack and nine, so partner has the king, ten and eight.

The rule answers three questions at trick one, in this order.

1. 1.How many higher cards does declarer hold? Subtract the ones you can see in dummy and in your hand from 11 minus the card led.
2. 2.Can I win cheaply? If declarer has none, play the lowest card that wins the trick. If declarer has one, it is often an honor, and you can work out which one from the cards you can see.
3. 3.What does partner hold? The cards above the one led that are not in dummy, your hand or declarer's are partner's. That tells you whether to return the suit and how.

The rule also tells you about length. A fourth-best lead promises at least four cards. If the card led is the 2, partner has exactly four (there is no lower card left), and you can count the whole suit as soon as declarer follows twice.

The rule is not only for defenders. Declarer sees dummy and the card led, so declarer can count East's higher cards the same way.

Since East cannot beat the 6, declarer plays the ♥8 from dummy and it wins the trick, keeping the ♥K-J for later. Declarer also knows that West holds the ♥Q, ♥T and ♥9. That tells declarer which defender is dangerous. West has the long hearts and the honors, so if a trick has to be lost in another suit, it should be lost to East.

The rule of 11 depends on fourth-best leads. Partnerships that lead other cards from length use the same idea with a different number.

• Third and fifth best. From an even number of cards these partnerships lead the third best, and from an odd number the fifth best (the lowest from five). A third-best lead uses the rule of 12, because the leader holds two higher cards. A fifth-best lead uses the rule of 10, because the leader holds four higher cards.
• Third best from any length. Some partnerships lead third best from every holding. Then the rule of 12 applies every time.

All three work the same way. Count the cards higher than the one led, subtract the ones the leader holds, and see where the rest must be.

The rule of 11 is exact, but only if the lead really is fourth best. It gives the wrong answer when partner led something else:

• the top of a sequence (the queen from Q-J-10-x),
• top of nothing or the middle card of three small (MUD),
• a short-suit lead, such as the top of a doubleton or a singleton against a suit contract,
• a lead in partner's own bid suit, where many players lead low from three to an honor rather than fourth best.

The arithmetic often tells you when this has happened. If partner leads the 9 and you can see three cards higher than the 9 in dummy and your own hand, the rule says there should be only two. So the 9 was not fourth best. It is probably top of nothing or a short suit, and partner does not have the length you hoped for. Your signals should change accordingly.

The rule of 11 works best alongside sound opening leads. Most partnerships still lead fourth best against notrump, and if yours does it consistently, both defenders can count the suit from trick one. If you want to practice choosing the lead itself, the Lead Trainer gives you real auctions and shows what each card costs.

What is the rule of 11 in bridge?

The rule of 11 is a counting shortcut for a fourth-best lead. Subtract the rank of the card led from 11. The result is the number of higher cards held by dummy, third hand and declarer together, so third hand can work out how many declarer holds.

Why does the rule of 11 work?

A card of rank N has 14 minus N cards above it in the suit. A fourth-best lead means the leader holds three of them, so the other hands hold 14 minus N minus 3, which is 11 minus N.

Does the rule of 11 work against suit contracts?

Yes, as long as the lead is fourth best. Against suit contracts more leads are short suits or sequences, so check that the arithmetic makes sense before relying on it.

What is the rule of 10 and the rule of 12?

They are the same calculation for other lead styles. Use the rule of 12 for third-best leads and the rule of 10 for fifth-best leads.

Can declarer use the rule of 11?

Yes. Declarer sees dummy and the card led, so declarer can count how many higher cards the leader's partner holds and play dummy's cards accordingly.