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Par Contract
Optimum contract and par contract are two closely related (and sometimes confused) bridge scoring terms in the card game contract bridge. 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 s ...
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Bridge Scoring
While a deal of bridge is always played following a unique set of rules, its scoring may vary depending on the type of event the deal is played on. There are two main categories of scoring: rubber and duplicate. Rubber scoring, and its popular variant Chicago, are mostly used in social play. Duplicate scoring is focused on tournament competition and has many variations that compare and rank the relative performance of partnerships and teams playing the same deals as their competitors. Terminology The following terms and concepts, defined in the glossary of contract bridge terms, are essential to understanding bridge scoring: * * * * * or Made * * * and grand slam * *Undoubled, and *, and Scoring elements Bridge scoring consists of nine elements. Not all elements are included in all game variants and the method of accumulation of the elements over several deals varies. * If the contract is made, the score for each such deal consists of: ** Contract points, assigned to ea ...
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Card Game
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 (such as poker). A small number of card games played with traditional decks have formally standardized rules with international tournaments being held, but most are folk games whose rules vary by region, culture, and person. Traditional card games are played with a ''deck'' or ''pack'' of playing cards which are identical in size and shape. Each card has two sides, the ''face'' and the ''back''. Normally the backs of the cards are indistinguishable. The faces of the cards may all be unique, or there can be duplicates. The composition of a deck is known to each player. In some cases several decks are shuffled together to form a single ''pack'' or ''shoe''. Modern card games usually have bespoke decks, often with a vast amount of cards, and can include number or action cards. This ...
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Contract Bridge
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 it at the regional level. The game consists of a number of , each progressing through four phases. The cards are dealt to the players; then the players ''call'' (or ''bid'') in an auction seeking to take the , specifying how many tricks the partnership receiving the contract (the declaring side) needs to take to receive points for the deal. During the auction, partners use their bids to also exchange information about their hands, including o ...
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Duplicate Bridge
Duplicate bridge is a variation of contract bridge where the same set of bridge deals (i.e. the distribution of the 52 cards among the four hands) are played by different competitors, and scoring is based on relative performance. In this way, every hand, whether strong or weak, is played in competition with others playing identical cards, and the element of skill is heightened while that of chance is reduced. This stands in contrast to Bridge played without duplication, where each hand is freshly dealt and where scores may be more affected by chance in the short run. Four-way card holders known as Bridge boards are used to enable each player's hand to be preserved from table to table, and final scores are calculated by comparing each pair's result with others who played the same hand. In duplicate bridge, players normally play all the hands with the same partner, and compete either as a partnership (in a 'Pairs tournament') or on a team with one or more other partnerships ('Te ...
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Game Theory
Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has applications in all fields of social science, as well as in logic, systems science and computer science. Originally, it addressed two-person zero-sum games, in which each participant's gains or losses are exactly balanced by those of other participants. In the 21st century, game theory applies to a wide range of behavioral relations; it is now an umbrella term for the science of logical decision making in humans, animals, as well as computers. Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum game and its proof by John von Neumann. Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathema ...
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Nash Equilibrium
In game theory, the Nash equilibrium, named after the mathematician John Nash, is the most common way to define the solution of a non-cooperative game involving two or more players. In a Nash equilibrium, each player is assumed to know the equilibrium strategies of the other players, and no one has anything to gain by changing only one's own strategy. The principle of Nash equilibrium dates back to the time of Cournot, who in 1838 applied it to competing firms choosing outputs. If each player has chosen a strategy an action plan based on what has happened so far in the game and no one can increase one's own expected payoff by changing one's strategy while the other players keep their's unchanged, then the current set of strategy choices constitutes a Nash equilibrium. If two players Alice and Bob choose strategies A and B, (A, B) is a Nash equilibrium if Alice has no other strategy available that does better than A at maximizing her payoff in response to Bob choosing B, and Bob ...
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Par (score)
In golf, par is the predetermined number of strokes that a proficient (scratch, or zero handicap) golfer should require to complete a hole, a round (the sum of the pars of the played holes), or a tournament (the sum of the pars of each round). For scoring purposes, a golfer's number of strokes is compared with the par score to determine how much the golfer was either "over par", "under par", or was "even with/equal to par". Holes are generally assigned par values between three and five based on the distance from the teeing ground to the putting green, and occasionally other factors such as terrain and obstacles. A typical 18-hole golf course will have a total par around 72, and a 9-hole par-3 course (where all holes are rated as par 3) will have a total par of 27. Determination of par Par is primarily determined by the playing length of each hole from the teeing ground to the putting green. Holes are generally assigned par values between three and five, which includes a regul ...
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Golf
Golf is a club-and-ball sport in which players use various clubs to hit balls into a series of holes on a course in as few strokes as possible. Golf, unlike most ball games, cannot and does not use a standardized playing area, and coping with the varied terrains encountered on different courses is a key part of the game. Courses typically have either 18 or 9 ''holes'', regions of terrain that each contain a ''cup'', the hole that receives the ball. Each hole on a course contains a teeing ground to start from, and a putting green containing the cup. There are several standard forms of terrain between the tee and the green, such as the fairway, rough (tall grass), and various ''hazards'' such as water, rocks, or sand-filled ''bunkers''. Each hole on a course is unique in its specific layout. Golf is played for the lowest number of strokes by an individual, known as stroke play, or the lowest score on the most individual holes in a complete round by an individual or team, k ...
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