There are two types of game theory: 1) working out how to win, lose or draw a game played for entertainment; or 2) applying the theory of a game to real life.

The latter meaning is covered by game theory as a branch of mathematics, operations research and economics, analyzing interactions with formalized incentive structures ("games") - whether purposeful games, or battles, or accidental games. The predicted and actual behavior of individuals in these games are studied, as well as optimal strategies . Seemingly different types of interactions can be characterized as having similar incentive structures, thus all being examples of one particular game.

Some theories seeks to find rational strategies in situations where the outcome depends not only on one's own strategy and "market conditions", but upon the strategies chosen by other players with possibly different or overlapping goals. It also finds wider application in fields such as political science and military strategy.

An example of the application of game theory to real life is the prisoner's dilemma as popularized by mathematician Albert W. Tucker; it has many implications for the nature of human cooperation. Biologists have used game theory to understand and predict certain outcomes of evolution, such as the concept of evolutionarily stable strategy introduced by John Maynard Smith in his essay Game Theory and the Evolution of Fighting. See also Maynard Smith's book Evolution and the Theory of Games.

Note it is difficult to apply game theory to life because everybody wants different things out of life-someone may go all out for a little piece of money, others may want huge amounts with little effect, and yet others wish for things as well as money.

Other branches of mathematics, in particular probability, statistics and linear programming, are commonly used in conjunction with game theory to analyse games.

The mechanisms of some games such as snakes and ladders, or ludo, depend very heavily on random inputs, to the extent that game theory cannot usefully analyse them. It can only theorise on strategies as strategic choices.

The difference between a rule (or law) and a theory

Technically speaking, there is no difference, but a rule tends to be more fundamental to playing the game. For instance in chess saying that you need to take as many pieces as possible is a rule, that you should start with say the Bishop's Gambit is a theory. Note too that rules tend to be more useful in playing the game. Theories (and this includes scientific theories like e=mc²) may be debunked later on. However in life rules too may sometimes be debunked.

Types of games and examples

Game theory classifies games into many categories that determine which particular methods can be applied to solving them (and indeed how one defines "solved" for a particular category). Some common categories are:

Zero-sum games are those in which the total benefit to all players in the game adds to zero (or more informally put, that each player benefits only at the expense of others). Chess and Poker are zero-sum games, because one wins exactly the amount one's opponents lose. Business, politics and the prisoner's dilemma, for example, may be condisered are non-zero-sum games because some outcomes are good for all players or bad for all players. It is easier, however, to analyze a zero-sum game, and it turns out to be possible to transform any game into a zero-sum game by adding an additional dummy player often called "the board," whose losses compensate the players' net winnings.

A convenient way to represent a game is given by its payoff matrix. Consider for example the two-player zero-sum game with the following matrix:

 

                                 Player 2 

                     Action A    Action B    Action C

           Action 1    30         -10          20 
 Player 1
           Action 2    10          20         -20

 

This game is played as follows: the first player chooses one of the two actions 1 or 2, and the second player, unaware of the first player's choice, chooses one of the three actions A, B or C. Once these choices have been made, the payoff is allocated according to the table; for instance, if the first player chose action 2 and the second player chose action B, then the first player gains 20 points and the second player loses 20 points. Both players know the payoff matrix and attempt to maximize the number of their points. What should they do?

Player 1 could reason as follows: "with action 2, I could lose up to 20 points and can win only 20, while with action 1 I can lose only 10 but can win up to 30, so action 1 looks a lot better." With similar reasoning, player 2 would choose action C (negative numbers in the table are good for him). If both players take these actions, the first player will win 20 points. But how about if player 2 anticipates the first player's reasoning and choice of action 1, and deviously goes for action B, so as to win 10 points? Or if the first player in turn anticipates this devious trick and goes for action 2, so as to win 20 points after all?

The fundamental and surprising insight by John von Neumann was that probability provides a way out of this conundrum. Instead of deciding on a definite action to take, the two players assign probabilities to their respective actions, and then use a random device which, according to these probabilities, chooses an action for them. The probabilities are computed so as to maximize the expected point gain independent of the opponent's strategy; this leads to a linear programming problem with a unique solution for each player. This method can compute provably optimal strategies for all two-player zero-sum games.

For the example given above, it turns out that the first player should chose action 1 with probability 57% and action 2 with 43%, while the second player should assign the probabilities 0%, 57% and 43% to the three actions A, B and C. Player one will then win 2.85 points on average per game.

Non Zero-Sum game The most famous example of a non-zero-sum game is the Prisoner's dilemma, as mentioned above. Any gain by one player does not necessarily correspond with a loss by another player. The 'kill or be killed' business ideal are non zero-sum games. For example, a business contract ideally is a positive-sum game, where each side is better off than if they didn't have the contract. Most games that people play for recreation are zero-sum.

Cooperative games are those in which the players may freely communicate among themselves before making game decisions and may make bargains to influence those decisions. Monopoly can be a cooperative game, while the Prisoner's dilemma is not. However, Monopoly is a zero-sum game as there can be only one winner, whereas the Prisoner's dilemma is a non-zero-sum game. Most of life can be described as a cooperative game, because we normally cooperate against our opponents.

Complete information games are those in which each player has the same game-relevant information as every other player. Chess and the Prisoner's dilemma are complete-information games, while Poker is not. Not much of life can be described as complete information game.

Risk aversion

For the above example to work, the participants in the game have to be assumed to be risk neutral. This means that, for example, they would value a bet with a 50% chance of receiving 20 'points' and a 50% chance of paying nothing as being worth 10 points. However, in reality people are often risk averse and prefer a more certain outcome - they will only take a risk if they expect to make money on average. Subjective expected utility theory explains how a measure of utility can be derived which will always satisfy the criterion of risk neutrality, and hence is suitable as a measure for the payoff in game theory.

One example of risk aversion can be seen on Game Shows. For example, if a person has a 1 in 3 chance of winning $50,000, or can take a sure $10,000, many people will take the sure $10,000.

Games and numbers

John Conway developed a notation for certain games and defined several operations on those games, originally in order to study Go endgames. In a surprising connection, he found that a certain subclass of these games can be used as numbers, leading to the very general class of surreal numbers.

History

Though touched on by earlier mathematical results, modern game theory became a prominent branch of mathematics in the 1940s, especially after the 1944 publication of The Theory of Games and Economic Behavior by John von Neumann and Oskar Morgenstern. This profound work contained the method for finding optimal solutions for two-person zero-sum games alluded to above.

Around 1950, John Nash developed a definition of an "optimum" strategy for multi player games where no such optimum was previously defined, known as Nash equilibrium. This concept was further refined by Reinhard Selten. These men were awarded The Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel in 1994 for their work on game theory, along with John Harsanyi who developed the analysis of games of incomplete information.

Conway's number-game connection was found in the early 1970s.

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Trick-taking games are card games in which play is divided into multiple rounds called tricks, during which each player plays one card from his hand, and the rules of the game determine which player wins that trick based on the cards played. Play ends when all players have played their cards. The object of such games varies; it is often to win the most tricks, but it may instead be to avoid winning tricks, to win exactly a certain number of tricks, or to acquire (or not acquire) certain cards. One might also include in this category other games such as the Chinese Tien Gow, played with dominoes.

A common feature of trick-taking games is the concept of following suit, in which each player is constrained in which card he may play by the obligation to match the suit of the first card played in that trick, called the lead, if he can. Another feature common to many games is the concept of trump (from the French triomphe, although the idea probably originated in Italy), in which special cards (sometimes all the cards of a certain suit) are designated to outrank all other cards played. In general, the player who wins the trick is the player who played the highest trump, or, if no trump is played, the player who played the highest card in the suit that was led. In some games players are obligated to play a higher card (and/or trump the suit to win, if they do not have the suit led) if possible. In most games the player who won the previous trick has to lead on the next one.

Popular trick-taking games include Ambition, Whist, Bridge, Euchre, Pinochle, Skat, Tarocchi, Hearts, Spades, Pitch (card game), Napoleon, Sheepshead, 500, Ninety-nine, Tarocchini, and Forty-five.

This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia.

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 given 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, where the latter must be higher than or equal to the former. Broadly said, the highest score is achieved when the number of tricks won is equal to (or close to) the number that was bid, so there is incentive to the players to accurately bid the number of tricks that their hands are capable of delivering. Thus, in the bidding stage, the pairs compete to see who proposes the highest number of tricks (and associated trump suit), and the side who wins the bidding must then fulfill that bargain by taking at least the specified number of tricks in play. The number of tricks bid and the trump suit (or lack thereof) are referred to as a contract. 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 points; otherwise, the contract is said to be defeated and points are awarded to their opponents.

Dealing

The game is played with one 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

To prepare for the play of the cards, the auction phase determines several things: the contract, which consists of the trump suit and the intended number of tricks; which partnership will play for the contract; and which of the players in that partnership will play the hand. In addition, doubling and redoubling may occur, which represents a "raising of the stakes" when the played hand is scored.

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

• Pass
• Make a new bid
• Double or Redouble

The auction consists of each player making a call, starting with the dealer and continuing clockwise until three players in a row have passed after any bid. (The word "bid" is also often used informally in place of "call".)

A player may always pass when it is his or her turn.

A bid specifies how many tricks the bidder believes that he can take using his hand and his partner's hand, and with which suit 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" suggests that his partnership can take nine tricks (book plus three) with hearts as the trump suit.

A player may bid at his turn as long as the bid is higher than the most recent bid. A bid is considered higher if it specifies either a higher level or the same level but with a higher-ranking suit. The denominations are ordered, 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 illegal, but 3♠ or 4♦ are legal.

If the most recent bid was made by the opponents, a player may "double" that bid if his partner has not already done so. This essentially 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). If the most recent bid was made by the player or the player's partner, and it has been doubled by an opponent but not yet redoubled by the player's partner, the player may "redouble," further increasing the potential score or penalty.

The auction ends either if all four players pass initially (in which case the hand is not played or scored) or when three players pass in a row after any bid(s) have been made. The last bid becomes the contract, and its denomination determines whether there will be a trump suit, and if so, what it is. 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 strain 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 goes:

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.

The play of the hand

The play of the hand is similar to other trick-taking games. To summarize, the play consists of thirteen tricks, each trick consisting of one card played from each of the four hands. The first card played in a trick is called the lead, and each player plays a card sequentially around the table clockwise. Any card may be selected 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, 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 cards are in the trump suit, in which case the hand that plays the highest trump card wins the trick. (Aces are high in bridge, followed by Kings, then Queens, and so on, with 2s the lowest card in each suit.) 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 entire hand face up on the table. The declarer is thereafter responsible for selecting cards to play from the dummy's hand at the dummy's turn, and from his own hand at his turn. The defenders each choose the cards to play from their own hands. The player who is dummy has practically no rights and must not interfere with the play; (s)he may only play cards from the dummy hand at declarer's order (so that the declarer does not have to lean over the table).

In the end, the goal for each pair is to take as many tricks as possible together (it doesn't matter which player takes them). However, the level of the contract makes a more relevant specific target: the number (level) of the contract is the number of odd tricks the declarer must take, that is, the number of tricks beyond 6. Thus, the declarer is always attempting to take at least a majority of the tricks. In the example above, the declarer must manage to take 10 tricks—6 (assumed) + 4 (bid)—with spades as trump, to make the contract. 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 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 are given 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). Slam is any contract on level 6 or 7, and it is given very large bonuses.

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.

This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia.

A number of card games similar to whist can be traced all the way back to the early 16th century. They were all trick-taking games with a variety of variations. 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 unknown Middle Eastern origin; the oldest known rule book, from 1886, calls it "Biritch, or Russian Whist". The OED reports speculation that the word may come from a Turkish term bir-üç, or "one-three", supposedly referring to the one exposed and three concealed hands.) 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 wrote down 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

Tournaments were possible because of duplicate bridge, a variation of the game where many sets of players play with the same hands. Duplicate had occasionally been 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

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

This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia.

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 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 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.

This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia.

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

When new to the game, a player should be familiar with these strategies for playing the hand:

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

Advanced techniques by declarer

Someone who plays regularly in tournaments should be familiar with these concepts:

• 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

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

The cards are dealt as in the diagram, and South is the dealer. As neither South nor West have sufficient high card strength to open the bidding, North opens with the bid of 1♥, which denotes a long suit and at least 12 high card points. East overcalls with 1♠, South supports partner's suit with 2♥, and West also supports spades with 2♠. North inserts a game try of 3♣, inviting the partner to bid the game of 4♥ with good club support and overall values, and South 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 North, 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, South 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 South to play a small spade. West plays low (small card) and North 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 North's hand. North enters the dummy using ♦A, and leads ♣Q in an attempt to finesse West's King. West covers with the King, North takes the Ace, and proceeds by caching 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.

This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia.

The card game auction bridge was developed from straight bridge and was a predecessor to contract bridge. Around the same time five hundred was created by the United States Playing Card Company in 1904.

The main difference between auction bridge and contract bridge is that in auction bridge a game is scored whenever the required number of tricks (9 in No Trump, 10 in Hearts or Spades, 11 in Clubs or Diamonds) is scored. In contract bridge the number of points from tricks taken past the bid do not count towards making a game. Because of this, accurate bidding becomes much more important in contract bridge: partners have to use the bidding to tell each other what their suits and strengths are, so a judgement can be made as to what the chances are of making a game.

Play

The bidding, play and laws were the same as contract bridge.

Scoring

A scoring table for Auction Bridge, from the Official Rules of Card Games, 1973 is as follows:

Odd-tricks: no trumps are worth 10; spades 9; hearts 8; diamonds 7; clubs 6.

Game was 30 points, and only odd-tricks counted towards game. The first side to win two games won the rubber and scored a 250 point bonus.

Each under-trick was worth 50 points to the opponents.

Small slam was worth 50 points; grand slam was worth 100 points.

Honours were scored as follows: 4 trump honours in one hand 80; 5 trump honours or 4 aces in no trumps in one hand 100. For an addition honour in partner's hand, or for 3 or more honours divided between both hands 10 each.

Contracts could be doubled and redoubled, which doubled or quadrupled the odd-trick and under-trick amounts. In addition there was a bonus of 50 points for making a doubled contract and for each over-trick, this was doubled if the contract was redoubled.

Links

• Rules of Card Games: Bridge

This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia.

In contract bridge, there are two basic types of scoring for a single deal: "duplicate" and "rubber" scoring, which share most features, but differ in how the components of the score are accumulated. In duplicate scoring, the outcome of a deal presents a single number assigned to the pair who won the deal (the other pair receiving the same negative score by implication); in rubber bridge, that number is divided into two components: "above the line" and "below the line", both assigned to the winning pair.

General

In general, if the contract was made, the score consists of the following components:

• Contract points, assigned to each odd trick bid
• Bonuses, assigned for:
  • level of the contract,
  • making a doubled or redoubled contract,
• Overtrick points, assigned for each trick which was taken over the contracted number of odd tricks.

If the contract was not made, the side that defeated the contract receives

• Penalty points, assigned for every undertrick

Contract points

Contract points are awarded for the level of the contract, and depend on the denomination and double/redouble (but not on vulnerability):

Denomination	Points per trick
	Undoubled	Doubled	Redoubled
No trumps	30 + 10 for 1st trick	60 + 20 for 1st trick	120 + 40 for 1st trick
majors (♥ and ♠)	30	60	120
minors (♣ and ♦)	20	40	80

Level bonus

There are four types of level bonus, awarded for partial contract, game, small slam and grand slam respectively. A game is any contract which is worth 100 or more contract points; for example, 4♥, 5♣ 2♠ doubled and 1NT redoubled are games. A partial contract (or partscore) is a contract worth less than a game. The bonuses for games and slams depend on vulnerability. The part-score bonus applies in duplicate and Chicago bridge, but not in classic rubber bridge scoring:

Level	Vulnerable	Non-vulnerable
Partscore	50	50
Game	500	300
Small slam	750	500
Grand slam	1500	1000

Slams are also games, so when scoring a slam, both game bonus and appropriate slam bonus are added. Other level bonuses are not cumulative.

Double and redouble bonus

When a (re)doubled contract was made, an additional bonus is added to the level bonus. It is colloquially referred to as an "insult", meaning that the opponents have "insulted" the pair by stating their opinion that the declarer is incapable of making the contract. 50 points are awarded for doubled, and 100 for redoubled contract made.

Overtrick points

When the declarer scores overtricks, they're normally counted as contract points (30 for NT and major suits, 20 for minor suits), except when the contract was (re)doubled, when they are awarded substantially more ("adding salt to the insult"). In that case, the value also depends on vulnerability:

	Vulnerable	Non-vulnerable
Doubled	200	100
Redoubled	400	200

Penalties

When the contract is defeated, regardless of its level and denomination, only the penalty points are assigned to the pair who defeated the contract. The penalties are summed up for every undertrick, and depend on number of undertricks, (re)double and vulnerability:

No. of undertricks	Vulnerable			Non-vulnerable
	Undoubled	Doubled	Redoubled	Undoubled	Doubled	Redoubled
1st undertrick	100	200	400	50	100	200
2nd and 3rd		300	600		200	400
4th and further		300	600		300	600

Without double and redouble, every undertrick has fixed cost of 100 or 50 points. The figures for (re)doubled undertricks are set up so that n vulnerable undertricks cost as much as n+1 non-vulnerable ones; for example, 4 doubled undertricks non-vulnerable cost (100+200+300+300) = 800, the same as 3 undertricks vulnerable (200+300+300).

Duplicate bridge

In duplicate bridge (and the kind of "home parties" known as Chicago), all the categories are summed up, resulting in a single figure. The following table shows some examples (X denotes a double and XX a redouble):

Contract	Tricks made	Vulnera- bility	Contract points	Level bonus	(Re)double bonus	Overtrick points	Penalties	Total
2 ♥	8	any	2×30 = 60	50	-	-	-	110
2 ♥ X	8	Nvul.	2×(2×30) = 120	300	50	-	-	470
3 NT	11	Vul.	10+(3×30) = 100	500	-	2×30	-	660
1 ♦ X	8	Nvul.	2×(1×20) = 40	50	50	1×100	-	240
5 ♠ XX	12	Vul.	4×(5×30) = 600	500	100	1×400	-	1600
6 NT	13	Nvul.	10+(6×30) = 190	300 + 500	-	30	-	1020
4 ♦	7	Nvul.	-	-	-	-	3×50	–150
4 ♦ X	7	Nvul.	-	-	-	-	100+(2×200)	–500
4 ♦ X	7	Vul.	-	-	-	-	200+(2×300)	–800

Rubber bridge

Rubber bridge uses the same values for tricks, bonuses and penalties, but they are divided into two categories:

1. Below the line are entered only the contract points
2. Above the line are entered slam bonuses, "insults", overtrick points and penalties wrung from the opponents. Partscore and game bonuses are not assigned; however, a form of game bonus is added at the end of the rubber, worth 700 points if the opponents did not score a game and 500 if they did. For details, see rubber bridge.

In addition, special (rummy-like) bonuses (referred to as "honors") are awarded in rubber bridge for particular holdings in one hand, regardless of the outcome of the deal:

• Four out of five top trump honors (A,K,Q,J,10) in one hand are awarded 100 points;
• All five top trump honors (A,K,Q,J,10) in one hand are awarded 150 points;
• All four aces in one hand in notrump contracts are awarded 150 points.

Recent scoring changes

If you read old Bridge books, you may notice some differences in the scoring rules.

As of 1987, World Bridge Federation imposed the following scoring changes for duplicate bridge, and as of 1993 also for rubber bridge (however, since there are no official competitions, rubber bridge players accept them as they see fit):

• The undertrick penalty when doubled, not vulnerable, used to be 100 for the first undertrick and 200 for each subsequent. This was changed because it was too easy to sacrifice against a grand slam. A vulnerable grand slam is worth 1500 (slam bonus) + 500 (game bonus) + 210 (major suit trick score) = 2210. Down 11, doubled not vulnerable, used to be 2100, a profitable sacrifice.

• Also, the "insult bonus" for making a redoubled contract used to be only 50. This was changed to 100, so that playing 5 of a minor, redoubled, making an overtrick, is always worth more than an undoubled small slam.

Links

• Scoring in ACBL official site

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Psychic bid (also psych) is a bid in contract bridge, grossly misstating the power and/or suit lengths of one's hand, used deliberately to confuse the opponents.

A psychic bid should mislead not only the opponents, but also the partner. So, a partnership utilising occasional psychic bids has to be cautious in ensuring full disclosure - not only of their formally agreed bidding system - but also of their habits. If within a certain partnership and under certain circumstances a misleading bid has been made more often, it is no longer considered a true psychic bid, but rather a partnership's habit. The partnership needs to disclose this information to the opponents.

Sponsoring organizations often impose a number of restrictions on psychic bids. For example, strong opening bids (such as game forcing 2♣) are not allowed to be psyched. In addition, if the partner is perceived to have bid abnormally due to taking account of a psyche, then the score may be adjusted.

Some psychic bids are so common in tournament bridge, that they are often referred to as "mini-psychs". A typical example is the following 1♠ bid on a hand with a fit for partner and spade shortness. For example, many consider the hand with ♠53 ♥Q642 ♦QJ85 ♣1084 to be an "automatic" 1♠ bid after partner opens 1♥ and RHO doubles.

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The beer card or the 7 of diamonds is a card in the card game of bridge which is given a special importance in popular bridge sub-culture. The "beer card rule" is not an official part of the rules of bridge but it is played commonly in universities in the United Kingdom and elsewhere.

The basic rule is that, if a player wins the last trick of the hand with the 7 of diamonds, his partner must buy them a pint of beer. The additional requirements vary depending whether the beer card trick winner is the declarer or one of the defenders. For the declarer, the requirements are that:

• Must make contract,
• Must win last trick with the ♦7,
• Diamonds must not be trumps (though some people play that only diamond part scores are excluded),
• Must take a justifiable line on the contract to win as many tricks as possible (i.e. not lose tricks to setup the beer or in order to keep the 7 until the last trick),

For a defender, the requirements are that:

• Contract must be defeated
• Must win last trick with the beer card
• Diamonds must not be trumps
• Must try to win as many tricks as possible (i.e. not lose tricks to setup the beer or in order to keep the 7 until the last trick)

If the contract is doubled then two beers are earned. If the contract is redoubled then four beers are earned.

Example

♠	7
♥	Q832
♦	AKQT9
♣	Q76
N S
♠	Q832
♥	AK
♦	J732
♣	AK5

South plays in the inferior contract of three notrump, against which the opponents cash the first four spade tricks. To maximize the chance of getting a beer, declarer must discard two top diamond honors and a small club from dummy. If the diamonds do not break 4-0, it's straightforward to cash nine winners, ending with the beer card. If the diamonds don't break, there's a chance that a defender will be pseudosqueezed and choose to discard a diamond. For declarer to discard three diamond honors risks losing the contract unncessarily, and so forfeits the beer, even if diamonds turn out to break normally.

 

Links

• NSW Bridge Association
• Edinburgh University Bridge Club

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In bridge, a Golden Fit occurs when one partnership has at least eight cards in one suit. Often, a partnership having a golden fit in one suit will bid their contract in that suit; however, partnerships with golden fits in minor suits may prefer to play in no-trump, as they will earn more points for each trick and in some cases, can bid a more reliable game contract in no-trump than in the minor suit.

High-card point count is a method of hand evaluation.

• Ace = 4
• King = 3
• Queen = 2
• Jack = 1

There is a total of 40 points in a deal, 10 per suit. An average hand has 10 points. For balanced hands, this is pretty accurate. For unbalanced hands, distribution and honors in long suits need to be considered as well. This method can also undervalue aces, kings, tens, and nines, and can overvalue queens and jacks.

A total of 26 points combined among partnership's hands means that game in no-trump or a major suit is likely. A total of 29 points is usually enough for game in a minor. A total of 33 is usually enough for a small slam, as the opponents cannot have 2 aces. A total of 37 is usually enough for a grand slam, as the opponents cannot have an ace. These totals can be lowered based on adjustments for distribution. Many expert players play that 25, or even 24, high card points is enough for a good game. A slam is frequently available on only 29 or even 26 high card points, but advanced bidding methods, such as conventions, are required to bid such slams with confidence.

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The Law of Total Tricks pertains to the card game of contract bridge, and is used to help determine how high to bid in a competitive auction. It is not really a law (because counterexamples are easy to find) but it describes a relationship that seems to exist somewhat regularly. Written by Jean-René Vernes for french players in the fifties as a rule of thumb, it was first described in English in a 1969 magazine article.

The "law" can be stated as follows:

The total number of tricks available on a deal is equal to the total number of trump cards both sides hold in their respective best suits.

For example, suppose that North-South have an eight-card heart fit and East-West have an eight-card spade fit. The total number of trumps is 16 so the "law" says the total number of tricks is also 16. That is, if North-South can take 8 tricks playing in hearts, then East-West can take 16 - 8 (also 8) tricks playing in spades; if North-South can take 9 tricks in hearts, the "law" says East-West can take only 7 tricks in spades.

The "law" is said to be most accurate when the high card points are fairly evenly divided between the two sides and the bidding is competitive. Experts also apply adjustment factors to improve accuracy.

When one combines the "law" with the scoring table, it turns out that the following is quite often winning strategy:

Bid to a number of tricks equal to the number of trumps you and your partner hold (and no higher) in a competitive auction.

Thus, if you have an eight-card fit, you are safe to bid to the two level but are unsafe to go to the three level. But, if you have a nine-card fit, the three level will be safe.

In this context, "safe" does not necessarily mean that you will make your contract. But if not, it means you should have a worthwhile save against the opponents' contract. For example, if the opponents have bid to two spades, and you have a nine-card heart fit, the "law" says you should bid three hearts. Assuming the opponents have an eight-card spade fit, there are 17 total trumps. If the opponents can take 8 tricks, the "law" says you can take 9. If the opponents can take 9 tricks, the "law" says you can take only 8. But down one (even doubled, if not vulnerable) is a less negative score for you than letting the opponents make three.

There are a number of bridge conventions that take advantage of the "law". For example, when partner opens one of a major suit (showing five or more in the suit) and you hold four of that suit, a Bergen raise gets you immediately to the three level. (You bid three of partner's major with 0-6 points, three clubs with 7-9 points and three diamonds with 10-12 points.)

In 2002, Anders Wirgren called the accuracy of the "law" into question, saying it works on only 35-40% of deals. However, Larry Cohen remains convinced it is a useful guideline, especially when adjustments are used properly.

References

• Cohen, Larry (1992). To Bid or Not to Bid: The LAW of Total Tricks. Natco Press. ISBN 0-9634715-0-3.
• Jabbour, Zeke (August, 2004). Lawless Territory. ACBL Bridge Bulletin, pp. 27-28.
• WIRGREN, Anders I Fought the Law of Total Tricks http://web.telia.com/~u40127101/

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1. Natural systems in general have the following features:

• Level-1 suit bids denote at least 4 or 5 cards in a major suit, and 3 or 4 cards in a minor suit, with strength of about (11)12-20(22) high card points. The suit bid is generally the longest. The former criterion inflicts further classification into four-card major and five-card major systems.
• Bid of 1NT always presents a balanced hand in a narrow high card points range. The common ranges are 15-17 or 16-18 HCP ("strong notrump") and 12-14 ("weak notrump").
• Bid of 2♣ typically presents a very strong hand (23 HCP up).
• Bid of 2NT presents a strong balanced hand, usually 20-22 HCP.
• Meaning of bids 2♦, 2♥ and 2♠ varies. Two common approaches are that it shows either a weak two bid or an "intermediate" hand (20-22 HCP) with a long suit bid.

The most widespread natural systems are:

• Acol, featuring 4-card majors and weak notrump, originating in Great Britain
• Standard American, originally with 4-card majors but later transforming into 5-card majors.
• 2/1 game forcing, based on Standard American and gradually superseding it.

1. Artificial systems can be further clasified into:

1. Strong club systems are the most popular artificial systems, where opening of 1♣ shows a strong hand (typically 16 HCP up). Other level-1 bids are typically natural, but limited to about 15 points. The most popular strong club systems are:
   
   • Vanderbilt club (the predecessor)
   • Precision club
   • Blue club
2. In Small club systems, the bid of 1♣ is ambiguous, showing several types of hands. That typically includes some range of balanced hands, some hands with long club suit, and very strong hands. The represents are:
   
   • Vienna club (the predecessor)
   • Roman club, developed and used by famous Blue team
   • Polish club, originating (and standard) in Poland but also gained certain popularity worldwide
3. Strong diamond systems are similar to strong club systems, but the bid of 1♦ shows a strong opening, and the bid of 1♣ is typically ambiguous, as in small club systems. An example is Leghorn diamond, played by some top Italian pairs in 1970s.
4. Strong pass systems are highly artificial and fairly rare. In those systems, an initial pass shows a hand of opening strength (11+ HCP); as result, weaker hands must be opened with a bid instead (such bids are called "ferts", short for fertilizers). Strong pass systems are mostly banned by World Bridge Federation and other governing organizations from all competitions except the highest-level ones, because opponents cannot be reasonably expected to cope with such unusual approach.

• Relay systems are based on relay bids – the artificial bids where one partner just bids the cheapest denomination (relay bid) and the other describes his distribution and high cards in detail (relay response) using a highly codified scheme. Such systems are out of the above classification (based on opening bid structure), as the relay feature takes place later in the auction. For example, relatively popular "Moscito system" has variants based on strong-club and strong-pass approaches. Symmetric relay is based on Precision club.

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2/1 game forcing (Two-over-one game forcing) is a bidding system in modern contract bridge, where a non-jump two-level response to a one-level opening bid commits a partnership to at least the game level. It is based on Standard American bidding and has largely superseded it; the principal difference is that a full opening bid is required for a response at the two level to an opening bid of one of a major. Thus, the response of 1NT to 1♥ or 1♠ opening is forcing or semi-forcing.

Some pairs don't play that 1♦–2♣ is game forcing (although some texts recommend that approach). Also, 2/1 game forcing doesn't apply to a passed hand, or if there is an intervening bid or double by an opponent. Some pairs play that 2/1 isn't absolutely game forcing; the pair can stop below game only when responder rebids his suit. For example, 1♥–2♣; 2♥–3♣ is nonforcing by some 2/1 players. A regular partnership should discuss this possibility.

The 2/1 auctions are 1♥–2♣, 1♥–2♦, 1♠–2♣, 1♠–2♦, and 1♠–2♥. Hands without an opening bid are required to respond 1NT to 1♥ or 1♠. In Standard American, 1NT response is nonforcing, but in 2/1 it is forcing for one round of bidding. Since this bid is forcing, hands with a three-card limit raise can start with 1N and later jump-support partner. One variant employed is to play 1NT response to 1♥ or 1♠ as semi-forcing.

Most pairs combine these basic features of 2/1 system with one or more of the following conventions:

• Jacoby transfers over 1NT opening,
• Jacoby 2NT, showing strong support with 4 or more cards
• Splinter bids

Example sequences

1♠ – 2♣
2♦ – 2♠
Forcing to game, with original spade support and good club suit. This is different than in standard bidding, in which such a sequence would show about 10 points, and club suit could be semi-fake.

1♠ – 2♣
2♠ – 2NT.
Forcing to game, with balanced hand and a good club suit.

1♠ – 2♣
1♦ – 3♣
Forcing, unless the partnership has agreed that this is an exception to the "2/1 rule."

1♦ – 2♣
Forcing for a round only (as in Standard American), except in the variant of 2/1 where that sequence is a game forcing as well.

1♠ – 1NT;
2♣ – 2NT;
Shows 10-11 points without support for spades.

1♠ – 1NT;
2♣ – 3♠
Shows 10-11 points with 3-card support for spades.

1♦ – 2♥
This is a jump response, and there are different ways of handling it. In Standard American, such a "jump shift" shows a very strong hand and is unequivocally forcing. However, since such hands do not occur with great frequency, it is more common today to use such a bid to show a weak hand with a long suit, unsuitable for defense. Another possibility is to play it as a "fit-showing jump", showing 8-10 points, a decent spade suit, and good diamond support.

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Acol is a bridge bidding system. It is the name of a road in Hampstead, London, where there was a bridge club in which the system started to evolve in the 1930s. It was popularised in Britain by Iain Macleod in his book "Bridge is an Easy Game", published in 1952. The Acol system is continually evolving but the underlying principle is to keep the bidding as natural as possible. It is common in the British Commonwealth but rarely played in America.

Bidding system structure

The choice between a weak 1NT opening (12-14 points, balanced) and a strong 1NT (15-17 points, balanced) influences much of the rest of the system.

Acol is an approach forcing system - whether or not a bid is forcing, i.e. systemically requires a response, depends on the previous bidding (approach). This is in contrast to level forcing systems, such as 2-over-1, where the level of the bid determines whether or not it is forcing.

It is also classified as a natural system, i.e. opening bids and responses almost always promise at least four cards in the suit. It is a four-card major system, unlike Standard American or European systems where, to open 1H or 1S, five cards in the suit are required.

Acol makes extensive use of limit bids. A limit bid is a bid which describes the hand in terms of both distribution and point count. A player making a limit bid has completely described his hand and may pass next round unless partner makes a forcing bid. A typical limit bid is the 1NT opening. Here the opener promises a limited point count (12-14 for a weak NT) and a particular distribution (4-3-3-3, 4-4-3-2 or 5-3-3-2). Responder now has a more or less complete picture of the partnership's combined strength and distribution and expects opener to pass any non-forcing and non-invitational bid.

Acol Variants

A version of Acol - called "Standard English" - has been developed by the English Bridge Union (EBU) to facilitate the learning of bridge and to provide a natural bidding system for novices and intermediate players. This system uses the Weak 1NT opening (12-14 points). Conventions such as Stayman and Blackwood convention are included. Players may choose to use Jacoby transfers as they progress their experience.

Benjaminised (Benji) Acol replaces the 2H and 2S openings with weak two bids (5-9 points and a 6 card suit). Any Acol 2 hand (8 winners with a given suit as trumps) is shown by bidding 2C which forces a 2D response allowing the suit to be shown. A 2D opener shows any hand with 23+ points.

Reverse Benji is the same as Benji except that the 2C and 2D bids are switched over. 2C is now the strongest bid as in standard Acol.

Standard Acol

The following is a brief summary of Standard Acol.

Opening bids

Opening bids promise at least 12 high card points (HCP), or the equivalent in HCP and shape. Apart from NT, opening bids guarantee the ability to make a rebid over any forcing response from partner.

• 1 of a suit - promises at least four cards in the suit bid. Not forcing.
• 1 NT - balanced hand (4-3-3-3, 4-4-3-2 or 5-3-3-2). Subject to partnership agreement, it may be either 12-14 HCP (weak), 15-17 or 16-18 HCP (strong) or vary between weak and strong according to vulnerability (variable). Limit bid.
• 2C - conventional game forcing bid, promising game-going values (normally 23+ HCP) and at least 5 quick tricks. Game forcing unless opener rebids 2NT.
• 2 of any other suit - shows a strong hand with at least eight playing tricks. Forcing for one round.
• 2NT - balanced hand, 20-22 HCP. Limit bid.
• 3 of a suit - preemptive, normally seven or more cards in the suit bid (may be six at favourable vulnerability), weak hand (not more than 10 HCP). Not forcing.
• 3NT - to play. Normally opener has a long solid minor suit. (Gambling 3NT)

Responses to 1 of a suit

• pass - less than 6 HCP
• 2 of opener's suit - at least four card support, 6-9 HCP. Limit bid.
• 3 of opener's suit - at least four card support, 10-12 HCP. Invites game if opener has requisite strength (14 HCP or more). Limit bid.
• 4 of opener's suit - at least four card support, to play.
• 1 NT - 6-9 HCP, denies ability to bid at 2 level. Not necessarily balanced. Limit bid.
• 2 NT - balanced, 10-12 HCP. Limit bid.
• 3 NT - balanced, 12-15 HCP. Limit bid.
• 1 of a new suit - promises at least four cards in the suit bid, 6 HCP upwards. Forcing for one round.
• 2 of a new suit (below 2 of opener's suit) - normally 5 card suit, at least a good 8 or 9 HCP. Forcing for one round.
• Jump in a new suit - 5 card suit (or support for partner), at least 16 HCP, Game force.

Responses to 1 NT

• 2C - Stayman. Opener responds 2D with no four card major, 2H with a four card heart suit and 2S with four spades (denies four hearts). Forcing for one round.
• 2 of any other suit - to play. Opener must pass.
• 3 of a suit - shows a five card suit, forcing for one round.
• 2NT - 11-12 HCP. invites game if opener is maximum (i.e. for a weak opening NT, if opener has more than a good 13 HCP).
• 3NT - to play.
• 4C - asks for aces. (Gerber)
• 4H, 4S - to play.
• 4NT - Slam invitation to 6NT. Opener bids 6NT with a maximum.
• 5NT - Slam invitation to 6NT. Opener bids 6NT unless a minimum. (Some play as invitation to 7NT; opener bids 6NT if minimum, 7NT with a maximum).

Responses to 2 NT

• 3C - Baron. Opener bids his lowest four card suit. Forcing. (Stayman may also be used as in responses to 1NT, i.e. 3D shows no 4 card major)
• 3 of other suit - shows a five card suit, forcing to game.
• Other responses as over 1NT.

Responses to 2 C

• 2D - negative. Responder lacks the strength for a positive response. Unless opener rebids 2NT (balanced, 23-24 HCP, which may be passed), the sequence is forcing to game.
• 2NT - fairly balanced, 8 or more HCP. Forcing to game.
• 2 of a suit - at least five in the suit, the equivalent of an ace and a king in high cards. Forcing to game.
• 3 of opener's suit - 5-8 HCP, at least 3 card support. Forcing to game.
• 3 of a suit - Solid suit of at least six cards. Forcing to game.

Responses to 2 of a suit

• 2NT - negative. Responder lacks the strength for a positive response.
• Simple bid of a new suit - 8 or more HCP, at least five in the suit. Forcing to game.
• 3 of opener's suit - 5-8 HCP, at least 3 card support. Forcing to game.
• 3NT - flat hand, 8-11 HCP. Not forcing.

Opener's suit rebid after one-level opening

• Rebid of own suit at lowest level - minimum hand, at least a five card suit, 12-15 HCP, non-forcing.
• Jump rebid of own suit - strong hand, normally at least 6 card suit, 15-19 HCP, non-forcing but highly invitational.
• Bid of new suit at lower level than first suit - minimum hand, 12-15 HCP, first suit has at least as many cards as second suit, non-forcing.
• Bid of new suit at higher level than first suit ("reverse") - strong hand, 16-19 HCP, first suit has more cards than second suit, forcing for one round.
• Jump in new suit at lower level than first suit - strong hand, 16-19 HCP, first suit has at least as many cards as second suit, forcing for one round.

Opener's NT rebid after one-level opening

(The following bids assume a weak NT opening)

After suit response at one level the traditional rebids are:

• 1NT - balanced, 15-16 HCP, limit bid
• 2NT - balanced, 17-18 HCP, limit bid
• 3NT - balanced, 19 HCP, limit bid

However, the modern approach modifies the ranges for the rebids thus:

• 1NT - balanced, 15-17 HCP, limit bid
• 2NT - balanced, 18-19 HCP, limit bid
• 3NT - Often an Acol two type of hand prepared to play in NT.

After a suit response at two level the traditional rebids are:

• 2NT - balanced, 15-17 HCP, limit bid
• 3NT - balanced, 18-19 HCP, limit bid

The modern approach is to use the 2NT rebid as forcing and use 3NT as 15-17 with support for the minor that responder has bid (one option).

After the 2NT (forcing) rebid, either bid naturally or use an enquiry (3c) to seek definition of the 2NT rebid.

Fourth suit forcing

A bid of the fourth suit at the 2 level by responder is a one round force, usually asking opener to bid no trumps with a stopper in the fourth suit. A fourth suit bid at the 3 level is similar, but forcing to game.

References

• Standard English http://www.ebu.co.uk/education/standard_english/default.htm

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Blue Club is a bridge bidding system, developed mainly by Benito Garozzo. It was used by the famous Blue Team and became very popular in 1960-1970 (nowadays being less and less used).

The main features are:

• Strong club system: 1♣ opening promises 17 or more HCP, with step answers showing controls.
• Four-card majors: 1♥ and 1♠ and 1♦ openings are limited (12-16 HCP),
• Canapé This is a powerful concept as with a 2 suited hand, your second bid is your strongest suit, whereas other more popular systems bid their weaker suit second - a potential recipe for disaster.
• 1NT ranging from 13-17 high card points. It can be either 13-15 pts which is essentially a replacement bid for a balanced club suit with 2 specific shapes, 3,3,3,4 and 3,3,2,5. 2nd is 16-17 pts and balanced.

Blue Club is a logical bidding system having been developed 40 odd years after bridge became popular and was developed as an entire concept. Other systems such as Standard American have become incredibly complicated to enable players to compete against systems such as Blue Club and Precision etc.

Blue Club is especially deadly in finding safe slams, slams that other systems miss. It is thought to be complicated and artificial but in reality is straightforward and a pleasure to play.

References

• "The Blue Club", adopted by Terence Reece ISBN 0571092659

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The Blackwood convention is a popular bidding convention in contract bridge that was developed by Easley Blackwood Sr.. It is intended to be used in cases where the combined hands of a partnership are so strong that a slam is a possibility. It allows one partner to gain information on the number of aces, and possibly the number of kings, in the other partner's hand.

When this convention is in force, a bid of 4NT (No Trump) asks the partner to provide information on the number of aces in his or her hand. With no aces or four aces partner replies 5♣; with one ace, 5♦; with two aces, 5♥ and with three aces, 5♠. The asking bidder usually has one or two aces, so it is easy to discover the partnership's combined assets. A continuing bid of 5NT asks for Kings with the replies following the same pattern.

This system is not without problems, however. With hands that have a void, a player is not able to tell whether partner's ace is in the void suit (where it would not be of great help) or in a side suit (where it would be very useful.) For this reason cue bidding to show aces is a superior method with hands that contain a void. In fact, most beginner-level players misuse this convention; they ask for aces when they really need other information from partner.

Beginners—and even more advanced players—often fail to comprehend the fundamental purpose of the Blackwood convention. They believe—incorrectly—that the convention is designed for the purpose of ascertaining if the partnership holds all four aces. In fact, the purpose of Blackwood is fundamentally to determine if the partnership is missing two (or more!) aces. If the partnership is missing only one ace, then 12 tricks are still attainable, assuming that the partnership resources are sufficient to capture this many tricks.

Blackwood should not be used when the information gleaned will not answer the question that needs to be answered. A simplified, but instructive, way to think about Blackwood is this: "I am concerned that we may lose the first two tricks, if we bid a slam. I can use Blackwood as a kind of insurance policy, to guarantee that this will not happen." But Blackwood will not help if, due to the structure of the hands, there are multiple ways to lose the first two tricks. It only helps, for the most part, if the exclusive risk of losing the first two tricks is due to the opponents' holding two cashable aces. Obviously, the opposition might hold the ace and king of a side suit, and could bang those tricks right down, resulting in an immediate set.

Thus, a player should use Blackwood only when he can ascertain that the partnership holds at least second-round controls in all suits (kings or, if a suit fit is found, singletons). Thus, a Blackwood query by the player holding two quick losers in a side suit is a wild gamble, as it is still possible that the suit is not controlled by an Ace or a King.

For the same reason, it is generally wrong to use Blackwood with a void. (This is not always true, but the author's rule is: Don't use Blackwood with a void unless you are absolutely sure you know what you are doing, and why you are doing it. If you don't understand why it is correct, in a given case, to use Blackwood with a void, then it's very likely that its usage will be incorrect.) You may be missing two aces, but your void may compensate for the lack of one of the enemy aces. Thus, Blackwood will not tell you what you want to know: Are we at risk of losing the first two tricks? If your side has two aces and a void, then you are not at risk of losing the first two tricks, so long as (a) your void is useful (i.e. does not duplicate the function of an ace that your side holds) and (b) you are not vulnerable to the loss of the first two tricks in the fourth suit (because, for instance, one of the partnership hands holds a singleton in that suit or the protected king, giving your side second round control).

Other problems can easily occur when Clubs is the agreed upon trump suit. The reply to Blackwood could take the partnership past their agreed suit and going to the next higher level may be one trick too high. The adage is 'don't use the convention if there is a possibility you won't like the reply.'

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Canapé is a bridge convention which refers to a system of bidding where the second suit bid is always longer (or at least as long) as the first. With a minimum 5-4 it may be necessary to bid the first suit twice before the short suit. It is often found in European systems such as Blue club. The chief advantage is that with a moderate 2 suiter, you often get to bid a short major, which has marked preemptive value.

Invention of the concept is attributed to early French master Pierre Albarran.

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In contract bridge, coup is a generic name for various techniques in play, denoting a specific pattern in the lie and the play of cards.

There are various types of coup which can be effected.

Pure Coups

There are many coups where the opponents can do little about:

Bath coup

The original coup was referred to as the Bath Coup, whereby a player holding the Ace, Jack and small card(s) plays small against the lead of a King-Queen sequence, so as to get two tricks (if the suit is continued) or gain tempo.

Crocodile coup

The Crocodile coup is a technique used by the defense. It is executed by overtaking your partner's winner, when he or she is about to be endplayed.

Deschapelles coup

The act of sacrificing a card that would ordinarily be an eventual winner (such as an offside King) to establish an entry into partner's hand. The Deschapelles Coup is used more often on defense than offense.

Devil's coup

The Devil's coup is the act of stopping defenders getting a trump trick from Qx opposite Jxx - surely the work of the Devil?

Coup en passant

The act of ruffing through the player who has bigger trump(s), so that the trump is taken either by ruffing or by making it master trump if the other player ruffs.

Galileo coup

The Galileo coup is so named because Galileo Galilei is usually credited with the invention of the telescope; this coup arises when the contract is in a suit in which the declaring side is missing both the Ace and King; if successful, the defenders end up being forced to play the Ace and King of trumps to the same trick, thus "telescoping" their two trump tricks into one.

Grand coup

A Trump coup where the cards ruffed in order to execute a trump reduction are winners.

Merrimac coup

The Merrimac coup is the act of sacrificing an honour (usually a King) in order to remove an entry from an opponent's hand.

Morton's fork coup

The forcing of an opponent to choose between establishing one or more extra tricks in the suit led and losing the opportunity to win a trick in the suit led.

Scissors coup

The Scissors coup is so named because it cuts communications between defenders, most commonly by discarding a key card from either the declarer's own hand or dummy. This enables declarer to prevent the defenders transferring the lead; usually for a defensive ruff.

Trump coup

The Trump coup happens in the end-game when declarer needs to finesse in trumps but doesn't have one to lead up. It is often assotiated with a Trump Reduction.

Vienna coup

The Vienna coup is the act of cashing an ace opposite the queen (or, more generically, an immediate winner opposite a menace) in order to enable a squeeze to work on either opponent.

Deceptive Coups

Some coups rely on the opponents making a mistake.

Grosvenor gambit

The act of deliberately misplaying a hand in order to induce a mistake by an opponent which results in either the same or a superior result. Even when the gambit does not yield a material gain, it usually induces a big psychological impact on the opponents who were offered a trick for free but couldn't have believed it were possible.

Idiot coup

The act of only losing one trick when missing AKx of trumps. Declarer leads through one of the defenders hoping they will play the king from Kx which then falls under their partner's stiff ace. Obviously going up with the king is foolish as with the ace declarer has a legitimate line escape a loser (play the ace and hope for stiff king or take a finesse), hence the name.

Illegal Coups

There are also a number of insidious and illegal coups which should only be tried out against friends in social bridge:

Alcatraz coup

The Alcatraz coup is performed by purposely revoking when declarer is uncertain which defender to finesse. After the trick is over, declarer knows which defender to finesse, "notices" and corrects his misplay, and finesses the correct defender. Note: performing an Alcatraz coup is explicitly against the rules of bridge, and can get you kicked out of tournaments.

Superglue coup

Another dishonest (and quite subtle) coup; the Superglue Coup is where a defender pulls out two cards together (as if they were superglued together). Declarer sees the cards and assumes they are adjacent in rank in the defender's hand. For example if declarer is missing KT3 and one defender pulls the K and 3 out together declarer can assume that the defender does not have the T! If declarer alters his line based on this information and loses to the T in the defender's hand then he has fallen victim to the Superglue Coup! An excellent couple of examples are at poorbridge.com.

Links

• An article describing the Grosvenor Gambit
• A list of amusing (and mostly unethical) coups

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Squeeze play (or simply squeeze) is a play in contract bridge that often occurs late in the game and involves the play of a card (often, but not necessarily, a winner) which forces an opponent to discard a vital card from his hand, thus giving up a trick (or two in some cases). The discarded card can be either a winner or any card that solidifies defender's defensive position.

Although the squeeze was already discovered and described in whist, its use was best described and perfected in contract bridge.

The squeeze operates on the principle that, in a n-card ending with n-1 combined winners, the two hands can have one potential trick (threat card) each, but there's no room in single defender's hand to cover both of those. In order for a squeeze to work, the victim might not hold any "idle" cards, but all his cards must be "busy", covering some sort of menace.

In general, a squeeze requires the following conditions to be fulfilled. In most common scenarios, all of them are present, but there are also squeezes where one or more of the them is not required:

• The declarer has all but one (in extreme situations, two) winners in combined hands. In other words, the count is rectified, i.e. the declarer has already lost all the tricks he was about to.
• In at least two suits are present cards which are not immediate winners, but present a menace or threat of becoming one;
• At least one of the menaces is placed after the squeezed defender(s) (squeezee).
• The declarer has sufficient entries (winners serving as communication between two hands) to cash the developed menaces.
• The squeezed defender(s) must not hold any idle cards, i.e. the ones that could be safely disposed of.

This mechanism can be shown on a simple squeeze.

		♠	AJ
		♥	K
		♦	-
		♣	-
♠	KQ	N   W S
♥	A
♦	-
♣	-
		♠	4
		♥	6
		♦	-
		♣	A

South leads the club ace in the following position, and West is squeezed between hearts and spades - if he throws away the heart ace, south discards the jack of spades in north, plays hearts and north makes the ♡K and the ♠A, if he throws away one of the spades, south discards the king of hearts in north, plays spades, and again north makes the two remaining tricks.

In this position:

• Three cards are remaining, and the declarer has two immediate winners (♠A and ♣A).
• ♠J and ♥K are the menaces;
• Both menaces are placed after the squeezee (West);
• ♠A serves as an entry to the promoted menace card;
• West has no idle cards.

This is a positional squeeze – East holding West's cards would not be squeezed as one of the two menaces (the spade Jack and the heart King) would be discarded before his turn to play. If north had discarded the king of hearts, east could discard the ace of hearts (provided west still had at least one heart), if north had discarded the spade jack (or the spade ace), east could have discarded a spade.

 

We will see more of this in simple squeezes.

These plays typically occur late in the game, because they often require the player to have an exact count and location of certain high cards in one or more suits, and must know exactly what cards an opponent will be forced to play, as the following example demonstrates:

		♠	AJ
		♥	K
		♦	2
		♣	-
♠	KQ	N W         E S		♠	3
♥	A			♥	-
♦	7			♦	Q
♣	-			♣	87
		♠	4
		♥	6
		♦	3
		♣	A

This time when the club ace is cashed, West simply sheds his small diamond, an idle card.

To avoid this kind of failure, south needs to 'rectify the count' - that is, he must lose all tricks except the ones he is entitled to and the one he intends to gain with the squeeze. In this case that would mean that he should grant the diamond queen to east first; however, in this case east returns a spade, taken in north, and the communication is lost: south cannot reach the club ace in his hand.

 

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ACBL

American Contract Bridge League

Agreement

An understanding between partners as to the meaning of a particular bid or play. The set of all the agreements in a partnership forms the Bidding system and the Signals.

Alert

An indication to the opponents that the partner's bid is artificial (or that its meaning might be otherwise unexpected). An alert is made by pronouncing "alert", displaying an appropriate card from the bidding box, or sometimes by just knocking on the table. Use of alert (alert procedure) is regulated by sponsoring organizations.

Artificial

1) A call or play that is not natural.

2) A bidding system that contains many such calls.

Autobridge

A non-digital game for one person, designed to teach bridge (see image).

Auction

1) see bidding.

2) Auction bridge, an older form of bridge, now replaced by Contract bridge.

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Balanced hand

A hand is said to be balanced if it has a distribution of 4-3-3-3, 4-4-3-2, or 5-3-3-2 (Also defined as "no voids, no singletons, and at most one doubleton"). Balanced hands are particularly suitable for notrump contracts.

Bid

A declaration of both level and denomination (suit or no trump) that generally indicates the number of tricks the bidder believes their partnership can win; certain bids can also be used as conventions.

Bid out of turn

A bid erroneously made when it was other player's turn to bid. Subject to penalty.

Bidding

The first phase of the game, where players try to establish the final contract by making subsequent bids.

Bidding system

The complete set of agreements and conventions assigned to every possible bid by a partnership.

Board

1) a device that keeps each player's cards separate for duplicate bridge.

Board-a-Match

A form of scoring for team events, parallel to matchpoint scoring in pair games, in which every deal scores the same – +1 for a win, 0 for a tie, and -1 for a loss. Now less common than IMP/victory point scoring.

Book

The basic six tricks that must be taken by the declaring side. Since there is a total of 13 tricks, these six tricks below the half are always assumed and are never taken into account in scoring. Thus, a contract on level 1 denotes taking at least (6+1) tricks.

Bonus

In scoring, the additional points awarded for making a contract, for making a doubled contract, or for making doubled or redoubled overtricks. There are different bonus amounts at the partscore, Game, small slam, and grand slam levels. Bonus amounts may depend on the vulnerability, and whether or not the contract is doubled or redoubled. Bonus amounts are different in rubber bridge and duplicate.

Break

When the cards of a suit in the hands of the opponents are split evenly, or nearly evenly, so that neither opponent has a particularly large or small holding in that suit, then suit is said to break. The corollary is a "bad break" when the suit does not split evenly.

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Caddy

A non-playing person designated to move boards between tables during a tournament.

Call

Any bid, pass, double, or redouble in the bidding stage.

Chicago

A form of bridge in which a rubber is completed every four deals, and the vulnerability is different in each of those deals. The scoring and sequence of dealer and vulnerability used in duplicate bridge are derived from those used in Chicago bridge. Chicago is said to have been devised by commuters who played bridge on daily train journeys, where the time available for play was limited by the length of the trip.

CHO

Centre Hand Opponent; a slang term for the partner.

Claim

A statement by declarer about how the remaining unplayed tricks will be won or lost. Normally the claiming player exposes their hand and describes the sequence of play for the remaining tricks and their disposition. This is usually done when the play of the rest of the hand is straightforward. See also concession.

Communication

1) The process of (or the ability to) move the lead between the two hands of a partnership, so as to lead each trick from the more advantageous hand.

2)The means to convey a message to the partner in bidding. The only legal means of communication is through bids themselves, rather than using hesitation or mannerism.

Competitive auction

A bidding sequence which involves both partnerships.

Concession

An admission by a player that he must lose some or all of the remaining tricks.

Contract

1) The statement of the pair who has won the bidding that they will take at least the given number of tricks. The contract consists of two components: the level, stating the number of tricks to be taken (plus the book tricks), and the denomination, denoting the trump suit (or its absence). The last bid in the bidding phase denotes the final contract.

2) Short for Contract Bridge as opposed to other forms of bridge, such as Duplicate bridge or Auction bridge.

Control

1) In play, declarer's ability to limit the number of tricks that opponents could cash (usually related with trump contracts).

2) A feature of a hand which prevents the opponents of taking any (or more than one) immediate tricks in a suit. Aces are always "1st-round" controls and Kings are "2nd-round" controls; in trump contracts, voids are also 1st-round controls and singletons 2nd-round ones.

Convention

An agreement on the meaning of particular (sequence of) bid(s) between two partners, where the meaning of the bid(s) is not necessarily (and most often is not) related to the length and strength of bid suits, that is, an agreement on an artificial call or play.

Convention card

A form filled out by a partnership that shows all the bidding and play conventions being used. Usually used during tournaments.

Cover card

A card (honor or extra trump) which is known to compensate one of partner's losers; for example, a King in trumps is known to cover partner's trump loser.

Crossruff

A playing technique in trump contracts where extra tricks are gained by taking ruffs in both hands alternately.

Cuebid

1) A bid of the opponents' suit in a competitive auction. Usually a conventional, forcing bid that shows strength or an unusual hand.

2) A bid that shows control in a suit (usually with an Ace or King, sometimes with a void) but does not indicate length or strength in the suit otherwise. Partnership agreements indicate when in an uncontested auction a bid is considered a cuebid. Usually used in exploring for a slam contract, or for showing stoppers needed for a notrump game.

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