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Rule of 11

In contract bridge, the Rule of 11 is applied when the opening lead is the fourth best from the defender's suit. By subtracting the rank of the card led from 11, the partner of the opening leader can determine how many cards higher than the card led are held by declarer, dummy and himself; by deduction of those in dummy and in his own hand, he can determine the number in declarer's hand.

Logic

The rule works because the opening leader is known to have exactly three cards higher than that led and the number of cards lower in rank to that card is also known. The following reasoning applies when the lead is known to be or is suspected to be the lead of opener's fourth best card in the suit:

Thus, 11-x represents the number of cards higher than the card led held collectively by dummy, declarer and partner of the opening leader. When dummy is tabled after the opening lead is made, partner of the opening leader can count the number of cards higher than the card led that are in dummy and in his own hand and, by deduction of this total from 11-x, can determine the number of higher cards declarer holds.

Example

When West leads the 7 in the hand below, East applies the Rule of 11. This shows that there are four cards higher than the 7 that dummy, declarer and East hold. Since East can see the Q and 8 in dummy and the A and 10 in his own hand, declarer can have no cards higher than the 7. Knowing this, if the dummy covers with the 8, East knows he can win the trick cheaply with the 10.

Q82
KJ973 W    N↑ S↓    E A105
64

However, the declarer can apply the Rule of 11, too. When West leads the 7 in the deal below, South can see the four higher cards in his hand and on the board. Accordingly he knows that the play of the 8 from the board will win the trick cheaply.

Q82
KJ973 W    N↑ S↓    E 64
A105

Since the Rule of 11 may help declarer as well as the defenders, some prefer leads other than the fourth-best. For example, Journalist Leads generally call for the lead of the third or fifth best.

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Tabletop games: Rules and Strategy