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Gambling And Information Theory
Statistical inference might be thought of as gambling theory applied to the world around us. The myriad applications for logarithmic information measures tell us precisely how to take the best guess in the face of partial information. In that sense, information theory might be considered a formal expression of the theory of gambling. It is no surprise, therefore, that information theory has applications to games of chance. Kelly Betting Kelly betting or proportional betting is an application of information theory to investing and gambling. Its discoverer was John Larry Kelly, Jr. Part of Kelly's insight was to have the gambler maximize the expectation of the ''logarithm'' of his capital, rather than the expected profit from each bet. This is important, since in the latter case, one would be led to gamble all he had when presented with a favorable bet, and if he lost, would have no capital with which to place subsequent bets. Kelly realized that it was the logarithm of the ga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayesian Inference
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" derive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Odds
In probability theory, odds provide a measure of the probability of a particular outcome. Odds are commonly used in gambling and statistics. For example for an event that is 40% probable, one could say that the odds are or When gambling, odds are often given as the ratio of the possible net profit ''to'' the possible net loss. However in many situations, you pay the possible loss ("stake" or "wager") up front and, if you win, you are paid the net win plus you also get your stake returned. So wagering 2 at , pays out , which is called When Moneyline odds are quoted as a positive number , it means that a wager pays When Moneyline odds are quoted as a negative number , it means that a wager pays Odds have a simple relationship with probability. When probability is expressed as a number between 0 and 1, the relationships between probability and odds are as follows. Note that if probability is to be expressed as a percentage these probability values should be multiplied ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wagering
Gambling (also known as betting or gaming) is the wagering of something of value ("the stakes") on a random event with the intent of winning something else of value, where instances of strategy are discounted. Gambling thus requires three elements to be present: consideration (an amount wagered), risk (chance), and a prize. The outcome of the wager is often immediate, such as a single roll of dice, a spin of a roulette wheel, or a horse crossing the finish line, but longer time frames are also common, allowing wagers on the outcome of a future sports contest or even an entire sports season. The term "gaming" in this context typically refers to instances in which the activity has been specifically permitted by law. The two words are not mutually exclusive; ''i.e.'', a "gaming" company offers (legal) "gambling" activities to the public and may be regulated by one of many gaming control boards, for example, the Nevada Gaming Control Board. However, this distinction is not univer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Advanced NFL Stats
Advanced Football Analytics (formerly Advanced NFL Stats) was a website dedicated to the analysis of the National Football League (NFL) using mathematical and statistical methods. The site's lead author was noted football researcher and analyst Brian Burke. Burke is a regular contributor to ''The New York Times'' NFL coverage, ''The Washington Post''s Commanders coverage, and supplies research for other notable publications and writers. Advanced Football Analytics features a variety of analytical techniques and applications. The site predicts game outcomes and rates teams using a logistic regression model based on team efficiency statistics. It also features a live in-game win probability model that estimates the chances either opponent will win a game in progress. Advanced Football Analytics uses its win probability model to analyze strategic coaching decisions such as whether to kick or attempt first down conversions. Research topics include game theory applications, luck and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Association Football Predictions
Statistical association football prediction is a method used in sports betting to predict the outcome of football matches by means of statistical tools. The goal of statistical match prediction is to outperform the predictions of bookmakers, who use them to set odds on the outcome of football matches. The most widely used statistical approach to prediction is ranking. Football ranking systems assign a rank to each team based on their past game results, so that the highest rank is assigned to the strongest team. The outcome of the match can be predicted by comparing the opponents’ ranks. Several different football ranking systems exist, for example some widely known are the FIFA World Rankings or the World Football Elo Ratings. There are three main drawbacks to football match predictions that are based on ranking systems: # Ranks assigned to the teams do not differentiate between their attacking and defensive strengths. # Ranks are accumulated averages which do not account for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Principle Of Indifference
The principle of indifference (also called principle of insufficient reason) is a rule for assigning epistemic probabilities. The principle of indifference states that in the absence of any relevant evidence, agents should distribute their credence (or "degrees of belief") equally among all the possible outcomes under consideration. In Bayesian probability, this is the simplest non-informative prior. Examples The textbook examples for the application of the principle of indifference are coins, dice, and cards. In a macroscopic system, at least, it must be assumed that the physical laws that govern the system are not known well enough to predict the outcome. As observed some centuries ago by John Arbuthnot (in the preface of ''Of the Laws of Chance'', 1692), :It is impossible for a Die, with such determin'd force and direction, not to fall on such determin'd side, only I don't know the force and direction which makes it fall on such determin'd side, and therefore I call it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Efficient-market Hypothesis
The efficient-market hypothesis (EMH) is a hypothesis in financial economics that states that asset prices reflect all available information. A direct implication is that it is impossible to "beat the market" consistently on a risk-adjusted basis since market prices should only react to new information. Because the EMH is formulated in terms of risk adjustment, it only makes testable predictions when coupled with a particular model of risk. As a result, research in financial economics since at least the 1990s has focused on market anomalies, that is, deviations from specific models of risk. The idea that financial market returns are difficult to predict goes back to Bachelier, Mandelbrot, and Samuelson, but is closely associated with Eugene Fama, in part due to his influential 1970 review of the theoretical and empirical research. The EMH provides the basic logic for modern risk-based theories of asset prices, and frameworks such as consumption-based asset pricing and int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Walk
In mathematics, a random walk, sometimes known as a drunkard's walk, is a stochastic process that describes a path that consists of a succession of random steps on some Space (mathematics), mathematical space. An elementary example of a random walk is the random walk on the integer number line \mathbb Z which starts at 0, and at each step moves +1 or −1 with equal probability. Other examples include the path traced by a molecule as it travels in a liquid or a gas (see Brownian motion), the search path of a foraging animal, or the price of a fluctuating random walk hypothesis, stock and the financial status of a gambler. Random walks have applications to engineering and many scientific fields including ecology, psychology, computer science, physics, chemistry, biology, economics, and sociology. The term ''random walk'' was first introduced by Karl Pearson in 1905. Realizations of random walks can be obtained by Monte Carlo Simulation, Monte Carlo simulation. Lattice random ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Self-information
In information theory, the information content, self-information, surprisal, or Shannon information is a basic quantity derived from the probability of a particular event occurring from a random variable. It can be thought of as an alternative way of expressing probability, much like odds or log-odds, but which has particular mathematical advantages in the setting of information theory. The Shannon information can be interpreted as quantifying the level of "surprise" of a particular outcome. As it is such a basic quantity, it also appears in several other settings, such as the length of a message needed to transmit the event given an optimal source coding of the random variable. The Shannon information is closely related to ''entropy'', which is the expected value of the self-information of a random variable, quantifying how surprising the random variable is "on average". This is the average amount of self-information an observer would expect to gain about a random variable wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gambler's Ruin
In statistics, gambler's ruin is the fact that a gambling, gambler playing a game with negative expected value will eventually go Bankruptcy, bankrupt, regardless of their betting system. The concept was initially stated: A persistent gambler who raises his bet to a fixed fraction of the gambler's bankroll after a win, but does not reduce it after a loss, will eventually and inevitably go broke, even if each bet has a positive expected value. Another statement of the concept is that a persistent gambler with finite wealth, playing a fair game (that is, each bet has expected value of zero to both sides) will eventually and inevitably go broke against an opponent with infinite wealth. Such a situation can be modeled by a random walk on the real number line. In that context, it is probable that the gambler will, with virtual certainty, return to their point of origin, which means going broke, and is ruined an infinite number of times if the random walk continues forever. This is a c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
