Optimum contract and par contract

Last updated April 29, 2019

Optimum contract and par contract are two closely related (and sometimes confused) terms in the card game contract bridge:

A card game is any game using playing cards as the primary device with which the game is played, be they traditional or game-specific. Countless card games exist, including families of related games. A small number of card games played with traditional decks have formally standardized rules, but most are folk games whose rules vary by region, culture, and person. Games using playing cards exploit the fact that cards are individually identifiable from one side only, so that each player knows only the cards he holds and not those held by anyone else. For this reason card games are often characterized as games of chance or “imperfect information”—as distinct from games of strategy or “perfect information,” where the current position is fully visible to all players throughout the game.

Contract bridge, or simply bridge, is a trick-taking card game using a standard 52-card deck. In its basic format, it is played by four players in two competing partnerships, with partners sitting opposite each other around a table. Millions of people play bridge worldwide in clubs, tournaments, online and with friends at home, making it one of the world's most popular card games, particularly among seniors. The World Bridge Federation (WBF) is the governing body for international competitive bridge, with numerous other bodies governing bridge at the regional level.

Optimum contract

The optimum contract is the one that offers the best chance of gaining the most scoring points whilst minimising the risk of failure. It is that contract that cannot be improved upon by further bidding nor could it have been improved upon by taking a different line in earlier bidding.

At Chicago or IMP scoring it is generally worth bidding game even with a slightly less than 50% chance of success due to the relatively high value of the bonuses (especially when vulnerable). In duplicate pairs scoring, the subtle difference between a major suit game, a NT game and a minor suit game make the declaration an important decision.

Each side has its own optimum contract and, for a side with poor hands, "pass" may be the optimum call.

Par contract

Where there is competitive bidding (i.e. both sides are bidding) the extra dimension of sacrificial bidding is added, and the theoretical optimum contract can be overtaken by the par contract. The par contract on a deal is that contract that results from optimal bidding by both sides and that neither side could improve by further bidding. It will either be equal to the optimum contract of one side or it will exceed the optimum contract of both sides. If the latter, it is only considered par if the doubled penalty is less than the value of the opposing optimum contract.

Par score or par result

The par result is that score that arises from the par contract and on which neither side could reasonably improve by changing their line of play.^[1] Game theoreticians would refer to such a par result as a Nash equilibrium.

Game theory is the study of mathematical models of strategic interaction between rational decision-makers. It has applications in all fields of social science, as well as in logic and computer science. Originally, it addressed zero-sum games, in which one person's gains result in losses for the other participants. Today, game theory applies to a wide range of behavioral relations, and is now an umbrella term for the science of logical decision making in humans, animals, and computers.

In game theory, the Nash equilibrium, named after the mathematician John Forbes Nash Jr., is a proposed solution of a non-cooperative game involving two or more players in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy.

The term par score originated in the game of golf.

Notes

↑ Francis, Henry G., Editor-in-Chief; Truscott, Alan F., Executive Editor; Francis, Dorthy A., Editor, Sixth Edition (2001). The Official Encyclopedia of Bridge (6th ed.). Memphis, TN: American Contract Bridge League. p. 336. ISBN 0-943855-44-6. OCLC 49606900.

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Related Research Articles

In the card game contract bridge, the Losing-Trick Count (LTC) is a method of hand evaluation that is generally only considered suitable to be used in situations where a trump suit has been established and when shape and fit are more significant than high card points (HCP) in determining the optimum level of the contract. The method is generally not considered suitable for no trump or misfit hands; also, the trump suit is generally considered to require at least eight cards in length with no partner holding less than three.

The card game auction bridge, the third step in the evolution of the general game of bridge, was developed from straight bridge in 1904. The precursor to contract bridge, its predecessors were whist and bridge whist.

In the card game contract bridge, the major suits are spades and hearts. The major suits are of prime importance for tactics and scoring as they outrank the minor suits while bidding and also outscore them. Much of the tactics of bidding in bridge revolves around the attempt by partners to find a "fit" in one of the major suits that will allow them to make a game contract. Another reason why the major suits is more desirable than the minor suits is that they need one less trick to make game. Of the two major suits, spades rank higher than hearts.

In contract bridge the minor suits are diamonds and clubs. They are given that name because contracts made in those suits score less than contracts made in the major suits, and they rank lower in bidding. In particular, one can make game with a four-level bid in a major suit, while a five-level bid is required in a minor. Of the two minor suits, diamonds rank higher than clubs.

Spades is a trick-taking card game devised in the United States in the 1930s. It can be played as either a partnership or solo/"cutthroat" game. The object is to take at least the number of tricks that were bid before play of the hand began. Spades is a descendant of the Whist family of card games, which also includes Bridge, Hearts, and Oh Hell. Its major difference as compared to other Whist variants is that, instead of trump being decided by the highest bidder or at random, the Spade suit always trumps, hence the name.

A game try in the card game of bridge is a bid that shows interest in bidding a game and asks partner to help in making the decision.

In the card game "contract bridge", a splinter bid is a convention whereby a double jump response in a side-suit indicates excellent support, a singleton or void in that side-suit, and at least game-going strength. Some partnerships agree that the maximum strength can be only that necessary to reach a game contract; stronger holdings with major suit support instead might temporize with a Jacoby 2NT bid.

Chicago, also known as Four-deal Bridge and Short Bridge, is a form of contract bridge and a variation of rubber bridge in which one or more sets of four deals are played and scored.

Zar Points (ZP) is a statistically derived method for evaluating contract bridge hands developed by Zar Petkov. The statistical research Petkov conducted in the areas of hand evaluation and bidding is useful to bridge players, regardless of their bidding or hand evaluation system. The research showed that the Milton Work point count method, even when adjusted for distribution, is not sufficiently accurate in evaluating all hands. As a result, players often make incorrect or sub-optimal bids. Zar Points are designed to take many additional factors into consideration by assigning points to each factor based on statistical weight. While most of these factors are already implicitly taken into account by experienced players, Zar Points provides a quantitative method that allows them to be incorporated into bidding.

Preempt is a bid in contract bridge whose primary objectives are (1) to thwart opponents' ability to bid to their best contract, with some safety, and (2) to fully describe one's hand to one's partner in a single bid. A preemptive bid is usually made by jumping, i.e. skipping one or more bidding levels. Since it deprives the opponents of the bidding space, it is expected that they will either find a wrong contract of their own, or fail to find any. A preemptive bid often has the aim of a sacrifice, where a partnership bids a contract knowing it cannot be made, but assumes that, the penalty will still be smaller than the value of opponents' bid and made contract.

These terms are used in contract bridge, using duplicate or rubber scoring. Some of them are also used in whist, bid whist, the obsolete game auction bridge, and other trick-taking games. This glossary supplements the Glossary of card game terms.

In duplicate bridge, a sacrifice is a deliberate bid of a contract that is unlikely to make in the hope that the penalty points will be less than the points likely to be gained by the opponents in making their contract. In rubber bridge, a sacrifice is an attempt to prevent the opponents scoring a game or rubber on the expectation that positive scores on subsequent deals will offset the negative score.

In the card game contract bridge, a takeout double is a low-level conventional call of "Double" over an opponent's bid as a request for partner to bid his best of the unbid suits. The most common takeout double is after an opponent's opening bid of one of a suit where the double shows a hand with opening values, support for all three unbid suits and shortness in the suit doubled. Normally, the partner of the doubler must bid his best suit but may pass if (a) his right hand opponent intervenes or (b) on the more rare occasions when his hand is such that he wishes to convert the takeout double to a penalty double.

In contract bridge, various bidding systems have been devised to enable partners to describe their hands to each other so that they may reach the optimum contract. Key to this process is that players evaluate and re-evaluate the trick-taking potential of their hands as the auction proceeds and additional information about partner's hand and the opponent's hands becomes available.

Slam-seeking conventions are codified artificial bids used in the card game contract bridge. Bidding and making a small slam or grand slam yields high bonuses ranging from 500 to 1500 points. However, the risk is also high as failure to fulfill the slam contract also means failure to score the bonus points for a game (300-500). Conventions have been devised to maximise the opportunity for success whilst minimising the risk of failure.

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

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EHAA is a highly natural bidding system in contract bridge characterized by four-card majors, sound opening bids, undisciplined weak two-bids in all four suits and a mini notrump, usually of 10–12 high card points.

Computer bridge is the playing of the game contract bridge using computer software. After years of limited progress, since around the end of the 20th century the field of computer bridge has made major advances. In 1996 the American Contract Bridge League (ACBL) established an official World Computer-Bridge Championship, to be held annually along with a major bridge event. The first championship took place in 1997 at the North American Bridge Championships in Albuquerque. Since 1999 the event has been conducted as a joint activity of the American Contract Bridge League and the World Bridge Federation. Alvin Levy, ACBL Board member, initiated this championship and has coordinated the event annually since its inception. The event history, articles and publications, analysis, and playing records can be found at the official website.

[1] Francis, Henry G., Editor-in-Chief; Truscott, Alan F., Executive Editor; Francis, Dorthy A., Editor, Sixth Edition (2001). The Official Encyclopedia of Bridge (6th ed.). Memphis, TN: American Contract Bridge League. p. 336. ISBN 0-943855-44-6. OCLC 49606900.