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Suit Combinations
In the card game contract bridge, a suit combination is a specific subset of the cards of one suit held respectively in declarer's and dummy's hands at the onset of play. While the ranks of the remaining cards held by the defenders can be deduced precisely, their location is unknown. Optimum suit combination play allows for all possible lies of the cards held by the defenders. The term is also used for the sequence of plays from the declarer and dummy hands, conditional on intervening plays by the opponents; in other words, declarer's plan or strategy of play given his holdings and his goal for the number of tricks to be taken. In addition to understanding the possible initial combinations and probabilities for the location of the opponents' cards in a suit, declarer can further inform himself from the bidding, the opening lead and from the prior play of cards in establishing the probable location of remaining cards. Examples The diagram at left shows a heart suit combinatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Card Game
A card game is any game that uses playing cards as the primary device with which the game is played, whether the cards are of a traditional design or specifically created for the game (proprietary). 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 may vary by region, culture, location or from circle (cards), circle to circle. 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 Shuffling, shuffled together to form a single ''pack'' or ''shoe''. Modern car ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expectation Value
In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first moment) is a generalization of the weighted average. Informally, the expected value is the mean of the possible values a random variable can take, weighted by the probability of those outcomes. Since it is obtained through arithmetic, the expected value sometimes may not even be included in the sample data set; it is not the value you would expect to get in reality. The expected value of a random variable with a finite number of outcomes is a weighted average of all possible outcomes. In the case of a continuum of possible outcomes, the expectation is defined by integration. In the axiomatic foundation for probability provided by measure theory, the expectation is given by Lebesgue integration. The expected value of a random variable is often denoted by , , or , with also often stylized as \mathbb or . Histo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vacant Places
In the card game bridge, the law or principle of vacant places is a simple method for estimating the probable location of any particular card in the two unseen hands. It can be used both to aid in a decision at the table and to derive the entire suit division probability table. At the beginning of a deal, each of four hands comprises thirteen cards and one may say there are thirteen vacant places in each hand. The probability that a particular card lies in a particular hand is one-quarter, or 13/52, the proportion of vacant places in that hand. From the perspective of a player who sees one hand, the probable lie of a missing card in a particular one of the other hands is one-third. In Contract bridge, once the play commences, the dummy is exposed and so, for any player, there are only two unseen hands where a card may lie. The principle of vacant places is a rule for updating those uniform probabilities as one learns about the deal during the auction and the play. Essentially, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Safety Play
Safety play in contract bridge is a generic name for plays in which declarer maximizes the chances for fulfilling the contract (or achieving a certain score) by ignoring a chance for a higher score. Declarer uses safety plays to cope with potentially unfavorable layouts of the opponent's cards. In so doing, declarer attempts to ensure the contract even in worst-case scenarios, by giving up the possibility of overtricks. Safety plays adapt declarer's strategy to the scoring system. In IMP-scoring tournaments and rubber bridge, the primary scoring reward comes from fulfilling the contract and overtricks are of little marginal value. Therefore, safety plays are an important part of declarer technique at quantitative scoring. In matchpoint games, which use comparative scoring, overtricks are very important. Therefore, although safety plays have a certain role at matchpoints, they are normally avoided if the odds for making the contract are good and overtricks are likely. Definit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Principle Of Restricted Choice (bridge)
A principle may relate to a fundamental truth or proposition that serves as the foundation for a system of beliefs or behavior or a chain of reasoning. They provide a guide for behavior or evaluation. A principle can make values explicit, so they are expressed in the form of rules and standards. Principles unpack the values underlying them more concretely so that the values can be more easily operationalized in policy statements and actions. In law, higher order, overarching principles establish rules to be followed, modified by sentencing guidelines relating to context and proportionality. In science and nature, a principle may define the essential characteristics of the system, or reflect the system's designed purpose. The effective operation would be impossible if any one of the principles was to be ignored. A system may be explicitly based on and implemented from a document of principles as was done in IBM's 360/370 ''Principles of Operation''. It is important to differen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finesse
In contract bridge and similar games, a finesse is a type of card play technique which will enable a player to win an additional trick or tricks should there be a favorable position of one or more cards in the hands of the opponents. The player attempts to win either the current trick or a later trick with a card of the suit he leads notwithstanding that the opponents hold a higher card in the suit; the attempt is based on the assumption that the higher card is held by a particular opponent. The specifics of the technique vary depending upon the suit combination being played and the number of tricks the player is attempting to win in that suit. Terminology To ''finesse a card'' is to play that card. Thus, in the example, the Queen is finessed. The outstanding King is the card finessed ''against'', or the card the player hopes to capture by the finessing maneuver. Thus, you finesse against a missing honor, but you finesse the card you yourself play, the card finessed being ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bridge Probabilities
A bridge is a structure built to span a physical obstacle (such as a body of water, valley, road, or railway) without blocking the path underneath. It is constructed for the purpose of providing passage over the obstacle, which is usually something that is otherwise difficult or impossible to cross. There are many different designs of bridges, each serving a particular purpose and applicable to different situations. Designs of bridges vary depending on factors such as the function of the bridge, the nature of the terrain where the bridge is constructed and anchored, the material used to make it, and the funds available to build it. The earliest bridges were likely made with fallen trees and stepping stones. The Neolithic people built boardwalk bridges across marshland. The Arkadiko Bridge, dating from the 13th century BC, in the Peloponnese is one of the oldest arch bridges in existence and use. Etymology The ''Oxford English Dictionary'' traces the origin of the word ''bridge' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transitive Relation
In mathematics, a binary relation on a set (mathematics), set is transitive if, for all elements , , in , whenever relates to and to , then also relates to . Every partial order and every equivalence relation is transitive. For example, less than and equality (mathematics), equality among real numbers are both transitive: If and then ; and if and then . Definition A homogeneous relation on the set is a ''transitive relation'' if, :for all , if and , then . Or in terms of first-order logic: :\forall a,b,c \in X: (aRb \wedge bRc) \Rightarrow aRc, where is the infix notation for . Examples As a non-mathematical example, the relation "is an ancestor of" is transitive. For example, if Amy is an ancestor of Becky, and Becky is an ancestor of Carrie, then Amy is also an ancestor of Carrie. On the other hand, "is the birth mother of" is not a transitive relation, because if Alice is the birth mother of Brenda, and Brenda is the birth mother of Claire, then it does ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mixed Strategy
In game theory, a move, action, or play is any one of the options which a player can choose in a setting where the optimal outcome depends ''not only'' on their own actions ''but'' on the actions of others. The discipline mainly concerns the action of a player in a game affecting the behavior or actions of other players. Some examples of "games" include chess, bridge, poker, monopoly, diplomacy or battleship. The term strategy is typically used to mean a complete algorithm for playing a game, telling a player what to do for every possible situation. A player's strategy determines the action the player will take at any stage of the game. However, the idea of a strategy is often confused or conflated with that of a move or action, because of the correspondence between moves and pure strategies in most games: for any move ''X'', "always play move ''X''" is an example of a valid strategy, and as a result every move can also be considered to be a strategy. Other authors treat strate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nash Equilibrium
In game theory, the Nash equilibrium is the most commonly used solution concept for non-cooperative games. A Nash equilibrium is a situation where no player could gain by changing their own strategy (holding all other players' strategies fixed). The idea of Nash equilibrium dates back to the time of Cournot, who in 1838 applied it to his model of competition in an oligopoly. 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 theirs 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 has no other strategy available that does better than B at maximizing his payoff in response to Alice c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pure Strategy
In game theory, a move, action, or play is any one of the options which a player can choose in a setting where the optimal outcome depends ''not only'' on their own actions ''but'' on the actions of others. The discipline mainly concerns the action of a player in a game affecting the behavior or actions of other players. Some examples of "games" include chess, bridge, poker, monopoly, diplomacy or battleship. The term strategy is typically used to mean a complete algorithm for playing a game, telling a player what to do for every possible situation. A player's strategy determines the action the player will take at any stage of the game. However, the idea of a strategy is often confused or conflated with that of a move or action, because of the correspondence between moves and pure strategies in most games: for any move ''X'', "always play move ''X''" is an example of a valid strategy, and as a result every move can also be considered to be a strategy. Other authors treat strate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 Board (bridge), 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 p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
