In bridge, almost everyone is familiar with the so called and most commonly understood and used Rule of 11 that can be applied invariably by both the defender who is not on lead and the declarer who views the opening lead and the open dummy.
This Rule is of course based on simple arithmetic and the primary prerequisite of its application rests on the partnership agreement that in the absence of any other inferential clues, the defender on lead is bound to open with the fourth highest card of his longest suit unless his suit has 3 touching or semi-touching honours like KQJ, AQJ, AKJ, KQ10, QJ10, KJ10, AJ10, etc.
The Rule works on certain premise as under:- subtract the card led by the opening leader from 11 and the result is the number of cards held by the other 3 players besides the opening leader that are higher than the card led. If you are wondering why 11 has been taken as the key number, it is based on the simple logic of the card denomination. Every suit has a J, Q, K and A, above 10 starting from 2, which means that if you were to give a numerical to the J, Q, K, and A, you would number them 11, 12, 13 and 14.
So if you subtract any card from 14, you find out how any higher cards are there in the suit. If the 4th best is led, the leader has exactly 3 higher cards in his own hand. So to find out the distribution of the other 3 players regarding cards held higher than the spot card led, if we subtract from 14, we also have to minus the 3 cards higher held in declarer's hand. Therefore, it is, convenient to simply subtract from 14-3 ie 1. How useful the Rule is for both the defender and the declarer can best be descried in the following 2 illustrations:
The first useful for the declarer is a contract of 3NT by NS bid on the following: One look tells us the success of the contract hinges on how you tackle spades. Without the Rule of 11, it could be a wild guess wouldn't it? But presuming west, lead, as per Rule 11 applied to be the fourth best, we subtract 7 from 11 and know that there are 4 cards higher than 7 lying between dummy, the other defender and the declarer.
Since dummy has 3 higher than 7 and declarer the fourth one, the defender east has presumably none. Thus you let the 7 ride to your 8 as winner and can therefore, score 4 spade tricks, which along with 3 hearts and 2 minor aces give you an easy ride for 3NT.
How useful Rule of 11 can be for defence is viewed from the inferential clue the defenders get NS are in 3NT on the following hand: The opening lead is 3D from west the 4th best in the suit. Do you foresee how useful the inference can be that if 3D is west's 4th best of his longest suit, then he holds a 4 card diamond holding and no other 5 carder.
What does that tell you - that declarer has 4 diamonds for sure and lacking support for partner's 5 hearts, can at most have 2 hearts for his NT opening. What about his spade holding - could be 3 or 4 leaving clubs as 3 or 4. Since spades are bare, east has to shift logically to clubs. But which card, if he leads the 4th best here west will be stuck with declarer posed over him with perhaps 2 honours. So the only hope for the defence lies with west holding a club honour either king or queen and therefore, the killing shift spot card is the 10C to give defenders 3 club tricks, the heart K and diamond ace to shy the contract - all because of the Rule of 11.
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North West East South
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K53 94 10862 AQJ7
AQ1075 8432 K6 J9
J5 Q973 A42 K1086
964 Q75 K1083 AJ2
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North South
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AQ102 853
AKJ Q109
A1054 72XX
J3 A6X
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The bidding:
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W N E S
- 1D P 1NT
P 3NT ALL PASS
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