|
Cribbage Statistics
In cribbage, the probability and maximum and minimum score of each type of hand can be computed. Distinct hands * There are 12,994,800 possible hands in Cribbage: 52 choose 4 for the hand, and any one of the 48 left as the starter card. \times 48 = 12,994,800 *Another, and perhaps more intuitive way of looking at it, is to say that there are 52 choose 5 different 5-card hands, and any one of those 5 could be the turn-up, or starter card. Therefore, the calculation becomes: \times 5 = 12,994,800 * 1,009,008 (approximately 7.8%) of these score zero points, or 1,022,208 if the hand is the crib, as the starter must be the same suit as the crib's four cards for a flush. * Not accounting for suit, there are 14,715 unique hands. Maximum scores * The highest score for one hand is 29: 555J in hand with the starter 5 of the same suit as the Jack (8 points for four J-5 combinations, 8 points for four 5-5-5 combinations, 12 points for pairs of 5s and one for the nob). There is also the â ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cribbage
Cribbage, or crib, is a card game, traditionally for two players, that involves playing and grouping cards in combinations which gain points. It can be adapted for three or four players. Cribbage has several distinctive features: the cribbage board used for score-keeping, the eponymous ''crib'', ''box'', or ''kitty'' (in parts of Canada)âa separate hand counting for the dealerâtwo distinct scoring stages (the play and the show) and a unique scoring system including points for groups of cards that total fifteen. It has been characterized as "Britain's national card game" and the only one legally playable on licensed premises (pubs and clubs) without requiring local authority permission. The game has relatively few rules yet yields endless subtleties during play, which accounts for its ongoing appeal and popularity. Tactical play varies, depending on which cards one's opponent has played, how many cards in the remaining pack will help the hand one holds, and what one's pos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MathWorld
''MathWorld'' is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc. and was partially funded by the National Science Foundation's National Science Digital Library grant to the University of Illinois at UrbanaâChampaign. History Eric W. Weisstein, the creator of the site, was a physics and astronomy student who got into the habit of writing notes on his mathematical readings. In 1995 he put his notes online and called it "Eric's Treasure Trove of Mathematics." It contained hundreds of pages/articles, covering a wide range of mathematical topics. The site became popular as an extensive single resource on mathematics on the web. Weisstein continuously improved the notes and accepted corrections and comments from online readers. In 1998, he made a contract with CRC Press and the contents of the site were published in print and CD-ROM form, titled "CRC Concise Encyclopedia of Mathematic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mean
There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value (magnitude and sign) of a given data set. For a data set, the ''arithmetic mean'', also known as "arithmetic average", is a measure of central tendency of a finite set of numbers: specifically, the sum of the values divided by the number of values. The arithmetic mean of a set of numbers ''x''1, ''x''2, ..., x''n'' is typically denoted using an overhead bar, \bar. If the data set were based on a series of observations obtained by sampling from a statistical population, the arithmetic mean is the ''sample mean'' (\bar) to distinguish it from the mean, or expected value, of the underlying distribution, the ''population mean'' (denoted \mu or \mu_x).Underhill, L.G.; Bradfield d. (1998) ''Introstat'', Juta and Company Ltd.p. 181/ref> Outside probability and statistics, a wide range of other notions of mean are o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard Deviation
In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range. Standard deviation may be abbreviated SD, and is most commonly represented in mathematical texts and equations by the lower case Greek letter Ï (sigma), for the population standard deviation, or the Latin letter '' s'', for the sample standard deviation. The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance. It is algebraically simpler, though in practice less robust, than the average absolute deviation. A useful property of the standard deviation is that, unlike the variance, it is expressed in the same unit as the data. The standard deviation of a popu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Skewness
In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. The skewness value can be positive, zero, negative, or undefined. For a unimodal distribution, negative skew commonly indicates that the ''tail'' is on the left side of the distribution, and positive skew indicates that the tail is on the right. In cases where one tail is long but the other tail is fat, skewness does not obey a simple rule. For example, a zero value means that the tails on both sides of the mean balance out overall; this is the case for a symmetric distribution, but can also be true for an asymmetric distribution where one tail is long and thin, and the other is short but fat. Introduction Consider the two distributions in the figure just below. Within each graph, the values on the right side of the distribution taper differently from the values on the left side. These tapering sides are called ''tail ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Excess Kurtosis
In probability theory and statistics, kurtosis (from el, ÎșÏ ÏÏÏÏ, ''kyrtos'' or ''kurtos'', meaning "curved, arching") is a measure of the "tailedness" of the probability distribution of a real-valued random variable. Like skewness, kurtosis describes a particular aspect of a probability distribution. There are different ways to quantify kurtosis for a theoretical distribution, and there are corresponding ways of estimating it using a sample from a population. Different measures of kurtosis may have different interpretations. The standard measure of a distribution's kurtosis, originating with Karl Pearson, is a scaled version of the fourth moment of the distribution. This number is related to the tails of the distribution, not its peak; hence, the sometimes-seen characterization of kurtosis as "peakedness" is incorrect. For this measure, higher kurtosis corresponds to greater extremity of deviations (or outliers), and not the configuration of data near the mean. It is co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Median
In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value. The basic feature of the median in describing data compared to the mean (often simply described as the "average") is that it is not skewed by a small proportion of extremely large or small values, and therefore provides a better representation of a "typical" value. Median income, for example, may be a better way to suggest what a "typical" income is, because income distribution can be very skewed. The median is of central importance in robust statistics, as it is the most resistant statistic, having a breakdown point of 50%: so long as no more than half the data are contaminated, the median is not an arbitrarily large or small result. Finite data set of numbers The median of a finite list of numbers is the "middle" number, when those numbers are list ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mode (statistics)
The mode is the value that appears most often in a set of data values. If is a discrete random variable, the mode is the value (i.e, ) at which the probability mass function takes its maximum value. In other words, it is the value that is most likely to be sampled. Like the statistical mean and median, the mode is a way of expressing, in a (usually) single number, important information about a random variable or a population. The numerical value of the mode is the same as that of the mean and median in a normal distribution, and it may be very different in highly skewed distributions. The mode is not necessarily unique to a given discrete distribution, since the probability mass function may take the same maximum value at several points , , etc. The most extreme case occurs in uniform distributions, where all values occur equally frequently. When the probability density function of a continuous distribution has multiple local maxima it is common to refer to all of the local ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cribbage (rules)
The rules here are based on those of the American Cribbage Congress and apply to two-, three- or four-player games, with details of variations being listed below. The deal Cribbage uses a standard 52-card deck of cards. The jokers are removed; the suits are equal in status. The players cut for first deal, with the player cutting the lowest card (the ace counts as one, and is the lowest card) dealing first. If the cutters tie, the cards are re-shuffled and re-cut. The deal then alternates from hand to hand. Note that because the crib (explained below) belongs to the dealer, winning the first deal confers a scoring advantage: if the game ends in an odd number of deals, the first dealer will have received an extra crib, sometimes enough to decide the game. The dealer shuffles, offers the deck to the player on their right to cut (required in tournament play), and deals cards singly to each player, starting with the player on the dealer's left. For two players, each is dealt six cards ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cribbage
Cribbage, or crib, is a card game, traditionally for two players, that involves playing and grouping cards in combinations which gain points. It can be adapted for three or four players. Cribbage has several distinctive features: the cribbage board used for score-keeping, the eponymous ''crib'', ''box'', or ''kitty'' (in parts of Canada)âa separate hand counting for the dealerâtwo distinct scoring stages (the play and the show) and a unique scoring system including points for groups of cards that total fifteen. It has been characterized as "Britain's national card game" and the only one legally playable on licensed premises (pubs and clubs) without requiring local authority permission. The game has relatively few rules yet yields endless subtleties during play, which accounts for its ongoing appeal and popularity. Tactical play varies, depending on which cards one's opponent has played, how many cards in the remaining pack will help the hand one holds, and what one's pos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
