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Contract Bridge Probabilities
In the game of bridge mathematical probabilities play a significant role. Different declarer play strategies lead to success depending on the distribution of opponent's cards. To decide which strategy has highest likelihood of success, the declarer needs to have at least an elementary knowledge of probabilities. The tables below specify the various prior probabilities, i.e. the probabilities in the absence of any further information. During bidding and play, more information about the hands becomes available, allowing players to improve their probability estimates. Probability of suit distributions (for missing trumps, etc.) in two hidden hands This table"Mathematical Tables" (Table 4). represents the different ways that two to eight particular cards may be distributed, or may ''lie'' or ''split'', between two unknown 13-card hands (before the bidding and play, or ''a priori''). The table also shows the number of combinations of particular cards that match any numerical split an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prior Probability
In Bayesian statistical inference, a prior probability distribution, often simply called the prior, of an uncertain quantity is the probability distribution that would express one's beliefs about this quantity before some evidence is taken into account. For example, the prior could be the probability distribution representing the relative proportions of voters who will vote for a particular politician in a future election. The unknown quantity may be a parameter of the model or a latent variable rather than an observable variable. Bayes' theorem calculates the renormalized pointwise product of the prior and the likelihood function, to produce the ''posterior probability distribution'', which is the conditional distribution of the uncertain quantity given the data. Similarly, the prior probability of a random event or an uncertain proposition is the unconditional probability that is assigned before any relevant evidence is taken into account. Priors can be created using a num ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Glossary Of Contract Bridge Terms
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 the following entries,'' boldface links ''are external to the glossary and'' plain links ''reference other glossary entries.'' 0–9 ;: A mnemonic for the original (Roman) response structure to the Roman Key Card Blackwood convention. It represents "3 or 0" and "1 or 4", meaning that the lowest step response (5) to the 4NT key card asking bid shows responder has three or zero keycards and the next step (5) shows one or four. ;: A mnemonic for a variant response structure to the Roman Key Card Blackwood convention. It represents "1 or 4" and "3 or 0", meaning that the lowest step response (5) to the 4NT key card asking bid shows responder has one or four keycards and the next step (5) shows three or zero. ;1RF: One round forc ... [...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 four 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. 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, as the lies of some cards become known – especially as the entire distributions of some suits become known – the odds on location of any othe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Permutation
In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set. Permutations differ from combinations, which are selections of some members of a set regardless of order. For example, written as tuples, there are six permutations of the set , namely (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1). These are all the possible orderings of this three-element set. Anagrams of words whose letters are different are also permutations: the letters are already ordered in the original word, and the anagram is a reordering of the letters. The study of permutations of finite sets is an important topic in the fields of combinatorics and group theory. Permutations are used in almost every branch of mathematics, and in many other fields of scie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kronecker Delta
In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers. The function is 1 if the variables are equal, and 0 otherwise: \delta_ = \begin 0 &\text i \neq j, \\ 1 &\text i=j. \end or with use of Iverson brackets: \delta_ = =j, where the Kronecker delta is a piecewise function of variables and . For example, , whereas . The Kronecker delta appears naturally in many areas of mathematics, physics and engineering, as a means of compactly expressing its definition above. In linear algebra, the identity matrix has entries equal to the Kronecker delta: I_ = \delta_ where and take the values , and the inner product of vectors can be written as \mathbf\cdot\mathbf = \sum_^n a_\delta_b_ = \sum_^n a_ b_. Here the Euclidean vectors are defined as -tuples: \mathbf = (a_1, a_2, \dots, a_n) and \mathbf= (b_1, b_2, ..., b_n) and the last step is obtained by using the values of the Kronecker delta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
A Priori Probability
An ''a priori'' probability is a probability that is derived purely by deductive reasoning. One way of deriving ''a priori'' probabilities is the principle of indifference, which has the character of saying that, if there are ''N'' mutually exclusive and collectively exhaustive events and if they are equally likely, then the probability of a given event occurring is 1/''N''. Similarly the probability of one of a given collection of ''K'' events is ''K'' / ''N''. One disadvantage of defining probabilities in the above way is that it applies only to finite collections of events. In Bayesian inference, " uninformative priors" or "objective priors" are particular choices of ''a priori'' probabilities. Note that "prior probability" is a broader concept. Similar to the distinction in philosophy between a priori and a posteriori, in Bayesian inference ''a priori'' denotes general knowledge about the data distribution before making an inference, while ''a posteriori'' denotes knowledge t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
A Priori Probability
An ''a priori'' probability is a probability that is derived purely by deductive reasoning. One way of deriving ''a priori'' probabilities is the principle of indifference, which has the character of saying that, if there are ''N'' mutually exclusive and collectively exhaustive events and if they are equally likely, then the probability of a given event occurring is 1/''N''. Similarly the probability of one of a given collection of ''K'' events is ''K'' / ''N''. One disadvantage of defining probabilities in the above way is that it applies only to finite collections of events. In Bayesian inference, " uninformative priors" or "objective priors" are particular choices of ''a priori'' probabilities. Note that "prior probability" is a broader concept. Similar to the distinction in philosophy between a priori and a posteriori, in Bayesian inference ''a priori'' denotes general knowledge about the data distribution before making an inference, while ''a posteriori'' denotes knowledge t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doubleton
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 the following entries,'' boldface links ''are external to the glossary and'' plain links ''reference other glossary entries.'' 0–9 ;: A mnemonic for the original (Roman) response structure to the Roman Key Card Blackwood convention. It represents "3 or 0" and "1 or 4", meaning that the lowest step response (5) to the 4NT key card asking bid shows responder has three or zero keycards and the next step (5) shows one or four. ;: A mnemonic for a variant response structure to the Roman Key Card Blackwood convention. It represents "1 or 4" and "3 or 0", meaning that the lowest step response (5) to the 4NT key card asking bid shows responder has one or four keycards and the next step (5) shows three or zero. ;1RF: One round forc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Balanced Hand
A balanced hand or balanced distribution in card games is a hand with an even distribution of suits. In the game of contract bridge, it denotes a hand of thirteen cards which contains no singleton or void and at most one . Three hand patterns are classified as truly balanced: 4-3-3-3, 4-4-3-2 and 5-3-3-2. The hand patterns 5-4-2-2 (an example of a two-suiter) and 6-3-2-2 (a single-suiter) are generally referred to as ''semi-balanced''. In natural bidding systems, balanced hands within specified high card point (HCP) ranges are generally opened with a notrump bid, or rebid in notrump. In the Netherlands, a bidding system called ''Saaie klaver'' ("'' Boring club''") that reserves the 1 opening for all balanced hands (''boring hands''), has gained some popularity. See also *Single suiter *Two suiter *Three suiter *Bridge probabilities * Boring club *Kamikaze 1NT Kamikaze 1NT is a preemptive 1NT opening in the game of contract bridge Contract bridge, or simply bridge, is a tric ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Single Suiter
In contract bridge, a single suiter (or single-suited hand) is a hand containing at least six cards in one suit and with all other suits being at least two cards shorter than this longest suit. Many hand patterns can be classified as single suiters. Typical examples are 6-3-2-2, 6-3-3-1 and 7-3-2-1 distribution. Single-suiters form the cornerstone of preemptive bidding. Weak single-suiters with six card length are traditionally opened preemptively at the two level, whilst seven carders are used to preempt at the three level. The modern trend is to lower these minimum length requirements, especially when non-vulnerable. Conventional preemptive openings used to introduce a weak single-suited hand include the multi 2 diamonds and the gambling 3NT conventions. Over an opposing opening, single suiters are usually introduced via a natural overcall. But see also list of defenses to 1NT. See also *Two suiter *Three suiter *Balanced hand *Preempt Preempt (also spelled "pre-empt") i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two Suiter
In contract bridge, a two suiter is a hand containing cards mostly from two of the four suits. Traditionally a hand is considered a two suiter if it contains at least ten cards in two suits, with the two suits not differing in length by more than one card. Depending on suit quality and partnership agreement different classification schemes are viable. The more modern trend is to lower the threshold of ten cards to nine cards and consider 5-4 distributions also two suiters. The six possible combinations are given the names "major suits" (spades and hearts), "minor suits" (diamonds and clubs), " black suits" (spades and clubs), " red suits" (hearts and diamonds), " pointed suits" (spades and diamonds), and " rounded suits" (hearts and clubs). When including two suited hands with 5-4 distribution, two suiters have a high likelihood of occurrence, and the modern preemptive style is to incorporate such two-suited hands in the arsenal of preemptive openings. Example of such a preemp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
