The Theory of Vacant Spaces

The designation theory is defined as an assumption based on limited information or knowledge, and basically a conjecture. A theory is fundamentally a belief or principle that guides action or assists comprehension or judgment. Based on this definition is the Theory of Vacant Spaces (aka Theory of Vacant Places). The originator of such a theory or assumption being applied to the game of bridge is unknown and may have been calculated previously to the present day version of the game of bridge.

One rather conclusive assumption is that Mr. Michael Glaubert of Italy researched the phenomenon, this significant but unaccountable fact or probability mathematically proved the acceptability of such a theory also in practice in regard to the game of bridge. Together with Mr. Hugh Kelsey they published their findings in their publication Bridge Odds For Practical Players in the year 1980. A revised edition appeared in the year 1982 (see below). Such findings were also published by Mr. Antonio Vivaldi and Mr. Gianni Baracco in their book Probabilitá E... Alternative in Italian (2000) and Probabilities & Alternatives in Bridge (2001) in English.


Definition of the Theory of Vacant Spaces

The theory of vacant spaces states that when the distribution of one or more suits is completely known, the probability that an opponent holds a particular card in any other suit is proportional to the number of vacant spaces remaining in his hand. The theory of vacant spaces says that a missing honor card is more likely to be with the opponent who holds the greater number of the missing cards in the suit.

Note: Basically the above description is the definition of the Theory of Vacant Spaces and will suffice for the bridge player. Other definitions can be worded more closely and narrowly, but the basic concept or even the calculated assumptions remain the same.


Sources for the Bridge Player

In the online publication Bridge Today (Source) of Mr. and Mrs. Matthew and Pamela Granovetter, issue June 2006, this theory is also discussed. This particular article of this Bridge Today issue has been preserved and archived in .pdf file format on this site for future reference.

Note: The cited example of Kelsy and Glaubert refers to Mr. Hugh Kelsey and Mr. Michael Glaubert. The cited example is from their publication Bridge Odds For Practical Players, first published in the year 1980 by Cassall & Co. in association with Peter Crawley. This publication was re-issued in the year 2001.

Note: The World Bridge Federation recommends this publication and adds the following: "The authors could hardly be better qualified for their task. Hugh Kelsey earned a world wide reputation for accurate bridge analysis and lucid prose, while Michael Glauert is a keen and proficient tournament player who held the first Chair of Mathematics at the University of East Anglia.", which is a traditional name for a region of eastern England, named after an ancient Anglo-Saxon kingdom, the Kingdom of the East Angles.

Another illustration of how the Theory of Vacant Places affects the play is presented by Mr. Dave Germaine (Source), a bridge and online bridge instructor teaching in Sun City, Huntley, Illinois, United States. This illustration has only been preserved and archived on this site in .pdf file format for future reference.

Note: The reader should not become confused with the difference of designations since this theory is sometimes referred to as the Theory of Vacant Spaces and the Theory of Vacant Places. Both are correct in their terminology.


Mr. Gianni Barracho and Mr. Antonio Vivaldi

The elements of imagination and inference are necessary for all bridge players to achieve a certain skill level in the game of bridge. Also necessary is a knowledge of the probabilities and the calculation of percentages relating to certain card combinations or the expectancy thereof. The publication of Probabilitá E... Alternative in Italian and Probabilities & Alternatives in Bridge in English, by Mr. Gianni Barracho and Mr. Antonio Vivaldi, illustrates, among other elements, to the bridge player the reasons and calculated perception as to how and when such calculations should influence the decision of the bridge player when declaring. Another section of the publication deals with the Principle of Restricted Choice, promoted and popularized by Mr. Alan Truscott.


Mr. Antonio Vivaldi and Mr. Gianni Baracco published their book first in the Italian language in the year 2000 by the publisher Mursia (Gruppo Editoriale) and then in the English language in the year 2001 by the publisher Batsford. The picture below shows Mr. Antonio Vivaldi. A picture of Mr. Gianni Baracco is not available.


Junior Camp in Nymburk, Czech Republic

Junior Camp - Daily Bulletin - Sports Centre, Nymburk, Czech Republic

The following description is a direct quote from the Daily Bulletin of this Junior Camp tournament.

In my final round Adèle Gogoman chose the right minute to play against the a priori percentages.


Left to your own devices you would tackle the Spade suit by leading the Ace and low to the 10, subsequently repeating the finesse. The reason is that this line allows you to pick up a guarded Queen (either three or four times) in the North hand. The alternative of leading out the Jack initially fails to take more than three tricks if South has Q9xx. But the play may be influenced by other factors.

West   North   East   South (D)
1   Pass   1   Pass
1 NT   Pass   3 NT   Pass
Pass   Pass        

Here against the auction set out above, there could be made quite a good case for North’s leading an active Heart, a neutral Club, or a passive Spade, expecting dummy to have only four Spades, and declarer to have no more than three Spades. As the cards lie the Club is neutral - but actually the lead from 10xxx might so easily cost a trick that it hardly qualifies as safe. On the actual hand I led a heart, and declarer put up the King, breathed a small sigh of relief, and before committing herself to the Spade suit, tested the Clubs. When South showed a singleton there, together with four or five Hearts, the theory of vacant spaces argues strongly that it is South who is more likely to hold the Queen rather than North. So declarer successfully finessed against South for the Queen, and finished up taking 10 tricks for a decent score.



In conclusion it must be noted that the bridge player normally does not take such probabilities, such alternative calculations into consideration when declaring the hand. The Theory of Vacant Spaces remains a theory and will not be accurate in all cases, nor will the bridge player be always aware of even consciously executing such an action during play of the hand. It will be more often the case that the player will rely on other inferences based on counting the cards of each suit in order to decide whether or not to initiate a finesse, for example, instead of employing a different approach.


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