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Proebsting's Paradox
In probability theory, Proebsting's paradox is an argument that appears to show that the Kelly criterion can lead to ruin. Although it can be resolved mathematically, it raises some interesting issues about the practical application of Kelly, especially in investing. It was named and first discussed by Edward O. Thorp in 2008.E. O. Thorp, Understanding the Kelly Criterion: Part II, Wilmott Magazine, September 2008 The paradox was named for Todd Proebsting, its creator. Statement of the paradox If a bet is equally likely to win or lose, and pays b times the stake for a win, the Kelly bet is: : f^ = \frac \! times wealth.J. L. Kelly, Jr, A New Interpretation of Information Rate, Bell System Technical Journal, 35, (1956), 917–926 For example, if a 50/50 bet pays 2 to 1, Kelly says to bet 25% of wealth. If a 50/50 bet pays 5 to 1, Kelly says to bet 40% of wealth. Now suppose a gambler is offered 2 to 1 payout and bets 25%. What should he do if the payout on new bets cha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theory
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms of probability, axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure (mathematics), measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event (probability theory), event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of determinism, non-deterministic or uncertain processes or measured Quantity, quantities that may either be single occurrences or evolve over time in a random fashion). Although it is no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kelly Criterion
In probability theory, the Kelly criterion (or Kelly strategy or Kelly bet) is a formula for sizing a sequence of bets by maximizing the long-term expected value of the logarithm of wealth, which is equivalent to maximizing the long-term expected Geometric mean, geometric growth rate. John Larry Kelly Jr., a researcher at Bell Labs, described the criterion in 1956. The practical use of the formula has been demonstrated for gambling, and the same idea was used to explain Diversification (finance), diversification in investment management., page 184f. In the 2000s, Kelly-style analysis became a part of mainstream investment theory and the claim has been made that well-known successful investors including Warren Buffett and William H. Gross, Bill Gross use Kelly methods. Also see intertemporal portfolio choice. It is also the standard replacement of Power of a test, statistical power in anytime-valid statistical tests and confidence intervals, based on E-values, e-values and e-proc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edward O
Edward is an English male name. It is derived from the Anglo-Saxon name ''Ēadweard'', composed of the elements '' ēad'' "wealth, fortunate; prosperous" and '' weard'' "guardian, protector”. History The name Edward was very popular in Anglo-Saxon England, but the rule of the Norman and Plantagenet dynasties had effectively ended its use amongst the upper classes. The popularity of the name was revived when Henry III named his firstborn son, the future Edward I, as part of his efforts to promote a cult around Edward the Confessor, for whom Henry had a deep admiration. Variant forms The name has been adopted in the Iberian peninsula since the 15th century, due to Edward, King of Portugal, whose mother was English. The Spanish/Portuguese forms of the name are Eduardo and Duarte. Other variant forms include French Édouard, Italian Edoardo and Odoardo, German, Dutch, Czech and Romanian Eduard and Scandinavian Edvard. Short forms include Ed, Eddy, Eddie, Ted, Teddy an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Todd Proebsting
Todd or Todds may refer to: Places Australia * Todd River, an ephemeral river United States * Todd Valley, California, also known as Todd, an unincorporated community * Todd, Missouri, a ghost town * Todd, North Carolina, an unincorporated community * Todd Creek (Missouri), a stream in Platte County, Missouri * Todd Creek, Colorado, a Census-designated place in Adams County, Colorado * Todd County, Kentucky * Todd County, Minnesota * Todd County, South Dakota * Todd Fork, a river in Ohio * Todd Township, Minnesota * Todd Township, Fulton County, Pennsylvania * Todd Township, Huntingdon County, Pennsylvania * Todds, Ohio, an unincorporated community People * Todd (given name) * Todd (surname) Arts and entertainment * ''Todd'' (album), a 1974 album by Todd Rundgren * Todd (''Cars''), a character in ''Cars'' * Todd (''Stargate''), a recurring character in the series ''Stargate Atlantis'' * The Todd (''Scrubs''), a character on ''Scrubs'' * Todd, a character in ''Live w ... [...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] |
Aaron Brown (financial Author)
Aaron C. Brown (born November 27, 1956) is an American finance practitioner, well known as an authorStephen Schurr, , Financial Times, March 20, 2006 on and gambling-related issues. He also speaks frequently at professional and academic conferences. He was Chief Risk Manager at AQR Capital Management. He was one of the original developers of |
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] |
Information Theory
Information theory is the mathematical study of the quantification (science), quantification, Data storage, storage, and telecommunications, communication of information. The field was established and formalized by Claude Shannon in the 1940s, though early contributions were made in the 1920s through the works of Harry Nyquist and Ralph Hartley. It is at the intersection of electronic engineering, mathematics, statistics, computer science, Neuroscience, neurobiology, physics, and electrical engineering. A key measure in information theory is information entropy, entropy. Entropy quantifies the amount of uncertainty involved in the value of a random variable or the outcome of a random process. For example, identifying the outcome of a Fair coin, fair coin flip (which has two equally likely outcomes) provides less information (lower entropy, less uncertainty) than identifying the outcome from a roll of a dice, die (which has six equally likely outcomes). Some other important measu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Paradoxes
Statistics (from German: ', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments. When census data (comprising every member of the target population) cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An experimental study involves taking measurements of the sy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
