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Principle Of Restricted Choice
The principle of restricted choice is a guideline used in card games such as contract bridge to intuit hidden information. It may be stated as "The play of a card which may have been selected as a choice of equal plays increases the chance that the player started with a holding in which his choice was restricted." Crucially, it helps play "in situations which used to be thought of as guesswork." For example, South leads a low spade, West plays a low one, North plays the queen, East wins with the king. The ace and king are equivalent cards; East's play of the king decreases the probability East holds the ace – and increases the probability West holds the ace. The principle helps other players infer the locations of unobserved equivalent cards such as that spade ace after observing the king. The increase or decrease in probability is an example of Bayesian updating as evidence accumulates and particular applications of restricted choice are similar to the Monty Hall problem. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contract Bridge
Contract bridge, or simply bridge, is a trick-taking game, trick-taking card game using a standard 52-card deck. In its basic format, it is played by four players in two Team game, competing partnerships, with partners sitting opposite each other around a table. Millions of people play bridge worldwide in clubs, bridge tournaments, tournaments, online and with friends at home, making it one of the world's most popular card games, particularly among Old Age, 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 to the players; then the players ''call'' (or ''bid'') in an 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 exchange infor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jeff Rubens
Jeff Rubens (born 1941) is an American contract bridge, bridge player, editor, and writer of books including ''Secrets of Winning Bridge'' and ''Expert Bridge Simplified''. He is best known for long association with ''The Bridge World'' monthly magazine, as co-editor under Edgar Kaplan from 1967 and as editor and publisher since Kaplan's death in 1997. Rubens is from Brooklyn, New York. Life Rubens attended Stuyvesant High School in New York City, where he was captain of the math team in 1957, the year he graduated. He has an undergraduate degree from Cornell University and a graduate degree from Brandeis University. He won seven North American championship events in the 1960s-70s, represented North America in the 1973 world championship, and "gave up competitive bridge for family reasons" soon after. Rubens is a retired professor of mathematics and computer science at Pace University in New York. Competition Rubens became an ACBL Life Master at 20 and won two North American c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayesian Updating
Bayesian inference ( or ) is a method of statistical inference in which Bayes' theorem is used to calculate a probability of a hypothesis, given prior evidence, and update it as more information becomes available. Fundamentally, Bayesian inference uses a prior distribution to estimate posterior probabilities. Bayesian inference is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is particularly important in the dynamic analysis of a sequence of data. Bayesian inference has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law. In the philosophy of decision theory, Bayesian inference is closely related to subjective probability, often called "Bayesian probability". Introduction to Bayes' rule Formal explanation Bayesian inference derives the posterior probability as a consequence of two antecedents: a prior probability and a "likelihood function" derived from ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monty Hall Problem
The Monty Hall problem is a brain teaser, in the form of a probability puzzle, based nominally on the American television game show ''Let's Make a Deal'' and named after its original host, Monty Hall. The problem was originally posed (and solved) in a letter by Steve Selvin to the ''The American Statistician, American Statistician'' in 1975. It became famous as a question from reader Craig F. Whitaker's letter quoted in Marilyn vos Savant's "Ask Marilyn" column in ''Parade (magazine), Parade'' magazine in 1990: Savant's response was that the contestant should switch to the other door. By the standard assumptions, the switching strategy has a probability of winning the car, while the strategy of keeping the initial choice has only a probability. When the player first makes their choice, there is a chance that the car is behind one of the doors not chosen. This probability does not change after the host reveals a goat behind one of the unchosen doors. When the host provides i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Suit Combination
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 combination ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
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] |
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] |
Bayes' Theorem
Bayes' theorem (alternatively Bayes' law or Bayes' rule, after Thomas Bayes) gives a mathematical rule for inverting Conditional probability, conditional probabilities, allowing one to find the probability of a cause given its effect. For example, if the risk of developing health problems is known to increase with age, Bayes' theorem allows the risk to someone of a known age to be assessed more accurately by conditioning it relative to their age, rather than assuming that the person is typical of the population as a whole. Based on Bayes' law, both the prevalence of a disease in a given population and the error rate of an infectious disease test must be taken into account to evaluate the meaning of a positive test result and avoid the ''base-rate fallacy''. One of Bayes' theorem's many applications is Bayesian inference, an approach to statistical inference, where it is used to invert the probability of Realization (probability), observations given a model configuration (i.e., th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alan Truscott
Alan Fraser Truscott (16 April 1925 – 4 September 2005) was a British-American bridge player, writer, and editor. He wrote the daily bridge column for ''The New York Times'' for 41 years, from 1964 to 2005, and served as Executive Editor for the first six editions of ''The Official Encyclopedia of Bridge'' from 1964 to 2002. Britain Truscott was born in Brixton, south London, and showed early prowess at chess. He attended Whitgift School in Croydon and served in the Royal Navy for three years around the end of World War II. From 1947, Truscott studied at Oxford, which he represented at both chess and bridge. With Oxford partner Robert d'Unienville, he was on the British team (along with Terence Reese and Boris Schapiro) that won a bronze medal at the 1951 European Bridge League championships, age only 26. Truscott represented Britain in the same event twice more, finishing second with partner Maurice Harrison-Gray in 1958 (again along with Reese–Schapiro) and first w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contract Bridge Card Play
A contract is an agreement that specifies certain legally enforceable rights and obligations pertaining to two or more parties. A contract typically involves consent to transfer of goods, services, money, or promise to transfer any of those at a future date. The activities and intentions of the parties entering into a contract may be referred to as contracting. In the event of a breach of contract, the injured party may seek judicial remedies such as damages or equitable remedies such as specific performance or rescission. A binding agreement between actors in international law is known as a treaty. Contract law, the field of the law of obligations concerned with contracts, is based on the principle that agreements must be honoured. Like other areas of private law, contract law varies between jurisdictions. In general, contract law is exercised and governed either under common law jurisdictions, civil law jurisdictions, or mixed-law jurisdictions that combine elements of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
