Suit combination

In the card game contract bridge, a suit combination is a specific set of cards of a particular suit visible in declarer's and dummy's hands at the onset of the play of the cards. While the ranks of the remaining cards held in the two unseen hands of the opponents can be deduced precisely, their location is unknown. Suit combinations allow for all possible lies of the cards of the subject suit in the two closed hands.

The term is also used for the sequence of plays from the declarer and dummy hands, conditional on intervening plays by the opponents; in other words, declarer's plan or strategy of play given his holdings and his goal for the number of tricks to be taken.

In addition to understanding the possible initial combinations and probabilities for the location of the opponents' cards in a suit, declarer can further inform himself from the bidding, the opening lead and from the prior play of cards in establishing the probable location of remaining cards.

The diagram at left shows a heart suit combination with six cards in dummy (North, at top) and four in declarer (South, at bottom). Declarer can deduce that the two opposing hands hold only three hearts - the king, the ten and the eight but their exact location are unknown. The table at right shows the eight possible lies of those three cards; the suit combination and its diagram implicitly include all eight possibilities.

As the number of cards in a particular suit held by declarer and dummy decreases, the number held by the opposing side must increase since there are always 13 cards in each suit. The number of possible combinations of the cards held by the opposing side increases by a multiple of two for every decrease of one in the number of cards held by declarer and dummy.

In the left deal diagram, North and South hold nine hearts and the four held by the opposing side can be held in 16 different ways; in the right deal diagram, eight are held leaving five for the opponents in 32 possible combinations.

In standard bridge exposition, not all small cards are explicitly identified and the representation of the hand is made more generic by replacing certain cards with an 'x' where the 'x' represents the 2 or any other card low enough to be equivalent to the 2. The 'x' represents a card below any other that is specified and has no trick-taking capability or potential. The following progression of alternatives allows for higher and higher spot-cards to be deemed insignificant to the analysis.

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Wikipedia