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Bridge
Bridge declarer play
Players	4
Age range	recommended for 12 and up
Setup time	< 2 minutes
Playing time	WBF tournament games = 7.5 minutes per deal
Rules complexity	Medium
Strategy depth	High
Random chance	Low - high depending on variant played
Skills required	Memory, Tactics

Contract bridge, usually known simply as bridge, is a trick-taking card game of skill, and partly of chance, for four players, who form two partnerships (sides). The partners sit opposite each other. The game consists of two main parts – bidding (or auction) and play, after which the hand is scored.

The bidding ends with a contract, which is a declaration by one partnership that their side shall take a stated quantity (or more) of tricks, with specified suit as trump or without trumps. The rules of play are rather simple and similar to other trick-taking games.

Game play

Two partnerships of two players each are needed to play bridge. The four players sit around a table with partners opposite one another. The compass directions are often used to refer to the four players, aligned with their seating pattern. Thus, South and North form one partnership and East and West form the other.

A session of bridge consists of many deals (also called hands or boards); the game play of each deal consists of four phases: the deal, the bidding (or auction), the play of the cards, and scoring.

The goal is to achieve as high a numerical score as possible with the dealt cards. The score is affected by two principal factors: the number of tricks bid in the auction, and the number of tricks taken during play. Broadly said, there is incentive to the players to accurately bid the number of tricks that their hands are capable of delivering, as the bonuses for bid tricks increase with the bid level (number of tricks). Thus, in the bidding stage, the pairs compete to see who proposes the highest number of tricks, and the side who wins the bidding must then fulfill that bargain by taking at least the contracted quantity of tricks in play to obtain a score. The number of tricks bid and the trump suit (or lack thereof) are referred to as a contract. The trump suit, or its absence (no trumps) is referred to as denomination or strain. If the side who wins the auction then takes the contracted number of tricks (or more), it is said to have fulfilled the contract and is awarded a score; otherwise, the contract is said to be defeated and points are awarded to the defenders.

Dealing

The game is played with a complete deck of 52 cards. One of the players is the dealer. In rubber bridge (or other "friendly" games), the cards are shuffled and the dealer distributes all the cards clockwise one at a time, starting with his left-hand opponent and ending with himself, so each player receives a hand of thirteen cards. At the same time, for convenience, the dealer's partner usually shuffles a second deck, to be ready for use on the following deal. The deal rotates clockwise, so the dealer's left-hand opponent will deal next.

In duplicate bridge, the hands are shuffled only once, at the beginning of the tournament, and dealt clockwise one at a time (there are also special machines for pre-dealing on large tournaments), and placed into bridge boards. At each subsequent table, each player pulls his cards from the board and counts them to ensure that the deal has not been corrupted. Unlike in other trick-taking games, the players do not throw their cards to the middle of the table in each trick; instead, each player keeps his played cards before him, to allow the completed deal to be returned to the board unaltered.

The auction

The auction determines the declaring side and the final contract, which consists of the denomination and level (amount of tricks). Only one of partners of the declaring side, referred to as declarer, will play the hand, while the other will become the dummy (i.e. doing nothing). In addition, if the final contract is doubled (by the opponents) or redoubled (by the contracting partnership) the scoring of the hand is increased, whether the contract is made or defeated.

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

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 to make one of the three preceding calls, i.e. "abstain")

(Note: although technically incorrect, the word "bid" is also often used informally in place of "call")

The auction starts with the dealer and proceeds clockwise with each player, having first evaluated their hands, making a call in order. The auction ends when 3 successive passes occur after a bid, double or redouble (or if all 4 players pass in the first round).

A bid specifies how many tricks the bidder believes that his partnership can take using his hand and his partner's hand, and with which strain as trump. Any bid starts with the assumption that the bidder can make at least six tricks, called book, plus the stated number of additional tricks. So the bid includes a level (from one to seven, representing how many tricks beyond six the bidder proposes to make) and a denomination (also called strain), which is either a suit or "no trump". For instance, "3 hearts" asserts that his partnership can take nine tricks (book plus three) with hearts as the trump suit. There are 35 possible bids, which include all combinations of 5 denominations and 7 levels (7-13 tricks).

A player wishing to bid at his turn must make a bid that is higher than the preceding bid. A bid is higher if it specifies any denomination on a higher level, or a higher-ranked denomination on the same level. The denominations are ranked in alphabetical order, from lowest to highest, as clubs (♣), diamonds (♦), hearts (♥), spades (♠), and no trump (NT). Thus, after a bid of 3♥, bids of 2♠ or 3♣ are not allowable, but 3♠ or 4♦ are. Thus, 1♣ is the lowest possible bid, followed by 1♦ etc, while 7NT is the highest possible bid.

A double can be made only after the opponents have made a bid. At its simplest, this states that the player is so confident that the opponents cannot make their bid during play that the player is willing to double their score if they do and the penalty if they do not. However, in modern bridge, the double is often used in conventional sense, to ask partner to bid or to pass information to partner. A "redouble" is a bid which can be made only following an opponents' "double"; it increases the points scored yet further. In practice the redouble can also be used systemically for other purposes. Double and redouble are in effect only until the next bid, i.e. any subsequent bid invalidates them.

Once the auction ends, the last bid (together with any double or redouble that followed it) becomes the contract, and the level of this bid determines the number of tricks required to achieve the contract and its denomination determines what suit, if any, will be trumps. The pair that did not win the contract is called the defense. 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 or her partner becomes the dummy. For example, suppose West is the dealer and the bidding was:

South	West	North	East
	pass	1♥	pass
1♠	pass	2♦	double
3♠	pass	4♠	pass
pass	pass

Then East and West would be the defenders, South would be the declarer (since South was the first to bid spades), North would be the dummy, and spades would be the trump suit; 10 tricks would be required by declarer (and dummy).

The play of the hand

The play consists of thirteen 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, and players play a card 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 in the same suit as the lead), unless they have no more cards of that suit. If a hand contains no cards of the led suit then 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 each trick plays the lead card of the next trick, until all the cards are 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 own hand in turn. The defenders each choose the cards to play from their own hands. Dummy is allowed to prevent declarer from infringing the rules of play but otherwise must not interfere with the play; thus dummy may attempt to prevent declarer from revoking (by asking eg "No more spades partner?") but must not comment on opponents' actions or make suggestions as to play; even seemingly trivial comments such as "You won that trick partner" are not permitted. In casual bridge games the dummy often does nothing but in duplicate bridge dummy must play cards from the dummy hand at declarer's verbal instruction (eg "jack of hearts please partner"). This is a less ambiguous method of card selection than declarer leaning over the table and touching a card.

In the end, the goal for each pair is to make as high a score as possible. However, the level of the contract makes a specific target: the number (level) of the contract is the number of tricks the declarer must take beyond 6. Thus, the declarer always attempts to take at least a majority of the tricks. In the example above, the declarer must manage to take 10 tricks (the assumed "book" of 6, plus 4 as bid, with spades as trumps), to make the contract and get a 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, and are rewarded points for doing so.

Scoring

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

The contract bid and made
Overtricks (tricks taken over the 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.

Most bidding revolves around efforts to bid and make a game. 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 the suit, since different suits are worth different amounts in scoring. The game level for no trump is 3 (9 tricks), the game level for hearts or spades (major suits) is 4 (10 tricks), and the game level for clubs or diamonds (minor suits) is 5 (11 tricks). High bonuses are also awarded for bidding and making small slam (level 6) and grand slam (level 7, i.e. all the tricks).

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 well as penalties for failure to make the contract. Methods for assigning vulnerability differ for duplicate) and rubber bridge.

There are two important variations in bridge scoring: rubber scoring and duplicate scoring. They share most features, but differ how the total score is accumulated. In rubber bridge, points for each pair are tallied either "above the line" or "below the line". In duplicate bridge, all the points are accumulated and present a single score, expressed as a positive number (sum of trick points and bonus points) to the winning pair, and by implication, as a negative number to the opponents. "Chicago" bridge is a form of friendly game which uses duplicate scoring, that is, a set consists of four deals with different vulnerabilities (whether a team has already made game), and every deal is scored as a single number.

In duplicate bridge, the same hand is played unchanged across two or more tables and the results are compared using various methods. The differences are expressed in matchpoints or IMPs. They are summed for every pair for every board they play, and the pair with highest total score becomes the winner of the tournament. Thus, even with bad cards, a pair can win the tournament if it has bid better and played better than the other players who played the same set of cards.

Laws of Duplicate Contract Bridge

Rules of contract bridge are standardized by World Bridge Federation and published in the book "Laws of Duplicate Contract Bridge"^[1]. The last edition is issued in 1997 and consists of 93 laws (articles). All duplicate bridge sponsoring organizations on lower levels must apply those rules. A large portion of the laws, though, is devoted to dealing with various irregular situations, and as such it is mostly used by tournament directors (referees) as the reference book. They are, of course, not binding for rubber and other "friendly game" players, and, instead, simpler rules for dealing with irregularities are often applied by the players themselves.

History

Trick-taking games can be traced back to the early 16th century. Whist became the dominant form, and enjoyed a loyal following for centuries.

According to the Oxford English Dictionary, the word bridge is the English pronunciation of "biritch", an older name of the game of uncertain origin; the oldest known rule book, from 1886, calls it "Biritch, or Russian Whist". This game, known today by the retronyms bridge-whist and straight bridge, became popular in the United States and the UK in the 1890s.

Biritch featured several significant developments from Whist: the trump suit was either chosen by the dealer, or he could pass the choice to his partner; there was a call of no trumps; and the dealer's partner laid his cards on the table as dummy to be played by the dealer. It also featured other characteristics found in modern bridge: points scored above and below the line; game was 3NT, 4H and 5D (although 8 club tricks and 15 spade tricks were needed!); the score could be doubled and redoubled; there were slam bonuses.

In 1904 auction bridge arose where 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 tricks contracted for were counted below the line towards game and for slam bonuses, which resulted in bidding becoming much more challenging and interesting. Also new was the concept of vulnerability to make it more expensive to sacrifice to protect the lead in a rubber, 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."

These days most bridge played is tournament bridge.

Tournaments

At its core, bridge is a game of skill played with randomly dealt cards, which makes each deal a game of chance. Despite this, chance can be largely eliminated by comparing pairs' results in identical situations. This is achievable when there are eight or more players, sitting at several tables, and the deals from each table are preserved and passed to the next table, thereby duplicating them for another 4 (or more) participants to play. At the end of a competition, the scores for each deal are compared against each other, and most points are awarded to the players doing the best with each particular deal. This measures skill despite the initial chance of the deal.

This form of the game is referred to as duplicate bridge and is played in 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, which it is often compared with for its complexity and mental skills required for high-level competition.

The basic premise of duplicate bridge was occasionally used for whist matches, as early as 1857. For some reason, duplicate was not thought to be suitable for bridge, and so 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 Federation. 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 USBF), and it remains the principal organizing body for bridge tournaments in North America. In 1958, the World Bridge Federation was founded, as bridge had become an international activity.

Today, the ACBL has over 160,000 members and runs 1100 tournaments per year with 3200 officially-associated bridge clubs.

Bidding boxes and bidding screens

Bidding box

In tournaments, "bidding boxes" are frequently used. A bidding box is a box of cards, each bearing the name of one of the legal calls in bridge. A player wishing to make a call displays the appropriate card from the box, rather than making a verbal declaration. This prevents unauthorized information from being conveyed via voice inflection. In top national and international events, "bidding screens" are used. These are diagonal screens which are placed across the table, preventing a player from seeing his partner during the game.

Important Bridge Players

Giorgio Belladonna
Easley Blackwood Sr.
Norberto Bocchi
Ely Culbertson
Giorgio Duboin
Benito Garozzo
Charles Goren
Bob Hamman
Oswald Jacoby
Jeff Meckstroth
Terence Reese
Eric Rodwell
Omar Sharif
Helen Sobel Smith
Samuel Stayman

Game Strategy

Bidding systems and conventions

Much complexity in bridge arises from the difficulty of successfully arriving at a good final contract in the auction. This is a fundamentally difficult problem: the two players in a partnership must try to communicate enough information about their hands to ultimately arrive at a makeable contract, but the information they can exchange is restricted in two ways:

Information may only be passed by the calls made and later by the cards played, and not by any other means.
The agreed-upon meaning of all information passed must be available to the opponents.

A bidding system is the typical solution to this problem: each player evaluates his or her own hand and makes bids to give or request information from their partner, with the goal of eventually arriving at an ideal contract. Bids, doubles, redoubles, and even passes can be either natural or conventional. A natural bid is a proposal to reach a contract in the named suit. A conventional bid is an attempt to communicate, offering and/or asking for information about the partnerships' hands, that is not intended to be a proposal for the final contract. A wide variety of bidding systems have been developed over the course of the 20th century. However, most modern systems have well-established common ground.

First of all, a fairly universal system of high card points is used to give a basic evaluation of the strength of a hand. Aces are counted as 4 points, kings as 3, queens as 2, and jacks as 1 point; therefore, the deck contains 40 points. 26 points shared between partners is considered sufficient for a partnership to bid, and make, game in a major or in no trump. 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. Because 26 points is usually considered sufficient to make game, 13 points in one hand is considered sufficient to open the bidding (that is, make the first bid in the auction), by bidding 1 of a suit.

A one no trump opening bid usually reflects a hand that has relatively balanced suits and high cards, and usually refers to a hand with 15-17 high card points. In some systems the number of points expected from a 1NT opening bid changes, but it almost always refers to a relatively narrow range of points.

Opening bids of 2 or higher are reserved for two types of bids: unusually strong bids and preemptive bids. Unusually strong bids communicate an especially high number of points; the availability of unusually strong bids allows a player with a weak hand to safely pass when their partner opens the bidding at one of a suit. Preemptive bids are often made with weak hands that especially favor a particular suit. For instance, with a hand of ♠ AK98742 ♥ 73 ♦ 42 ♣ 76, an opening bid of 3♠ is a very reasonable sacrificial bid, designed to make it difficult for the opposing team to determine a contract for themselves (which is good here, since they are likely to have the bulk of the points).

Most systems include the weak two bid convention, in which opening bids of 2♥, 2♦, or 2♠ are reserved for preemptive bids, while 2♣ is used for very strong hands. This is a first example of a conventional bid: an opening bid of 2♣ in no way suggests 2♣ as a final contract: indeed, in these systems 2♣ may be bid without any clubs.

Another common convention is the 5-card major convention, in which an opening bid of 1♥ or 1♠ promises at least 5 cards in that suit. This leads to some awkward bids, for instance, when a player has four cards in each major, and is forced to open the bidding with 1 of a 3-card minor suit.

Doubles are sometimes used in bidding conventions. 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 bid, implying support for the unbid suits and asking partner to choose one of them.

There are many other conventions. Some of the most famous are Stayman, Jacoby transfers and Blackwood.

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 highly conventional system that uses the 1♣ opening bid for strong hands (but sets the threshold rather lower than most other systems) and requires many other changes in order to handle other situations. Many experts today use a system called 2/1 game forcing. In the UK, Acol is the standard system. There are even a variety of techniques used for hand evaluation. The most basic is the Milton Work point count, but this is sometimes augmented by other guidelines such as losing trick count, law of total tricks or Zar Points.

Play techniques

Terence Reese, a prolific author of bridge books, points out that there are only four ways of taking a trick by force, and two of these are very easy:

playing a high card that no one else can beat
trumping an opponent's high card
establishing long cards (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 in front of your king, your king may take a trick)

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 too complicated to describe in a short article. However, some basic ideas of probability may be considered:

Some of the most important probabilities have to do with the position of high cards.

The probability that a given opponent holds one particular card, e.g. the king: 50%
The probability that a given opponent holds two particular cards, e.g. the king and the queen: approximately 25%
The probability that a given opponent holds at least one of two particular cards, e.g. the king or the queen: approximately 75%

When developing long cards, it is important to know the likelihood that the opponents' cards in the suit are evenly divided between them. Generally speaking, if they hold an even number of cards, they are unlikely to be exactly divided; if the opponents have an odd number in the suit, the cards will probably be divided as evenly as possible. For example, if declarer and dummy have eight trumps between them, the opponents' trumps are probably (68% chance) divided 3-2 (one opponent with three trumps, the other with two) and trumps can be drawn in three rounds. If declarer is trying to play with a seven card trump suit, it is more likely that the outstanding trumps are divided 4-2 (48%) than that the cards are evenly divided 3-3 between the opponents (36%).

Basic techniques by declarer

trumping
crossruff
establishing long suits
finesse
holdup (mostly at NT contracts)
managing entries
drawing trumps

Advanced techniques by declarer

counting the hand (tracking the distribution of suits and high cards in the opponents' hands using inferences from the bidding and play)
coup
duck
dummy reversal
endplay
principle of restricted choice
safety play
squeeze

Basic techniques by defenders

opening lead
when to lead trump

Advanced techniques by defenders

avoiding an endplay or squeeze
counting the hand (tracking the distribution of suits and high cards in the unseen hands using inferences from the bidding and play)
false carding
opening lead—using information from auction
signaling
uppercut

Example

		♠	J3
		♥	J874
		♦	A10765
		♣	Q3
♠	KQ872	N W E S		♠	10954
♥	A2			♥	96
♦	J42			♦	KQ9
♣	1072			♣	K964
		♠	A6
		♥	KQ1053
		♦	83
		♣	AJ85

The cards are dealt as in the diagram, and North is the dealer. As neither North nor East have sufficient high card strength to open the bidding, South opens with the bid of 1♥, which denotes a long suit and at least 12 high card points. West overcalls with 1♠, North supports partner's suit with 2♥, and East also 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, and North complies, having extra values in form of ♦A, fourth trump, and doubleton Queen of clubs. The bidding was:

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

In bidding, North-South were trying to investigate if their cards are worthy for making a game, which yields bonus points if bid and made. East-West were competing with 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 trumps.

West (left of South, who is the declarer, having been first to bid hearts) has to make the opening lead and chooses the King of spades, playing it face down. After that, North lies his cards on the table and becomes dummy; West turns his leading card face up, and the declarer makes a plan of playing: the bottom line is, since he has to concede trump ace, a spade, and a diamond, he must not lose a trick in clubs.

After a while, the declarer dictates North to play a small spade. East plays low (small card) and South takes the ♠A, gaining the lead. He proceeds by drawing trumps, leading the ♥K. West takes his Ace and cashes the ♠Q. Since he may not continue spades for fear of a ruff and discard, he plays a diamond. Declarer ducks from the table, and East scores the ♦Q. Not having anything better to do, he returns the remaining trump, taken in South's hand. South enters the dummy using ♦A, and leads ♣Q in an attempt to finesse East's King. East covers with the King, South takes the Ace, and proceeds by cashing now high ♣J, then ruffs a small club with a dummy's trump. He ruffs a diamond in hand for an entry back, and ruffs the last club in dummy. Finally, he claims the remaining tricks by showing his hand, as it now contains only high trumps and there's no need to continue the play.

(The trick-by-trick notation can be also expressed using a table, but textual explanation is usually preferred, for reader's convenience. Plays of small cards or discards are not explicated, unless they were important for the outcome).

North-South have scored the required 10 tricks, and their opponents took the remaining 3. The contract is fulfilled, and North enters +620 for his side (North-South are in charge for bookkeeping in duplicate tournaments) in the traveling sheet. Every player returns his own cards into the board, and the next deal is played.

Bridge on the Internet

There are several free and some subscription-based servers available for playing bridge on the Internet. OKBridge1 is the oldest of the still-running Internet Bridge services; players of all standards, from beginners to world champions may be found playing there. SWAN Games2 is a more recent competitor. Bridge Base Online³ is mostly free, and now has a much larger membership base than either of the above. 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.

There are many advantages to playing Bridge online:

The ability to choose when you play.
The ability to choose your opponents. In a club game, you may be forced to play against pairs that are much weaker, rude, or much stronger. Playing online, you can play against opponents of nearly equal ability.
Most servers offer an accurate player rating system. The ACBL and EBU masterpoints systems give credit for how much one has played rather than how well; most online systems have a rating system which attempts to measure one's ability without regard to the number of games played.
There are fewer restrictions on which conventions one is allowed to use.
You can not make inferences from partner's tone of voice or other cues available in real life. However, intentional cheating, such as instant messaging your partner, is easier.
A detailed record of every hand may be kept, to help resolve complaints.
It is impossible to make an illegal play by accident, as the software won't accept a play or call which does not conform to the rules.

The main disadvantage to playing online is that bridge is a social game, and many people play because they enjoy the social atmosphere of the bridge club.

Computer Bridge

After many years of little progress, at the end of the twentieth century computer bridge made big strides forward. 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.

World Champions Computer Bridge

1997 Bridge Baron
1998 GIB
1999 GIB
2000 Meadowlark Bridge
2001 Jack
2002 Jack
2003 Jack
2004 Jack
2005 Wbridge5

Strong bridge playing programs such as Jack probably do not rank among the top 100,000 human players worldwide. No computer program has yet to beat a good human pair consistently (as of 2006).

References

^ WBF Laws of Duplicate Contract Bridge

Gambling Guide

Bridge

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