Optimum contract and par contract
Encyclopedia
Optimum contract and par contract are two closely related (and sometimes confused) terms in the card game
contract bridge
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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 choice of denomination an important decision.
Each side has its own optimum contract and, for a side with poor hands, "pass" may be the optimum call.
The par contract on a deal is that contract which results from optimal bidding by both sides and which 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.
would refer to such a par result as a Nash equilibrium
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The term par score
originated in the game of golf
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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...
contract bridge
Contract bridge
Contract bridge, usually known simply as bridge, is a trick-taking card game using a standard deck of 52 playing cards played by four players in two competing partnerships with partners sitting opposite each other around a small table...
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Optimum contract
The optimum contract is that contract which offers the best chances, in unopposed bidding, of gaining bonus points for part-score, game or slam whilst minimising the risk of failure. It is that contract which 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 choice of denomination 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 (ie 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 which results from optimal bidding by both sides and which 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 which arises from the par contract and on which neither side could reasonably improve by changing their line of play. Game theoreticiansGame theory
Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...
would refer to such a par result as a Nash equilibrium
Nash equilibrium
In game theory, Nash equilibrium is a solution concept of a 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 his own strategy unilaterally...
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The term par score
Par (score)
The word "par" is a term in the game of golf used to denote the pre-determined number of strokes that a scratch golfer should require to complete a hole, a round , or a tournament...
originated in the game of golf
Golf
Golf is a precision club and ball sport, in which competing players use many types of clubs to hit balls into a series of holes on a golf course using the fewest number of strokes....
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