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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] |
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] |
Probability
Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th ed., (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', vol. 1, 3rd ed., (1968), Wiley, . This number is often expressed as a percentage (%), ranging from 0% to 100%. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%). These concepts have been given an axiomatic mathematical formaliza ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Complexity
Combinatorial game theory measures game complexity in several ways: #State-space complexity (the number of legal game positions from the initial position) #Game tree size (total number of possible games) #Decision complexity (number of leaf nodes in the smallest decision tree for initial position) #Game-tree complexity (number of leaf nodes in the smallest full-width decision tree for initial position) #Computational complexity (asymptotic difficulty of a game as it grows arbitrarily large) These measures involve understanding the game positions, possible outcomes, and Computational complexity theory, computational complexity of various game scenarios. Measures of game complexity State-space complexity The ''state-space complexity'' of a game is the number of legal game positions reachable from the initial position of the game. When this is too hard to calculate, an upper bound can often be computed by also counting (some) illegal positions (positions that can never arise i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Event (probability Theory)
In probability theory, an event is a subset of outcomes of an experiment (a subset of the sample space) to which a probability is assigned. A single outcome may be an element of many different events, and different events in an experiment are usually not equally likely, since they may include very different groups of outcomes. An event consisting of only a single outcome is called an or an ; that is, it is a singleton set. An event that has more than one possible outcome is called a compound event. An event S is said to if S contains the outcome x of the experiment (or trial) (that is, if x \in S). The probability (with respect to some probability measure) that an event S occurs is the probability that S contains the outcome x of an experiment (that is, it is the probability that x \in S). An event defines a complementary event, namely the complementary set (the event occurring), and together these define a Bernoulli trial: did the event occur or not? Typically, when the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Effective Hand Strength Algorithm
Effective Hand Strength (EHS) is a poker algorithm conceived by computer scientists Computer science is the study of computation, information, and automation. Computer science spans theoretical disciplines (such as algorithms, theory of computation, and information theory) to applied disciplines (including the design an ... Darse Billings, Denis Papp, Jonathan Schaeffer and Duane Szafron that was published for the first time in the It has since then been considered as a reference in the realm of poker artificial intelligence and has been the basis of further research such as: * * * Algorithm The algorithm is a numerical approach to quantify the strength of a poker hand where its result expresses the strength of a particular hand in percentile (i.e. ranging from 0 to 1), compared to all other possible hands. The underlying assumption is that an Effective Hand Strength (EHS) is composed of the current Hand Strength (HS) and its potential to improve or deteriora ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorial Game Theory
Combinatorial game theory is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information. Research in this field has primarily focused on two-player games in which a ''position'' evolves through alternating ''moves'', each governed by well-defined rules, with the aim of achieving a specific winning condition. Unlike game theory, economic game theory, combinatorial game theory generally avoids the study of games of chance or games involving imperfect information, preferring instead games in which the current state and the full set of available moves are always known to both players. However, as mathematical techniques develop, the scope of analyzable games expands, and the boundaries of the field continue to evolve. Authors typically define the term "game" at the outset of academic papers, with definitions tailored to the specific game under analysis rather than reflecting the field’s full scope. Combinatorics, Comb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combination
In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter (unlike permutations). For example, given three fruits, say an apple, an orange and a pear, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple and an orange; or a pear and an orange. More formally, a ''k''-combination of a set ''S'' is a subset of ''k'' distinct elements of ''S''. So, two combinations are identical if and only if each combination has the same members. (The arrangement of the members in each set does not matter.) If the set has ''n'' elements, the number of ''k''-combinations, denoted by C(n,k) or C^n_k, is equal to the binomial coefficient \binom nk = \frac, which can be written using factorials as \textstyle\frac whenever k\leq n, and which is zero when k>n. This formula can be derived from the fact that each ''k''-combination of a set ''S'' of ''n'' members has k! permu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Low Hand
Lowball or low poker is a variant of poker in which the normal ranking of hands is inverted. Several variations of lowball poker exist, differing in whether aces are treated as high cards or low cards, and whether straights and flushes are used. Low-poker ranking Lowball inverts the normal ranking of poker hands. There are three methods of ranking low hands, called ace-to-five low, deuce-to-seven low, and ace-to-six low. The 'ace-to-five' method is most common. A sub-variant within this category is 'high-low poker', in which the highest and lowest hands split the pot, with the highest hand taking any odd chips if the pot does not divide equally. Sometimes straights and/or flushes count in determining which hand is highest but not in determining which hand is lowest, being reckoned as a no-pair hand in the latter instance, so that a player with such a holding can win both ways and thus take the entire pot. Lowball variants The most popular forms of lowball are ace-to-five lowball ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Playing Card
A playing card is a piece of specially prepared card stock, heavy paper, thin cardboard, plastic-coated paper, cotton-paper blend, or thin plastic that is marked with distinguishing motifs. Often the front (face) and back of each card has a finish to make handling easier. They are most commonly used for playing card games, and are also used in magic tricks, cardistry, card throwing, and card houses; cards may also be collected. Playing cards are typically palm-sized for convenient handling, and usually are sold together in a set as a deck of cards or pack of cards. The most common type of playing card in the West is the French-suited, standard 52-card pack, of which the most widespread design is the English pattern, followed by the Belgian-Genoese pattern. However, many countries use other, traditional types of playing card, including those that are German, Italian, Spanish and Swiss-suited. Tarot cards (also known locally as ''Tarocks'' or ''tarocchi'') are an ol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Texas Hold 'em
Texas hold 'em (also known as Texas holdem, hold 'em, and holdem) is the most popular variant of the card game of poker. Two cards, known as hole cards, are dealt face down to each player, and then five Community card poker, community cards are dealt face up in three stages. The stages consist of a series of three cards ("the flop"), later an additional single card ("the turn" or "fourth street"), and a final card ("the river" or "fifth street"). Each player seeks the best List of poker hands, five-card poker hand from any combination of the seven cards: the five community cards and their two hole cards. Players have Betting in poker, betting options to check, call, raise, or fold. Rounds of betting take place before the flop is dealt and after each subsequent deal. The player who has the best hand and has not folded by the end of all betting rounds wins all of the money bet for the hand, known as the pot. In certain situations, a "split pot" or "tie" can occur when two player ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hand Rankings
In poker, players form sets of five playing cards, called ''hands'', according to the rules of the game. Each hand has a rank, which is compared against the ranks of other hands participating in the showdown to decide who wins the pot. In high games, like Texas hold 'em and seven-card stud, the highest-ranking hands win. In low games, like razz, the lowest-ranking hands win. In high-low split games, both the highest-ranking ''and'' lowest-ranking hands win, though different rules are used to rank the high and low hands. Each hand belongs to a category determined by the patterns formed by its cards. A hand in a higher-ranking category always ranks higher than a hand in a lower-ranking category. A hand is ranked within its category using the ranks of its cards. Individual cards are ranked, from highest to lowest: A, K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3 and 2. However, aces have the lowest rank under ace-to-five low or ace-to-six low rules, or under high rules as part of a five-high s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
