The originator of this mathematical calculation remains unknown. Evidence shows that this particular rule preceded before the organized game of bridge since it was also employed in the game of Whist, and Auction Whist. Mention of the rule of eleven has been recorded as early as the early 1900s.


The publication New England Magazine, An Illustrated Monthly, New Series, Volume 22, covering March to August 1900, states in an article the following: A book to be welcomed with gratitude is Vol. I of "Nature's Miracles", one of Professor Elisha Gray's Familiar Talks on Science. It is doubtful if his father and mother would, what comradeship of the whole family might ensue! Many travellers go to foreign lands - and return, also, alas! - without so much as suspecting their poverty of equipment for the enjoyment of their voyaging and journeying. It would really be more pleasure to old and your to be able to say just what the trade winds are, how dew is formed, or why the sky is blue, than it is to follow the rule of eleven in whist, important as that is, and the answers could be lodged in the mind in half the time.

Mr. Robert Frederick Foster, born May 31, 1853, in Scotland, and died 1945 of New York City, United States, claims to have invented the rule of eleven in the winter of 1880--1881. The rule is explained in the first edition of his Foster's Whist Manual, which was first published in the year 1890. The Official Encyclopedia of Bridge, Sixth Edition, published by the American Contract Bridge League in the year 2001, page 399, notes that while Mr. Robert Frederick Foster is generally credited with first writing about the rule in the year 1890, it is said to have been discovered independently by Mr. E.M.F. Benecke of Oxford, England, at about the same time.

Note: The publication by Mr. Robert Frederick Foster titled Foster's Whist Manual was first published in the year 1890 by the publishing house Bretano of New York, New York, and Chicago, Illinois, United States, LC: 05022747.

Note: In Whist: A Monthly Journal, devoted to the interests of the Game, Editor Mr. Cassius M. Paine, and published by The Whist Publishing Company of Milwaulkee, Wisconsin, United States, Volume IX, June 1899 to May 1900, refers to the principle as The Eleven Rule. The author of the article is strongly presumed to be Mr. Mark Forrest. The article, however, is listed in Vol. X., No. 9, Milwaukee, February 1901. The explanation of the rule of eleven has not changed since this time.

Additional Notes

This formula was devised by someone who was actually playing Whist at the time, Mr. Robert Frederick Foster of Scotland in the year 1881, and also devised independently by Mr. E.M.F. Benecke of Oxford, England, around the same time. Mr. Robert Frederick Foster established his reputation with his publication of the book Foster's Complete Hoyle, published in the year 1897, and a copy of which was embedded into the time capsule at the 1939 New York World's Fair.

Source - Page 168: Author Mr. E.V. Shepard, Scientific Auction Bridge: A Clear Exposition of the Game to Aid Both the Beginner and the Experienced Player, With Explicit and Easy Rules for Bidding and Playing, 1913, Publisher: Harper, New York, New York, United States, and London, England, LC: 13006351.

However, the rule of eleven was published in his writing of the Foster's Whist Manual: A Complete System of Instruction in the Game, published presumably in the year 1885, by the publishing house of Brentano, of New York, New York, United States. The source of this information is from Bibliographies of Works on Playing Cards And Gaming by Norton T. Horr, 1905, published by Longmans, Green and Co., of London, England.

The rule of eleven states that the player subtracts the number of the first card lead from the number 11, and then the result is the number of cards higher contained in the hands of the partner of the leader and the declarer and the dummy. This information is useful not only to the declarer, but also to the partner of the leader, who can apply the same mathematical calculation.

Note: This principle, guideline, rule applies only to the opening lead, and not to any other leads when leading to the second trick or any trick thereafter.

This information can be useful in deciding which card to play, either from the hand of the partner of the leader, or the hand of the declarer or from dummy.

Ever since bridge became a popular game players have been trying to come up with new ideas to improve the game. Some have succeeded and some have not succeeded all that well, but progress was made. The bridge community is quite selective and sometimes a new idea takes a long time before becoming accepted.

This is especially true if the new idea is based on mathematics. Anyone, who can count up to 13, can play bridge. There are 13 cards in every suit and once they are played, there are no more to be played.

The rule of eleven is another mathematical calculation, equation, formula. Its application becomes active, only when the player is absolutely certain that the lead is the fourth down from the suit lead. Once the bridge player, either defender or declarer, has ascertained this partnership agreement, then the bridge player begins counting. The principle behind the rule of eleven is the same whether the contract is a suit contract or a No Trump contract.

Examples and Explanations

Example 1
Declarer: South
Contract: 3 No Trump
Vulnerability: None
Lead: 6 of Diamonds

According to the rule of eleven, the partner of the leader, East, subtracts 6 from 11 and the result is 5. There are 5 cards higher than the 6 of Diamonds in the hands of the dummy, declarer, and the partner of the leader. Likewise, the declarer subtracts the number 6 from 11 and the result is 5 cards higher than the 6 of Diamonds in the hands of the dummy, of the declarer, and of the partner of the leader.

East looks at dummy and his hand, and counts 3 cards higher than the 6 of Diamonds. East has 1 card higher than the 6 of Diamonds. East, therefore, has only one card of the possible five cards higher than the 6 of Diamonds.

Declarer looks at dummy and his hand, and counts 4 cards higher than the 6 of Diamonds. This knowledge is vital information to the declarer. The declarer can win with the 9 of Diamonds, follow with the Ace of Diamonds, and play the 4 of Diamonds, which leaves an additional Diamond trick in the dummy. The declarer, as a result of this information, can play in such a manner as to win three tricks in the suit of Diamonds.

Example 2
Declarer: South
Contract: 3 No Trump
Vulnerability: None
Lead: 7 of Spades

Declarer sees the 7 of Spades, and assumes it is the fourth down from the longest and strongest suit. Declarer subtracts 7 from 11 and counts 4 higher cards than the 7 of Spades. Declarer counts only 1 card in his hand and dummy higher than the 7 of Spades.

East also assumes that the 7 of Spades is fourth down from the longest and strongest suit of his partner. East also arrives at 4 cards higher than the 7 of Spades. East can see all of these 4 cards: King of Spades in the dummy, and Ace-10-9 in his own hand. If declarer calls for the King of Spades, East plays the Ace of Spades and returns a Spade. With this lead East-West win 4 Spade tricks and the setting trick is the Ace of Clubs, thereby defeating the contract.

If declarer decides to play low on the first trick, East lets the 7 of Spades ride, because he knows that there is no higher Spade than the 7 of Spades in the hand of the declarer. West continues to play the 8 of Spades, and declarer plays low, as does East. There is no way that declarer will take one Spade trick. East-West set the contract by applying the rule of eleven.

The rule of eleven has a lot of merit and can be used effectively. Each partner must be attuned to recognize when it is appropriate to use it, or even to consider it. The rule of eleven has its most application against a No Trump contract since it is generally accepted practice that the leader plays the fourth card down from his longest and strongest suit. The rule of eleven can also be effectively employed against a suit contract.



If you wish to include this feature, or any other feature, of the game of bridge in your partnership agreement, then please make certain that the concept is understood by both partners. Be aware whether or not the feature is alertable or not and whether an announcement should or must be made. Check with the governing body and/or the bridge district and/or the bridge unit prior to the game to establish the guidelines applied. Please include the particular feature on your convention card in order that your opponents are also aware of this feature during the bidding process, since this information must be made known to them according to the Laws of Duplicate Contract Bridge. We do not always include the procedure regarding Alerts and/or Announcements, since these regulations are changed and revised during time by the governing body. It is our intention only to present the information as concisely and as accurately as possible.