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Gambling Mathematics
The mathematics of gambling is a collection of probability applications encountered in Game of chance, games of chance and can be included in game theory. From a mathematical point of view, the games of chance are experiments generating various types of aleatory events, and it is possible to calculate by using the properties of probability on a finite space of possibilities. Experiments, events, and probability spaces The technical processes of a game stand for experiments that generate aleatory events. Here are a few examples: The occurrences could be defined; however, when formulating a probability problem, they must be done extremely carefully. From a mathematical point of view, the events are nothing more than subsets, and the space of events is a Boolean algebra. We find elementary and compound events, exclusive and nonexclusive events, and independent and non-independent events. In the experiment of rolling a die: * Event (whose literal definition is the occurrence of 3 o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spanish 21
Spanish 21 is a blackjack variant owned by Masque Publishing Inc., a gaming publishing company based in Colorado. Unlicensed, but equivalent, versions may be called Spanish blackjack. In Australia and Malaysia, an unlicensed version of the game, with no dealer hole card and significant rule differences, is played in casinos under the name " Pontoon". It was first introduced about 1995. Rules Spanish 21 is played on a blackjack table with a custom layout and uses the following rules: * The game is played with six or eight decks dealt from a shoe, or from a continuous shuffling machine (CSM). Spanish 21 is played with 48-card Spanish decks, although standard French suited 52-card decks are used with the 4 ten-spot cards removed. All cards have the same values as in blackjack. * The dealer gets a hole card. * Like traditional blackjack, the dealer hits on 16 and stands on 17. In some venues, the dealer hits on a soft 17 (abbreviated as H17), though most venues have the dealer stand ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poker Probability
In poker, the probability of each type of 5-card poker hand, hand can be computed by calculating the proportion of hands of that type among all possible hands. History Probability and gambling have been ideas since long before the invention of poker. The development of probability theory in the late 1400s was attributed to gambling; when playing a game with high stakes, players wanted to know what the chance of winning would be. In 1494, Fra Luca Pacioli released his work which was the first written text on probability. Motivated by Pacioli's work, Girolamo Cardano (1501-1576) made further developments in probability theory. His work from 1550, titled ''Liber de Ludo Aleae'', discussed the concepts of probability and how they were directly related to gambling. However, his work did not receive any immediate recognition since it was not published until after his death. Blaise Pascal (1623-1662) also contributed to probability theory. His friend, Chevalier de Méré, was an avid ga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Of Bookmaking
In gambling parlance, making a book is the practice of laying bets on the various possible outcomes of a single event. The phrase originates from the practice of recording such wagers in a hard-bound ledger (the "book") and gives the English language the term bookmaker for the person laying the bets and thus "making the book". Making a "book" (and the notion of overround) A bookmaker strives to accept bets on the outcome of an event in the right proportions in order to make a profit regardless of which outcome prevails. See Dutch book and coherence (philosophical gambling strategy). This is achieved primarily by adjusting what are determined to be the true odds of the various outcomes of an event in a downward fashion (i.e. the bookmaker will pay out using his actual odds, an amount which is less than the true odds would have paid, thus ensuring a profit). The odds quoted for a particular event may be fixed but are more likely to fluctuate in order to take account of the size of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mutually Exclusive
In logic and probability theory, two events (or propositions) are mutually exclusive or disjoint if they cannot both occur at the same time. A clear example is the set of outcomes of a single coin toss, which can result in either heads or tails, but not both. In the coin-tossing example, both outcomes are, in theory, collectively exhaustive, which means that at least one of the outcomes must happen, so these two possibilities together exhaust all the possibilities. However, not all mutually exclusive events are collectively exhaustive. For example, the outcomes 1 and 4 of a single roll of a six-sided die are mutually exclusive (both cannot happen at the same time) but not collectively exhaustive (there are other possible outcomes; 2,3,5,6). Logic In logic, two propositions \phi and \psi are mutually exclusive if it is not logically possible for them to be true at the same time; that is, \lnot (\phi \land \psi) is a tautology. To say that more than two propositions are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expected Value
In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first Moment (mathematics), moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean, 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 Integral, 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 a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Online Bingo
Online bingo is the game of bingo (either the US or UK variant) played on the Internet. Sites offering the game launched around 1996, and the global gross gaming yield outside of the United States was estimated at US$500 million in 2006, forecast to grow to $1 billion by 2010. Unlike physical balls used in regular bingo halls, online bingo sites use a random number generator. Most bingo halls also offer links to online poker and casino offerings as the patrons are often in the target market. One notable feature of online bingo is the chat functionality, with sites striving to foster a sense of community and interaction between players to assist customer retention. History One of the earliest known online bingo games, launched in 1996, was a free bingo game called "Bingo Zone". To play, members had to provide demographic information; in turn, members would receive targeted ads based on the demographics provided. Another early pioneer for free online bingo was Uproar, which launc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Slot Machine
A slot machine, fruit machine (British English), poker machine or pokie (Australian English and New Zealand English) is a gambling machine that creates a game of chance for its customers. A slot machine's standard layout features a screen displaying three or more reels that "spin" when the game is activated. Some modern slot machines still include a lever as a skeuomorphic design trait to trigger play. However, the mechanical operations of early machines have been superseded by random number generators, and most are now operated using buttons and touchscreens. Slot machines include one or more currency detectors that validate the form of payment, whether coin, banknote, voucher, or token. The machine pays out according to the pattern of symbols displayed when the reels stop "spinning". Slot machines are the most popular gambling method in casinos and contribute about 70% of the average U.S. casino's income. Digital technology has resulted in variations in the original slo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Three Sigma Rule
3 (three) is a number, numeral and digit. It is the natural number following 2 and preceding 4, and is the smallest odd prime number and the only prime preceding a square number. It has religious and cultural significance in many societies. Evolution of the Arabic digit The use of three lines to denote the number 3 occurred in many writing systems, including some (like Roman and Chinese numerals) that are still in use. That was also the original representation of 3 in the Brahmic (Indian) numerical notation, its earliest forms aligned vertically. However, during the Gupta Empire the sign was modified by the addition of a curve on each line. The Nāgarī script rotated the lines clockwise, so they appeared horizontally, and ended each line with a short downward stroke on the right. In cursive script, the three strokes were eventually connected to form a glyph resembling a with an additional stroke at the bottom: ३. The Indian digits spread to the Caliphate in the 9th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal Distribution
In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is f(x) = \frac e^\,. The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter \sigma^2 is the variance. The standard deviation of the distribution is (sigma). A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. Their importance is partly due to the central limit theorem. It states that, under some conditions, the average of many samples (observations) of a random variable with finite mean and variance is itself a random variable—whose distribution c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binomial Distribution
In probability theory and statistics, the binomial distribution with parameters and is the discrete probability distribution of the number of successes in a sequence of statistical independence, independent experiment (probability theory), experiments, each asking a yes–no question, and each with its own Boolean-valued function, Boolean-valued outcome (probability), outcome: ''success'' (with probability ) or ''failure'' (with probability ). A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a sequence of outcomes is called a Bernoulli process; for a single trial, i.e., , the binomial distribution is a Bernoulli distribution. The binomial distribution is the basis for the binomial test of statistical significance. The binomial distribution is frequently used to model the number of successes in a sample of size drawn with replacement from a population of size . If the sampling is carried out without replacement, the draws ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard Deviation
In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its Expected value, mean. A low standard Deviation (statistics), 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. The standard deviation is commonly used in the determination of what constitutes an outlier and what does not. Standard deviation may be abbreviated SD or std dev, and is most commonly represented in mathematical texts and equations by the lowercase Greek alphabet, Greek letter Sigma, σ (sigma), for the population standard deviation, or the Latin script, Latin letter ''s'', for the sample standard deviation. The standard deviation of a random variable, Sample (statistics), sample, statistical population, data set, or probability distribution is the square root of its variance. (For a finite population, v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
