Independent Chip Model

picture info	Independent Chip Model In poker, the Independent Chip Model (ICM), also known as the Malmuth–Harville method, is a mathematical model that approximates a player's overall equity in an incomplete tournament. David Harville first developed the model in a 1973 paper on horse racing; in 1987, Mason Malmuth independently rediscovered it for poker. In the ICM, all players have comparable skill, so that current stack sizes entirely determine the probability distribution for a player's final ranking. The model then approximates this probability distribution and computes expected prize money. Poker players often use the term ICM to mean a simulator that helps a player strategize a tournament. An ICM can be applied to answer specific questions, such as: * The range of hands that a player can move all in with, considering the play so far * The range of hands that a player can call another player's all in with or move all in over the top; and which course of action is optimal, considering the remaining op ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Poker Poker is a family of Card game#Comparing games, comparing card games in which Card player, players betting (poker), wager over which poker hand, hand is best according to that specific game's rules. It is played worldwide, with varying rules in different places. While the earliest known form of the game was played with just 20 cards, today it is usually played with a standard 52-card deck, although in countries where short packs are common, it may be played with 32, 40 or 48 cards.Parlett (2008), pp. 568–570. Thus poker games vary in deck configuration, the number of cards in play, the number Poker dealer, dealt face up or face down and the number Community card poker, shared by all players, but all have rules that involve one or more rounds of Betting in poker, betting. In most modern poker games, the first round of betting begins with one or more of the players making some form of a forced bet (the ''blind (poker), blind'' or ''ante''). In standard poker, each player bets a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Computationally Intractable In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and explores the relationships between these classifications. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used. The theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantifying their computational complexity, i.e., the amount of resources needed to solve them, such as time and storage. Other measures of complexity are also used, such as the amount of communication (used in communication complexity), the number of gates in a circuit (used in circuit complexity) and the number of processors (used in parallel computing). One of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Relative Error The approximation error in a given data value represents the significant discrepancy that arises when an exact, true value is compared against some approximation derived for it. This inherent error in approximation can be quantified and expressed in two principal ways: as an absolute error, which denotes the direct numerical magnitude of this discrepancy irrespective of the true value's scale, or as a relative error, which provides a scaled measure of the error by considering the absolute error in proportion to the exact data value, thus offering a context-dependent assessment of the error's significance. An approximation error can manifest due to a multitude of diverse reasons. Prominent among these are limitations related to computing machine precision, where digital systems cannot represent all real numbers with perfect accuracy, leading to unavoidable truncation or rounding. Another common source is inherent measurement error, stemming from the practical limitations of inst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Extreme Point In mathematics, an extreme point of a convex set S in a Real number, real or Complex number, complex vector space is a point in S that does not lie in any open line segment joining two points of S. The extreme points of a line segment are called its ''endpoint (geometry), endpoints''. In linear programming problems, an extreme point is also called ''vertex (geometry), vertex'' or ''corner point'' of S. Definition Throughout, it is assumed that X is a Real number, real or Complex number, complex vector space. For any p, x, y \in X, say that p x and y if x \neq y and there exists a 0 < t < 1 such that $p = t x + (1-t) y.$ If $K$ is a subset of $X$ and $p \in K,$ then $p$ is called an of $K$ if it does not lie between any two points of $K.$ That is, if there does exist $x, y \in K$ and $0 < t < 1$ such that $x \neq y$ and $p = t x + (1-t) y.$ The s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Finite Element Method Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. Computers are usually used to perform the calculations required. With high-speed supercomputers, better solutions can be achieved and are often required to solve the largest and most complex problems. FEM is a general numerical method for solving partial differential equations in two- or three-space variables (i.e., some boundary value problems). There are also studies about using FEM to solve high-dimensional problems. To solve a problem, FEM subdivides a large system into smaller, simpler parts called finite elements. This is achieved by a particular space discretization in the space dimensions, which is implemented by the construction of a mesh of the object: the numer ... [...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]
picture info	Conditional Probability In probability theory, conditional probability is a measure of the probability of an Event (probability theory), event occurring, given that another event (by assumption, presumption, assertion or evidence) is already known to have occurred. This particular method relies on event A occurring with some sort of relationship with another event B. In this situation, the event A can be analyzed by a conditional probability with respect to B. If the event of interest is and the event is known or assumed to have occurred, "the conditional probability of given ", or "the probability of under the condition ", is usually written as or occasionally . This can also be understood as the fraction of probability B that intersects with A, or the ratio of the probabilities of both events happening to the "given" one happening (how many times A occurs rather than not assuming B has occurred): P(A \mid B) = \frac. For example, the probability that any given person has a cough on any given day ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Joint Distribution A joint or articulation (or articular surface) is the connection made between bones, ossicles, or other hard structures in the body which link an animal's skeletal system into a functional whole.Saladin, Ken. Anatomy & Physiology. 7th ed. McGraw-Hill Connect. Webp.274/ref> They are constructed to allow for different degrees and types of movement. Some joints, such as the knee, elbow, and shoulder, are self-lubricating, almost frictionless, and are able to withstand compression and maintain heavy loads while still executing smooth and precise movements. Other joints such as sutures between the bones of the skull permit very little movement (only during birth) in order to protect the brain and the sense organs. The connection between a tooth and the jawbone is also called a joint, and is described as a fibrous joint known as a gomphosis. Joints are classified both structurally and functionally. Joints play a vital role in the human body, contributing to movement, stability, and o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	All In (poker) In the game of poker, the play largely centers on the act of betting, and as such, a protocol has been developed to speed up play, lessen confusion, and increase security while playing. Different games are played using different types of bets, and small variations in etiquette exist between cardrooms, but for the most part the following rules and protocol are observed by the majority of poker players. Procedure Players in a poker game act in turn, in clockwise rotation (acting out of turn can negatively affect other players). When it is a player's turn to act, the first verbal declaration or action they take binds them to their choice of action; this rule prevents a player from changing their action after seeing how other players react to their initial action. Until the first bet is made each player in turn may "check", which is to not place a bet, or "open", which is to make the first bet. After the first bet each player may "fold", which is to drop out of the hand losing any ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]