Contract bridge

Contract bridge

Bridge declarer play
Alternative name(s)	Bridge
Type	trick-taking
Players	4
Skill(s) required	Memory, tactics, probability, communication
Cards	52
Deck	French
Play	Clockwise
Card rank (highest to lowest)	A K Q J 10 9 8 7 6 5 4 3 2
Playing time	WBF tournament games = 7.5 minutes per deal
Random chance	Low to moderate depending on variant played
Related games
Whist, Auction bridge

See also: Glossary of contract bridge terms

Contract bridge, usually known simply as bridge, is a trick-taking card game using a standard deck of 52 playing cards played by four players in two competing partnerships^[1] with partners sitting opposite each other around a small table.^[2] For purposes of scoring and reference, each player is identified by one of the points of the compass and thus North and South play against East and West^[3]. The game consists of several deals^[4] each progressing through four phases: dealing the cards, the auction (also referred to as bidding), playing the hand, and scoring the results.^[5] Dealing the cards and scoring the results are procedural activities while the auction and playing the hand are the two actively competitive phases of the game.

Dealing: Partnerships are self-determined or by a cut of the cards, the two highest cut playing against the two lowest; the first dealer is the player cutting the highest card. Cards are dealt clockwise, one at a time and face down starting on the dealer's left so that each player receives thirteen cards. In duplicate bridge the dealer is predetermined by the board; the board also contains the four hands which have been dealt and placed in the board prior to commencement of the game.

Auction or Bidding: The bidding starts with the dealer and rotates around the table clockwise with each player making a call,^[6] the purpose being to determine which partnership will contract to take more tricks given a particular trump suit or with notrump, i.e. the strain.^[7] The partnership which makes the highest final bid is known as the declaring side and is said to have 'won' the contract. The player on the declaring side who, during the auction, first stated the strain ultimately becoming trumps or notrumps is referred to as the declarer.

Playing: The rules of play are similar to other trick-taking games with the additional feature that the hand of declarer's partner is displayed face up on the table after the opening lead has been made by the member of the defending side to the left of declarer; the displayed hand is referred to as the dummy and is played by declarer.

Scoring: After all thirteen tricks have been played, the hand's score is determined by comparing the actual number of tricks taken by the declaring partnership with that proposed in the contract and awarding points accordingly. The available scoring points for the declaring side are dependent upon both the level and strain of the contract and are awarded to them only when the contract is 'made', i.e. at least the contracted for number of tricks are won by them; failure to do so results in the defending side receiving points instead and they are said to have 'defeated' the contract. Individual scores of several hands are accumulated to determine the overall game score.

While the game involves skill and chance, it has many variants and event types designed to emphasize skill, vary the method of scoring, set limits on the nature of the bidding systems which may be used, set the pace and duration of play, define player eligibility, enable larger team composition, provide country representation in international play, and to group players of similar interests, skill levels, age, or gender, or combinations thereof. The most common game variants are rubber bridge and duplicate bridge. In rubber bridge, two partnerships participate in the game at one table and the objective is to score the most points in the play of several hands. In duplicate bridge, there are more tables and partnerships and the hands are dealt and played in such a manner that each partnership plays the same set of hands as their East-West or North-South counterparts and with the scoring based upon relative performance. Competitions in duplicate bridge range from small clubs with a handful of tables, to large tournaments such as the World Bridge Championships^[8] where hundreds of tables play the same hands. The game variant and associated method of scoring have significant influence on bidding and card play strategies.

Game play

A session of bridge consists of a number of deals (also called hands or boards). A hand is dealt (or may have been pre-dealt), the bidding (or auction) proceeds to a conclusion and then the hand is played. Finally, the hand's result is scored.

The goal of a single deal is to achieve a high score with the cards dealt. The score for the hand is affected by two principal factors: the contract (number of tricks bid in the auction, the denomination, and which side has bid it) and the number of tricks taken during play. It may also be affected by the vulnerability. The contract, a feature which distinguishes contract bridge from its predecessors, is an undertaking made during the auction by one partnership that they will take at least the stated number of tricks, either with a specified suit as trumps, or without trumps (notrumps). The contract has two components: level and strain (also called denomination).

There are seven levels, numbered 1-7, and the number of tricks required is six plus the level number, so may be anywhere between 7 and 13. The five strains are ranked, from lowest to highest, as clubs (♣), diamonds (♦), hearts (♥), spades (♠), and notrump (NT). The two lower-ranked suits (♣ and ♦) are called the minor suits (or minors), and the higher-ranked suits (♥ and ♠) are called majors. Minor suit contracts score less, so are less frequently chosen.

For instance, the contract "3 hearts" is a promise that the partnership will take nine tricks (six plus three) with hearts as the trump suit. Thus, there are 7 × 5 = 35 possible basic contracts; 1♣ being the lowest, followed by 1♦ etc., up to 7NT.

In the bidding stage or auction, the pairs compete to determine who proposes the highest-ranked contract, and the side that wins the bidding must then strive in the play of the hand to fulfil that bargain by winning at least the contracted number of tricks if it is to obtain a score. Broadly speaking, there is an incentive to bid accurately to the optimum contract and then to play to make the contracted number of tricks (or more if good play or luck allows). If the side that wins the auction (declaring side) then takes the contracted number of tricks (or more), it is said to have made the contract and is awarded a score; otherwise, the contract is said to be defeated or set and points are awarded to the opponents (defenders).

It can sometimes be advantageous to bid a contract that one does not expect to make and to be defeated, thus losing some points, rather than allow the opposing side to bid and make a contract which would score them an even greater number of points. This is known as a sacrifice, and is quite common if both sides are contesting the final contract. This aspect is more common in duplicate bridge than in rubber bridge owing to the different scoring systems in effect.

Dealing

The game is played with a standard deck of 52 cards. In rubber bridge (or other non-duplicate games), the cards are shuffled before each deal, and the dealer deals the cards clockwise one at a time, starting with the left-hand opponent, so that each player receives a hand of 13 cards. The deal rotates clockwise each hand.

In duplicate bridge, the hands are shuffled and dealt only once, at the beginning of the session. Players do not throw their cards to the center of the table during the play but instead play them immediately in front of themselves and turn them face down at the end of each trick. The direction that each face down card is pointed indicates which side won each trick, so that at the end of the hand, the number of tricks taken by each side can be determined. At the end of the hand each player returns his hand, intact, to the correct slot in the bridge board in which it is transported to other tables so that everyone can play the same deals. The results for different players playing the same deal are then compared. This removes much of the element of chance from scores. It also means that in the case of an irregularity or dispute over a hand before the cards are returned to the board, they can be reviewed and it can be determined who played which cards in what order.

In some competitions, boards are pre-dealt prior to the competition, especially if the same hands are to be played at many locations (for example in a large national or international tournament). Sometimes computerised dealing machines are used for pre-dealing hands at large tournaments and in many clubs. As the boards arrive for play at each subsequent table, the four players take their cards from the board and should count them to ensure that there are 13 cards in their hand before looking at the cards, so that any irregularity can be corrected before the auction and play commence.

In some countries, the rules require that after the hand is played for the first time, the players write the hands down on the travelling scoresheet, which can be consulted later if the cards are accidentally mixed up. Alternatively, if the boards are pre-dealt, "curtain cards" may be supplied which have each hand printed on them, so that each player can check at the beginning of the deal that he has the right cards. Pre-dealt hands also have the advantage that, at the end of the session, diagrams of each deal can be made available to the players for later analysis.

Auction or bidding

The auction determines the declaring side and the final contract. Only one of the partners of the declaring side, referred to as declarer, plays the hand, while the other is dummy, and does not participate actively in the play of the hand. In addition to establishing the level and denomination,^[9] the final contract may be doubled (by the opponents) or redoubled (by the declaring side after the opponents had already doubled), in which case the score for the hand is increased, whether the contract is made or defeated.

During the auction, each player makes a call in turn, which must be one of the following:

• a Bid (stating a level and a denomination)
• Double (when the last call other than pass was a bid by an opponent)
• Redouble (when the last call other than pass was a double by an opponent)
• Pass (when unwilling or unable to make one of the three preceding calls)

(Note: although both are technically incorrect, the word "bid" is often used informally in place of "call" and "suit" may occasionally imply inclusion of "notrump")

The auction starts with the dealer and proceeds clockwise with each player, having first evaluated their hand, making a call in order. The auction ends when three successive passes occur at some point after the dealer's first call. If all four players pass in the first round, the deal is not played (in rubber bridge the deal is not scored and the hand is redealt by the original dealer, while in duplicate the score is recorded as zero for each pair since re-dealing a hand that has been 'passed out' is prohibited by the rules).

A bid specifies a level and denomination, and ostensibly denotes a willingness to play the corresponding contract. A player wishing to bid must make a bid that is sufficient; a bid is sufficient if it specifies any denomination at a higher level than the last bid, or a higher-ranked denomination at the same level. Thus, after a bid of 3♥, bids of 2♠ or 3♣ are not allowable, but 3♠ or 4♦ are. A bid that skips one level of bidding is called a (single) jump, for instance 2♠ over 1♥ is a jump, but 2♥ over 1♠ is not a jump. Similarly, a double jump is a bid that skips two levels of bidding, for instance 3♠ over 1♥ or 4♥ over 1♠.

A double can be made only after the opponents have made a bid. The natural meaning of a double is that the player is confident that the opponents cannot fulfil their contract, and the player is willing to risk increasing the opponents' score if they succeed, in exchange for receiving a larger penalty if the opponents fail. However, in modern bridge, the double more often has a conventional (artificial) meaning (especially after a low level bid, for example 1♠), to ask partner to bid or to pass information to partner. A "redouble" can be made only after an opponent's double; it further increases the points scored and the penalty for failure yet further. However a redouble is almost always conventional, and very few redoubled contracts end up being played. In practice, the double and redouble are often used systemically for other purposes, though if they are in effect for the final contract they increase the score regardless of their intended meaning. Double and redouble remain in effect only until the next bid — any subsequent bid cancels them.

Once the auction ends, the last bid (together with any double and/or redouble that followed it) becomes the contract, the level of this bid determines the number of tricks required to fulfil the contract and its strain determines what suit, if any, will be trumps.

It should be noted that the primary purpose of early bids is to exchange information rather than to determine the final contract. For most players, many calls (bids, doubles and redoubles, and sometimes even passes) are not made with the intention that they become the final contract, but to describe the strength and distribution of the player's hand, so that the partnership can make an informed guess which is the best contract, and/or to obstruct the opponents' bidding. The set of agreements used by a partnership about the meaning of each call is referred to as a bidding system, full details of which must be made available to the opponents; 'secret' systems are not allowed. An opponent can ask the bidder's partner to explain the meaning of the call.

The pair that did not win the contract is called the defence. The pair that made the last bid is divided further: the player who first made a bid in the denomination of the final contract becomes the declarer and his partner becomes the dummy. For example, suppose West is the dealer and the bidding was:

West	North	East	South
Pass	1♥	Pass	1♠
Pass	2♦	Dbl	3♠
Pass	4♠	Pass	Pass
Pass

Then East and West would be the defenders, South would be the declarer (being the first to bid spades), North would be the dummy, and spades the trump suit; 10 tricks would be required by declarer (and dummy). Since East's double of 2♦ was cancelled by the subsequent South's 3♠ bid, it does not affect the contract. For the purpose of determining the declarer, bids in the denomination of the final contract by the defence are ignored.

Bidding boxes contain a special card for each possible call. When these are in use, players make a call by taking the appropriate card from the bidding box and placing it on the table. This avoids the need for players to bid out loud. This prevents players at nearby tables from overhearing the bidding and also avoids voice inflexions passing information to a partner. Pre-printed bidding pads, on which the calls can be written, are sometimes used instead in Australia and New Zealand.

Play of the hand

The play consists of 13 tricks, each trick consisting of one card played from each of the four hands. Aces are high in bridge, followed by kings, queens, jacks, 10s, 9s ... down to 2s, the lowest card in each suit. The first card played in a trick is called the lead; after the lead, play proceeds clockwise around the table. Any card may be selected from a hand as the lead, but the remaining hands must follow suit, meaning they must play a card of the same suit as the lead, unless the hand in question has no more cards of that suit, in which case any card may be played. The hand that plays the highest card in the suit of the lead wins the trick, unless any of the played cards are of the trump suit, in which case the hand that plays the highest trump card wins the trick. The hand that wins the trick plays the lead card of the next trick, until all the cards have been played.

The first lead, called the opening lead, is made by the defender to the left of the declarer. After the opening lead is played, the dummy lays his/her hand face up on the table in four columns, one for each suit, with the column of the trump suit (if there is one) on the right as dummy looks at the table. The declarer is responsible for selecting cards to play from the dummy's hand and from his own hand in turn. The defenders each choose the cards to play from their own hands. Dummy is allowed to try to prevent declarer from infringing the rules, but otherwise must not interfere with the play; for example, dummy may attempt to prevent declarer from leading from the wrong hand (by stating, e.g., "you won the last trick in dummy") but must not comment on opponents' actions or make suggestions as to play. In casual bridge games the dummy often does nothing, but in duplicate bridge dummy must play cards from the dummy hand at declarer's instruction (e.g., by saying "jack of hearts please, partner", or less frequently by touching or pointing at the card that declarer wishes to play).

The contract level sets a specific target: in the example above, the declarer must attempt to win ten tricks (the assumed "book" of six, plus four as bid, with spades as trumps), to make the contract and get a positive score. Success in this goal is rewarded by points in the scoring phase for the declarer's side. If the declarer fails to make the contract, the defenders are said to have set or defeated the contract (declarer has gone down), and are awarded points for doing so.

If a declarer does not have enough tricks immediately available to make his contract, he can try to develop additional tricks through a variety of methods. These include:

• losing tricks to the defenders' high cards in order to "promote" the remaining cards of that suit in his hand.
• running out long suits after the defenders' cards in that suit are exhausted, to force defenders to discard useful cards.
• the finesse, in which a low card is led toward a high card in the hope of trapping a high card held by the defender who must play in between.
• in trump contracts, the declarer may attempt to cover losers in his hand by trumping them in dummy, while also taking care to draw out the defenders' trumps if necessary.
• cutting communications between the two defenders, for instance by allowing them to win early tricks in a suit until they are unable to use the suit as an entry.
• more advanced techniques include the "squeeze" in which a defender is forced to choose which card to discard before declarer has to make his own discard choice.

Scoring

Main article: Bridge scoring

The goal for each pair is to make as high a score as possible. However, if the contract is made, the level of the contract is the primary factor affecting the scoring, rather than the number of tricks taken in play: for example, if the declarer takes all 13 tricks without trumps, there is a huge score difference between the cases of contract being 1NT and 7NT. This premium for contracting to take more tricks ensures competitiveness in the auction: even if a partnership holds most of the high cards and their opponents have no interest in bidding, they are still encouraged to bid high in order to achieve the best possible score, which in turn often results in contracts that are difficult to make.

When the declarer makes the contract, the declarer's side receives points for:

• Every trick bid and made (20 for minor suit contracts, 30 for major suit and no-trump ones, with an additional 10 points for the first trick at no-trump)
• Overtricks (tricks taken over the contract level), again with 20 for minor suits, 30 for majors and no-trump
• Bonuses for contract level
• Other specific bonuses

When the declarer fails to make the contract, the defending pair receives points for undertricks — the number of tricks by which declarer fell short of the goal.

Because of the structure of bonuses, certain bid levels have special significance. The most important level is game, which is any contract whose bid trick value is 100 or more points. Game level varies by suit, since different suits are worth different amounts in scoring. The game level for no-trump is 3 (9 tricks, 3 x 30 + 10 = 100), the game level for hearts or spades (major suits) is 4 (10 tricks, 4 x 30 = 120), and the game level for clubs or diamonds (minor suits) is 5 (11 tricks, 5 x 20 = 100). Because of the value of the game bonus, much of the bidding revolves around investigating the possibility of making game. Even higher bonuses are also awarded for bidding and making small slam (level 6, i.e. 12 tricks) and the rather rare grand slam (level 7, i.e. all 13 tricks). The contracts below game level are called partial contracts or part scores.

The concept of vulnerability affects scoring and introduces a wider range of tactics in bidding and play. Every partnership is beforehand assigned one of two states: vulnerable or non-vulnerable. When a pair is vulnerable, game and slam bonuses are higher, as are penalties for failure to make the contract. Methods for assigning vulnerability differ between duplicate and rubber bridge.

There are two important variations in bridge scoring: rubber scoring and duplicate/Chicago scoring. They share most features, but differ in how the total score is accumulated. In rubber bridge, the declaring partnership counts points for successfully taken contracted tricks "below the line" on a scoresheet (which can be accumulated to make a game), while penalties and bonuses are tallied "above the line". The first partnership to accumulate two games gets a "rubber" bonus. In duplicate bridge, all the points are accumulated for each hand by itself and present a single score, expressed as a positive number (sum of trick points and bonus points) for the winning pair, and by implication, as a negative number for their opponents. (A third form, "Chicago" bridge, is a form of "friendly" game that uses duplicate scoring, with every deal scored as a single number, but usually with only one table (i.e., not duplicated elsewhere) and with vulnerability assigned in a very simple fashion.) Part-scores are not carried forward from one hand to the next.

In duplicate bridge, the same cards are played unchanged at two or more tables, and the results are then compared. Scores at each table are recorded on travelling slips that move with the boards or on pickup slips taken to the director. More recently, wireless electronic scoring is becoming more common. For this, each table has a purpose-built keypad on which players enter the score which is then transmitted directly to the scoring computer, doing away with paper slips.

Depending on the type of tournament, after the different scores on a board are compared, the relative scores are converted either to match points (MP) or to international match points (IMP). Regardless of the actual contract, the competitor (pair or team) with the best performance on each board gets the highest number of MP or IMP for that board, and vice versa. The competitor with the highest total number of MP or IMP becomes the winner of the tournament. Thus, even with bad cards, competitors can win the tournament if they have bid better and/or played better than the other players who played the same set of cards.

Match points (or (for teams) "Board-a-match") scoring simply awards a team or pair two match points for every other pair that had a lower score playing the same hands on that board and one match point for every other pair that had exactly the same score. (In the USA, the points awarded not 2 and 1, but 1 and ½.)

IMPs convert differences in scores using a sliding scale. 0 IMPS are awarded for a 0-10 point difference. This requires slightly different tactics at the table.

Rules

The rules of the game are referred to as the 'Laws' as promulgated by various bridge organizations.

Laws of duplicate bridge

Main article: Laws of Duplicate Bridge

The official rules of duplicate bridge are promulgated by the World Bridge Federation (WBF) as the "International Code of Laws of Duplicate Bridge, 2007".^[10] The Laws Committee of the WBF, composed of world experts, updates the Laws every 10 years; it also issues a Laws Commentary advising on interpretations it has rendered.

In addition to the basic rules of play there are many additional rules covering playing conditions and the rectification of irregularities which are primarily for use by tournament directors who act as referees and have overall control of procedures during competitions. In addition, some details of procedure are left to the discretion of the zonal bridge organisation for tournaments under their aegis and some (for example, the choice of movement) to the sponsoring organisation (e.g. the club).

The zonal organisations of the WBF also publish editions of the Laws. For example, the American Contract Bridge League publishes "Laws of Duplicate Bridge, 2008",^[11] "Laws of Contract Bridge, 2003"^[12] and additional supporting documentation including: Director Decisions, Tech Files and Casebook (appeals from national bridge championships).^[13]

Laws of rubber bridge

"Rubber bridge" is a version of the game played by four players on their own. Each hand is only played once so there is no comparison of scores. Thus it contrasts with duplicate bridge. A succession of hands are played and the scores made by each side are accumulated until one side has won two "games", at which point the overall scores are totalled and the winner is determined. (As in duplicate, a minimum trick score of 100 is required for game.)

There are some differences in bridge scoring at rubber compared with duplicate:

• "part scores" (trick scores less than 100) are accumulated to count toward game, but are not carried forward to the following game.
• there is no bonus for making a part score.
• there is a bonus for "honours": holding in one hand either at least four trump-suit honours (A, K, Q, J, 10) or all four aces at notrump.
• "vulnerability" (which affects the size of penalties and bonuses) is determined by previous games within the rubber, whereas in duplicate it is predetermined by the number of the board.

In the rubber bridge game variant known as Chicago, vulnerability is predetermined (in rounds of four deals) but scoring is otherwise similar to duplicate bridge.

Laws of online play

In 2001, the World Bridge Federation promulgated a set of Laws for online play.^[14]

History

Main article: History of contract bridge

Bridge is a member of the family of trick-taking games and is a development of Whist, which had become the dominant such game enjoying a loyal following for centuries. According to the Oxford English Dictionary, Bridge is the English pronunciation of a game called Biritch, which was also known as Russian Whist.

The oldest known Biritch rule book^[15] dated 1886 is by John Collinson. It and his subsequent letter to The Saturday Review dated May 28, 1906, document the origin of Biritch as from the Russian community in Constantinople^[16] and having some features in common with Solo Whist. The game had many significant bridge-like developments: dealer chose the trump suit, or nominated his partner to do so; there was a call of notrumps (biritch); dealer's partner's hand became dummy; points were scored above and below the line; game was 3NT, 4H and 5D (although 8 club odd tricks and 15 spade odd tricks were needed); the score could be doubled and redoubled; and there were slam bonuses. This game, and variants of it known as bridge^[17] and bridge-whist,^[18] became popular in the United States and the UK in the 1890s despite the long-established dominance of whist.^[19]

In 1904 auction bridge was developed, in which the players bid in a competitive auction to decide the contract and declarer. The object became to make at least as many tricks as were contracted for and penalties were introduced for failing to do so.

The modern game of contract bridge was the result of innovations to the scoring of auction bridge made by Harold Stirling Vanderbilt and others. The most significant change was that only the tricks contracted for were scored below the line toward game or a slam bonus, a change that resulted in bidding becoming much more challenging and interesting. Also new was the concept of vulnerability, making sacrifices to protect the lead in a rubber more expensive, and the various scores were adjusted to produce a more balanced game. Vanderbilt set out his rules in 1925, and within a few years contract bridge had so supplanted other forms of the game that "bridge" became synonymous with "contract bridge."

In the USA, most of the bridge played today is duplicate bridge, which is played at clubs, in tournaments[4] and online[5]. In the UK, rubber bridge is still popular in both homes and clubs, as is duplicate bridge. It has been noted that the popularity of contract bridge has waned in recent years for a variety of reasons.^[20]

Tournaments

Bridge is a game of skill played with randomly dealt cards, which makes it also a game of chance, or more exactly, a tactical game with inbuilt randomness, imperfect knowledge and restricted communication. The chance element is in the deal of the cards; in competitions and clubs the chance element is largely eliminated by comparing results of multiple pairs in identical situations. This is achievable when there are eight or more players, sitting at two or more tables, and the deals from each table are preserved and passed to the next table, thereby duplicating them for the next table of participants to play. At the end of a session, the scores for each deal are compared, and the most points are awarded to the players doing the best with each particular deal. This measures skill because each player is being judged only on the ability to bid with, and play, the same cards as other players. However very often even the most skillful play will only succeed some of the time, and the skilled player may be unlucky because an alternative, less expert play achieves a better result. But in the long run the expert player will score better.

This form of the game is referred to as duplicate bridge and is played in clubs and tournaments, which can gather as many as several hundred players. Duplicate bridge is a mind sport, and its popularity gradually became comparable to that of chess, with which it is often compared for its complexity and the mental skills required for high-level competition. Bridge and chess are the only "mind sports" recognized by the International Olympic Committee, although they were not found eligible for the main Olympic program.^[21]

The basic premise of duplicate bridge had previously been used for whist matches as early as 1857. Initially, bridge was not thought to be suitable for duplicate competition; it wasn't until the 1920s that (auction) bridge tournaments became popular.

In 1925 when contract bridge first evolved, bridge tournaments were becoming popular, but the rules were somewhat in flux, and several different organizing bodies were involved in tournament sponsorship: the American Bridge League (formerly the American Auction Bridge League, which changed its name in 1929), the American Whist League, and the United States Bridge Association. In 1935, the first officially recognized world championship was held. By 1937, however, the American Contract Bridge League had come to power (a union of the ABL and the USBA), and it remains the principal organizing body for bridge tournaments in North America. In 1958, the World Bridge Federation was founded to promote bridge world-wide, coordinate periodic revision to the Laws (each ten years, next in 2017) and conduct world championships^[22].

Bidding boxes and bidding screens

Bidding box

In tournaments, "bidding boxes" are frequently used, as noted above. In top national and international events, "bidding screens" are used. These are placed diagonally across the table, preventing partners from seeing each other during the game; often the screen is removed after the auction is complete.

Game strategy

Bidding

Main articles: Bidding system and Convention (bridge)

Much of the complexity in bridge arises from the difficulty of arriving at a good final contract in the auction. This is a difficult problem: the two players in a partnership must try to communicate sufficient information about their hands to arrive at a makeable contract, but the information they can exchange is restricted—information may be passed only by the calls made and later by the cards played, not by other means; in addition, the agreed-upon meaning of each call and play must be available to the opponents.

Since a partnership that has freedom to bid gradually at leisure can exchange more information, and since a partnership that can interfere with the opponents' bidding (as by raising the bidding level rapidly) can cause difficulties for their opponents, bidding systems are both informational and strategic. It is this mixture of information exchange and evaluation, deduction, and tactics that is at the heart of bidding in bridge.

A number of basic rules of thumb in bridge bidding and play are summarized as bridge maxims.

Bidding systems and conventions

A bidding system is a set of partnership agreements on the meanings of bids. A partnership's bidding system is usually made up of a core system, modified and complemented by specific conventions (optional customizations incorporated into the main system for handling specific bidding situations) which are pre-chosen between the partners prior to play. The line between a well-known convention and a part of a system is not always clear-cut: some bidding systems include specified conventions by default. Bidding systems can be divided into mainly natural systems such as Acol and Standard American, and mainly artificial systems such as the Precision Club.

Calls are usually considered to be either natural or conventional (artificial). A natural bid is one in which the suit and level bid is essentially passing the information "I have some cards in this suit and (usually) some high cards in my hand"; a natural double says in effect "I don't think the opponents can make their contract, so I want to raise the stakes". By contrast, a conventional (artificial) call offers and/or asks for information by means of pre-agreed coded interpretations, in which some calls convey very specific information or requests that are not part of the natural meaning of the call. Thus in response to 4NT, a 'natural' bid of 5♦ would state a preference towards a diamond suit or a desire to play the contract in 5 diamonds, whereas if the partners have agreed to use the common Blackwood convention, a bid of 5♦ in the same situation would say nothing about the diamond suit, but tell the partner that the hand in question contains exactly one ace.

Conventions are valuable in bridge because of the need to pass information beyond a simple like or dislike of a particular suit, and because the limited bidding space can be used more efficiently by taking situations in which a given call will have less utility, because the information it would convey is not valuable or because the desire to convey that information would arise only rarely, and giving that call an artificial meaning that conveys more useful (or more frequently useful) information. There are a very large number of conventions from which players can choose; many books have been written detailing bidding conventions. Well-known conventions include Stayman (to ask for the showing of any 4 card major suit in a 1NT opener's hand), Jacoby transfers (a request by the weak hand for the stronger partner to bid a particular suit first, and therefore to become the declarer), and the Blackwood convention (to ask for information on the number of aces and kings held, used in slam bidding situations).

The term preempt refers to a high level tactical bid by a weak hand, relying upon a long suit rather than high-value cards for tricks. Preemptive bids serve a double purpose — they allow players to indicate they are bidding on the basis of a long suit in an otherwise weak hand, which is important information to share, and they also consume substantial bidding room before a possibly strong opposing pair can identify whether they have a good possibility to play the hand, or in what suit or at what level they should do so. Several systems include the use of opening bids or other early bids with weak hands including long (usually six to eight card) suits at the 2, 3 or even 4 or 5 levels as preempts.

Basic natural systems

As a rule, a natural suit bid indicates a holding of at least four (or more, depending on the situation and the system) cards in that suit as an opening bid, or a lesser number when supporting partner; a natural NT bid indicates a balanced hand.

Most systems use a count of high card points as the basic evaluation of the strength of a hand, refining this by reference to shape and distribution if appropriate. In the most commonly used point count system, aces are counted as 4 points, kings as 3, queens as 2, and jacks as 1 point; therefore, the deck contains 40 points. In addition, the distribution of the cards in a hand into suits may also contribute to the strength of a hand and be counted as distribution points. A better than average hand, containing 12 or 13 points, is usually considered sufficient to open the bidding, i.e., to make the first bid in the auction. A combination of two such hands (i.e., 25 or 26 points shared between partners) is often sufficient for a partnership to bid, and generally to make, game in a major suit or notrump (more are usually needed for a minor suit game, as the level is higher).

In natural systems, a 1NT opening bid usually reflects a hand that has a relatively balanced shape (usually between two and four (or less often five) cards in each suit) and a sharply limited number of high card points, usually somewhere between 12 and 18 — the most common ranges use a span of exactly three points, (e.g., 12-14, 15-17 or 16-18), but some systems use a 4 point range, usually 15-18.

Opening bids of 3 or higher are preemptive bids, i.e., bids made with weak hands that especially favor a particular suit, opened at a high level in order to define the hand's value quickly and to frustrate the opposition. For example, a hand of ♠ KQJ9872 ♥ 7 ♦ 42 ♣ 763 would be a candidate for an opening bid of 3♠, designed to make it difficult for the opposing team to bid and find their optimum contract even if they have the bulk of the points, as it is nearly valueless unless spades are trumps, it contains good enough spades that the penalty for being set should not be higher than the value of an opponent game, and the high card weakness makes it more likely that the opponents have enough strength to make game themselves.

Openings at the 2 level are either unusually strong (2NT, natural, and 2♣, artificial) or preemptive, depending on the system. Unusually strong bids communicate an especially high number of points (normally 20 or more) or a high trick-taking potential (normally 8 or more).

Opening bids at the one level are made with hands containing 12–13 points or more and which are not suitable for one of the preceding bids. Using Standard American with 5-card majors, opening hearts or spades usually promises a 5-card suit. Partnerships who agree to play 5-card majors open a minor suit with 4-card majors and then bid their major suit at the next opportunity. This means that an opening bid of 1♣ or 1♦ will sometimes be made with only 3 cards in that suit.

Doubles are sometimes given conventional meanings in otherwise mostly natural systems. A natural, or penalty double, is one used to try to gain extra points when the defenders are confident of setting (defeating) the contract. The most common example of a conventional double is the takeout double of a low-level suit bid, implying support for the unbid suits or the unbid major suits and asking partner to choose one of them.

Variations on the basic themes

Bidding systems depart from these basic ideas in varying degrees. Standard American, for instance, is a collection of conventions designed to bolster the accuracy and power of these basic ideas, while Precision Club is a system that uses the 1♣ opening bid for all or almost all strong hands (but sets the threshold for "strong" rather lower than most other systems — usually 16 high card points) and may include other artificial calls to handle other situations (but it may contain natural calls as well). Many experts today use a system called 2/1 game forcing (enunciated as two over one game forcing), which amongst other features adds some complexity to the treatment of the one notrump response as used in Standard American. In the UK, Acol is the most common system; its main features are a weak one notrump opening with 12-14 high card points and several variations for 2-level openings.

There are also a variety of advanced techniques used for hand evaluation. The most basic is the Milton Work point count, (the 4-3-2-1 system detailed above) but this is sometimes modified in various ways, or either augmented or replaced by other approaches such as losing trick count, honor point count, law of total tricks, or Zar Points.

Common conventions and variations within natural systems include:

• Point count required for 1 NT opening bid ('mini' 10-12, 'weak' 12-14, 'strong' 15-17 or 16-18)
• Whether an opening bid of 1♥ and 1♠ requires a minimum of 4 or 5 cards in the suit (4 or 5 card majors)
• Whether 1♣ (and sometimes 1♦) is 'natural' or 'suspect' (also called 'phoney' or 'short'), signifying an opening hand lacking a notable heart or spade suit
• Whether opening bids at the two level are 'strong' (20+ points) or 'weak' (i.e., pre-emptive with a 6 card suit). (Note: an opening bid of 2♣ is usually played in otherwise natural systems as conventional, signifying any exceptionally strong hand)
• Blackwood (either the original version or Roman Key Card)
• Stayman (together with Blackwood, described as "the two most famous conventions in Bridge".^[23])
• Whether the partnership will play Jacoby transfers (bids of 2♦ and 2♥ over 1NT or 3♦ and 3♥ over 2NT respectively require the 1NT or 2NT bidder to rebid 2♥ and 2♠ or 3♥ and 3♠), minor suit transfers (bids of 2♠ and either 2NT or 3♣ over 1NT respectfully require the 1NT bidder to bid 3♣ and 3♦) and Texas transfers (bids of 4♦ and 4♥ respectively require the 1NT, or 2NT bidder to rebid 4♥ and 4♠)
• What types of cue bids (e.g. rebidding the opponent's suit) the partnership will play, if any.
• Whether doubling a contract at the 1, 2 and sometimes higher levels signifies a belief that the opponents' contract will fail and a desire to raise the stakes (a penalty double), or an indication of strength but no biddable suit coupled with a request that partner bid something (a takeout double).
• Whether doubling or overcalling over opponents 1NT is natural or conventional. Most common artificial agreement is Cappelletti, where 2♣ is a transfer to be passed or corrected to a major, 2♦ means both majors and a major shows that suit plus a minor.
• How the partnership's bidding practices will be varied if their opponents intervene or compete.
• Which (if any) bids are forcing and require a response.

Within play, it is also commonly agreed what systems of opening leads, signals and discards will be played:

• Conventions for the opening lead govern how the first card to be played will be chosen and what it will mean,
• Signals indicate how cards played within a suit are chosen — for example, playing a noticeably high card when this would not be expected can signal encouragement to continue playing the suit, and a low card can signal discouragement and a desire for partner to choose some other suit. (Some partnerships use "reverse" signals, meaning that a noticeably high card discourages that suit and a noticeably low card encourages that suit, thus not "wasting" a potentially useful intermediate card in the suit of interest.)
• Discards cover the situation when a defender cannot follow suit and therefore has free choice what card to play or throw away. In such circumstances the thrown-away card can be used to indicate some aspect of the hand, or a desire for a specific suit to be played.
• Count signals cover the situation when a defender is following suit (usually to a suit that the declarer has led). In such circumstances the order in which a defender plays his spot cards will indicate whether an even or odd number of cards was originally held in that suit. This can help the other defender count out the entire original distribution of the cards in that suit. It is sometimes critical to know this when defending.
• Suit preference signals cover the situation where a defender is returning a suit which will be ruffed by his partner. If he plays a high card he is showing an entry in the higher side suit and viceversa. There are some other situations where this tool may be used.
• Surrogate signals cover the situation when it is critical to show length in a side suit and it will be too late if defenders wait till that suit is played. Then, the play in the first declarer played suit is a count signal regarding the critical suit and not the trump suit itself. In fact, any signal made about a suit in another suit might be called as such.

Advanced bidding techniques

Every call (including "pass", also sometimes called "no bid") serves two purposes. It confirms or passes some information to a partner, and also denies by implication any other kind of hand which would have tended to support an alternative call. For example, a bid of 2NT immediately after partner's 1NT not only shows a balanced hand of a certain point range, but also would almost always deny possession of a five-card major suit (otherwise the player would have bid it) or even a four card major suit (in that case, the player would probably have used the Stayman convention).

Likewise, in some partnerships the bid of 2♥ in the sequence 1NT - 2♣ - 2♦ - 2♥ between partners (opponents passing throughout) explicitly shows five hearts but also confirms four cards in spades: the bidder must hold at least five hearts to make it worth looking for a heart fit after 2♦ denied a four card major, and with at least five hearts, a Stayman bid must have been justified by having exactly four spades, the other major (since Stayman (as used by this partnership) is not useful with anything except a four card major suit).^[24] Thus an astute partner can read much more than the surface meaning into the bidding. Alternatively, many partnerships play this same bidding sequence as "Crawling Stayman" by which the responder shows a weak hand (less than eight high card points) with shortness in diamonds but at least four hearts and four spades; the opening bidder may correct to spades if that appears to be the better contract.

The situations detailed here are extremely simple examples; many instances of advanced bidding involve specific agreements related to very specific situations and subtle inferences regarding entire sequences of calls.

Play techniques

Main article: List of play techniques (bridge)

Terence Reese, a prolific author of bridge books, points out^{[citation needed]} that there are only four ways of taking a trick by force, two of which are very easy:

• playing a high card that no one else can beat
• trumping an opponent's high card
• establishing long suits (the last cards in a suit will take tricks if the opponents don't have the suit and are unable to trump)
• playing for the opponents' high cards to be in a particular position (if their ace is to the right of your king, your king may be able to take a trick, especially if, when that suit is led, the player to your right has to play their card before you do)

Nearly all trick-taking techniques in bridge can be reduced to one of these four methods. The optimum play of the cards can require much thought and experience and is the subject of whole books on bridge.

Example

For more details on this topic, see Contract bridge glossary.

Board 1 Matchpoints South in 4♥ Not Vulnerable		♠	J 3
		♥	J 8 7 4
		♦	A 10 7 6 5
		♣	Q 3
♠	K Q 8 7 2	N W               E S		♠	10 9 5 4
♥	A 2			♥	9 6
♦	J 4 2			♦	K Q 9
♣	10 7 2			♣	K 9 6 4
Lead: ♠ K		♠	A 6
		♥	K Q 10 5 3
		♦	8 3
		♣	A J 8 5

West	North	East	South
	Pass	Pass	1♥
1♠	2♥	2♠	3♣
Pass	4♥	Pass	Pass
Pass

The cards are dealt as in the typical bridge hand diagram. North is the dealer and starts the auction which proceeds as shown in the bidding table.

As neither North nor East have sufficient strength to open the bidding, they each pass, denying such strength. South, next in turn, opens with the bid of 1♥, which denotes a reasonable heart suit (at least 4 or 5 cards long, depending on the system) and at least 12 high card points. On this hand, south has 14 high card points. West overcalls with 1♠, since he has a longish spade suit of reasonable quality and 10 high card points (an overcall can be made on a hand that is not quite strong enough for an opening bid). North supports partner's suit with 2♥, showing heart support and about 6-8 points. East supports spades with 2♠. South inserts a game try of 3♣, inviting the partner to bid the game of 4♥ with good club support and overall values. North complies, as North is at the higher end of the range for his 2♥ bid, and has a fourth trump (the 2♥ bid promised only three), and the doubleton queen of clubs to fit with partner's strength there. (North could instead have bid 3♥, indicating not enough strength for game, asking south to pass and so play 3♥.)

In the auction, North-South are trying to investigate whether their cards are sufficient to make a game (ten tricks in hearts or spades, 11 tricks in clubs or diamonds), which yields bonus points if bid and made. East-West are competing in spades, hoping to play a contract in spades at a low level. 4♥ is the final contract, 10 tricks being required for N-S to make with hearts as trump.

South is the declarer, having been first to bid hearts, and the player to South's left, West, has to choose the first card in the play, known as the opening lead. West chooses the spade king because spades is the suit the partnership has shown strength in, and because they have agreed that when they hold two touching honors (or adjacent honors) they will play the higher one first. West plays the card face down, to give their partner and the declarer (but not dummy) a chance to ask any last questions about the bidding or to object if they believe West is not the correct hand to lead. After that, North's cards are laid on the table and North becomes dummy, as both the North and South hands will be controlled by the declarer. West turns the lead card face up, and the declarer studies the two hands to make a plan for the play. On this hand, the trump ace, a spade, and a diamond trick must be lost, so declarer must not lose a trick in clubs.

If the ♣K is held by West, South will find it very hard to prevent it making a trick (unless West leads a club). However, there is an almost-equal chance that it is held by East, in which case it can be 'trapped' against the ace, and will be beaten, using a tactic known as a finesse.

After considering the cards, the declarer directs dummy (North) to play a small spade. East plays low (small card) and South takes the ♠A, gaining the lead. (South may also elect to duck, but for the purpose of this example, let us assume South wins the ♠A at trick 1). South proceeds by drawing trump, leading the ♥K. West decides there is no benefit to holding back, and so wins the trick with the ace, and then cashes the ♠Q. For fear of conceding a ruff and discard, West plays the ♦2 instead of another spade. Declarer plays low from the table, and East scores the ♦Q. Not having anything better to do, East returns the remaining trump, taken in South's hand. The trumps now accounted for, South can now execute the finesse, perhaps trapping the king as planned. South enters the dummy (i.e. wins a trick in the dummy's hand) by leading a low diamond, using dummy's ♦A to win the trick, and leads the ♣Q from dummy to the next trick. East covers the queen with the king, and South takes the trick with the Ace, and proceeds by cashing the remaining master ♣J. (If East doesn't play the king, then South will play a low club from South's hand and the queen will win anyway, this being the essence of the finesse). The game is now safe: South ruffs a small club with a dummy's trump, then ruffs a diamond in hand for an entry back, and ruffs the last club in dummy (sometimes described as a crossruff). Finally, South claims the remaining tricks by showing his or her hand, as it now contains only high trumps and there's no need to play the hand out to prove they are all winners.

(The trick-by-trick notation used above can be also expressed in tabular form, but a textual explanation is usually preferred in practice, for reader's convenience. Plays of small cards or discards are often omitted from such a description, unless they were important for the outcome).

North-South score the required 10 tricks, and their opponents take the remaining 3. The contract is fulfilled, and North enters the pair numbers, the contract, and the score of +620 for the winning side (North is in charge of bookkeeping in duplicate tournaments) on the traveling sheet. North asks East to check the score entered on the traveller. All players return their own cards to the board, and the next deal is played.

On the prior hand, it is quite possible that the ♣K is held by West. For example, by swapping the ♣K and ♥A between the defending hands. Then the 4♥ contract would fail by one trick (unless West had led a club early in the play). However the failure of the contract would not mean that 4♥ is a bad contract on this hand. The contract depends on the club finesse working, or a mis-defense. The bonus points awarded for making a game contract far outweigh the penalty for going one off, so it is best strategy in the long run to bid game contracts such as this one.

Similarly, there is a minuscule chance that the ♣K is in the west hand, but the west hand has no other clubs. In that case, declarer can succeed by simply cashing the ♣A, felling the ♣K and setting up the ♣Q as a winner. However the chance of this is far lower than the simple chance of approximately 50% that East started with the ♣K. Therefore the superior percentage play is to take the club finesse, as described above.

Playing on the Internet

There are several free and some subscription-based servers available for playing bridge on the Internet. OKbridge is the oldest of the still-running Internet Bridge services: was established as a commercial entèrprise in 1994, but the program started to be used interactively in August 1990 on players of all standards. Beginners to world class may be found playing there. .^[25] OKbridge is a subscription-based club, with services such as customer support and ethics reviews. Another subscription-based online Bridge club, founded in 1994, is Bridge Club Live (BCL). Calling itself "the friendliest Bridge club of the world", BCL organizes annual 4–6 day meetings, in a different country each year, to get its members together. SWAN Games was founded ai April, 2000. In match 2004 announced a partnership to provide Internet services to SBF members and is a competitor in subscription-based online Bridge clubs.^[25] Bridge Base Online is the most populated online bridge club in the world, with more than 100 000 daily connections. and 500 000 hands played each day.^[26] in part because it is free to play regular games. These clubs of various features, such as opportunities to earn ACBL masterpoints, to play in online tournaments, to compile lists of friends, and to earn money playing Bridge. Bridge Base Online also has a Vugraph feature showing important international events for anyone interested to watch. Additionally to written commentaries from top level players, voice commentaries have been incorporated since mid 2011. Software and hardware has been tested in 2011 in order to have digital cameras recognizing the cards being played which will permit to avoid using human operators.

Some national contract bridge organizations now offer online bridge play to their members, including the English Bridge Union, the Dutch Bridge Union and the Australian Bridge Federation. MSN and Yahoo! Games have several online rubber bridge rooms. In 2001, World Bridge Federation issued a special edition of the lawbook adapted for internet and other electronic forms of the game.

Differences relevant to online play include:

• Flexibility when to play, and choice of opponent skill level.
• Player rating systems may attempt to measure ability without regard to the number of games played or the number of years spent accumulating masterpoints.
• Fewer restrictions on the conventions that are permitted.
• Unauthorised information cannot be passed by tone of voice or body language (but can much more easily be passed by external communication).
• Detailed records can be kept, to help resolve complaints.
• The software prevents improper plays and calls, such as insufficient bids, revokes (failure to follow suit when able), and actions out of turn.

There are also a number of disadvantages:

• Inability to decide on bidding convention ahead of time, because partners are (usually) strangers.
• A reduced social element.
• Players may leave before a hand finishes, or in the middle of a planned session, either intentionally or because of connection difficulties.

Computer bridge

After many years of little progress, computer bridge made great progress at the end of the 20th century. In 1996, the American Contract Bridge League (ACBL) initiated official World Championships Computer Bridge, to be held annually along with a major bridge event. The first Computer Bridge Championship took place in 1997 at the North American Bridge Championships in Albuquerque, New Mexico.

Strong bridge playing programs such as Jack (World Champion in 2001, 2002, 2003, 2004, 2006 and 2009), Wbridge5 (World Champion in 2005, 2007 and 2008), RoboBridge^[27] and many-time finalist Bridge Baron, would probably rank among the top few thousand human pairs worldwide. A series of articles published in 2005 and 2006 in the Dutch bridge magazine IMP describes matches between Jack and seven top Dutch pairs. A total of 196 boards were played. Overall, the program Jack lost, but by a small margin (359 versus 385 imps).

Card games related to bridge

• Ombre
• Skat
• Euchre
• Whist
• Primero
• Spoil Five
• Quadrille
• Lanterloo
• Nap
• King
• 500

See also

• Beer card
• Bridge Murder case
• List of bridge books
• List of bridge competitions and awards
• List of bridge magazines
• List of bridge people

References

1. ^ Reese, Terence (1980). Bridge. Teach Yourself Books. Hodder and Stoughton. ISBN 0-340-32438-4. , page 1.
2. ^ In face-to-face games, a convenient table size is from 32 to 40 inches (80 to 100 centimeters) square [1][2][3] or similarly round table allowing each player to reach to the centre of the table during the play of the cards; in online computer play, players from anywhere in the world sit at a virtual table.
3. ^ Francis et al 2001, p. 81. See COMPASS POINTS.
4. ^ The terms deal, hand and board may be used interchangeably in bridge literature. More accurately, a hand is one player's holding of 13 cards, a deal is the four hands in one allocation of 52 cards; a board is a term more applicable to duplicate bridge and refers to a deal.
5. ^ Kantar, Eddie (2006). Bridge for Dummies, 2nd Edition. Wiley Publishing, Inc.. ISBN 978-0-471-92426-5. , page 11.
6. ^ When calls are made orally (as opposed to using bidding boxes) they use a limited number of permissible words (to reduce the possibility of passing unauthorised information). When the English language is used, these are: (1) a bid, being a number from "one" to "seven" inclusive together with a strain (also known as denomination) in the singular or plural ("club"/"clubs", "diamond"/"diamonds", "heart"/"hearts", "spade"/"spades" and "notrump"), for example "one heart", "two notrump" or "three spades", (2) "pass" or, in some countries, "no bid", (3) "double", and (4) "redouble".
7. ^ While in the official Laws of Duplicate Bridge, the four suits (spades, hearts, diamonds and clubs) and notrump are defined as the denomination, in bridge literature they are generally referred to as the strain.
8. ^ See also the Bermuda Bowl, the World Team Olympiad and the North American Bridge Championships.
9. ^ Barbara Seagram; Linda Lee (June 2008). Beginning Bridge. Master Point Press. pp. 7–. ISBN 9781897106334. http://books.google.com/books?id=choHxGThcKsC&pg=PA7. Retrieved 20 August 2010. 
10. ^ "World Bridge Federation Laws of Duplicate Bridge". Worldbridge.org. http://www.worldbridge.org/departments/laws. Retrieved 2011-11-05. 
11. ^ ACBL Laws of Duplicate Bridge, 2008. Requirements for convention charts, alerts, and other laws are also available at the ACBL website.
12. ^ ACBL Laws of Contract Bridge, 2003.
13. ^ A cross-referenced listing including documentation is available at the BridgeHands website.
14. ^ World Bridge Federation Laws of Electronic Bridge, 2001 for online play.
15. ^ "Alternate source for Biritch, or Russian Whist by John Collinson, 1886". Pagat.com. http://www.pagat.com/boston/biritch.html. Retrieved 2011-11-05. 
16. ^ Depaulis, Thierry; Fuchs, Jac (Sept-Oct 2003). First Steps of Bridge in the West: Collinson's 'Biritch'. The Playing-Card, Vol. 32, No. 2. pp. 67-76.
17. ^ (Elwell 1905 and Benedict 1900)
18. ^ (Melrose 1901)
19. ^ (Foster 1889)
20. ^ Turning Tricks — The rise and fall of contract bridge" The New Yorker, September 17, 2007
21. ^ "Review of the Olympic programme and the recommendations on the programme of the games of the XXIX Olympiad, Beijing 2008; page 8". 2011-10. http://www.olympic.org/Documents/Reports/EN/en_report_527.pdf. 
22. ^ Francis et al 2001, p. 576. See WORLD BRIDGE FEDERATION (WBF).
23. ^ Bridge Lessons series, Stayman & Transfer (Deal 1), by Andrew Robson
24. ^ Taken from Andrew Robson Bridge Lessons series, "Stayman & Transfer", deal 14
25. ^ ^{a b} The Official Encyclopedia of Bridge, Brent Manley, 7th edition, 2011, ACBL, 6575 Windchase Blvd., Horn Lake MS 38737-1523, USA, pg. 597, ISBN=978 0 939460 99 1, pgs. 1033 (634+2CDs: 634 book plus 399 bibliographies and results)
26. ^ The Official Encyclopedia of Bridge, Brent Manley, 7th edition, 2011, ACBL, 6575 Windchase Blvd, Horn Lake MS 38737-1523, USA, pg. 597, pgs. 1033 (634 plus additional 399 in CD format), ISBN=978 0 939460 99 1
27. ^ "RoboBridge". RoboBridge. 2011-10-22. http://www.RoboBridge.com. Retrieved 2011-11-05. 

Bibliography

• Francis, Henry G., Editor-in-Chief; Truscott, Alan F., Executive Editor; Francis, Dorthy A., Editor, Sixth Edition (2001). The Official Encyclopedia of Bridge (6th ed.). Memphis, TN: American Contract Bridge League. ISBN 0-943855-44-6. OCLC 49606900.