|
Poker Probability (Texas Hold 'em)
In poker, the probability of each type of 5-card 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 Paccioli released his work which was the first written text on probability. Motivated by Paccioli'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 gambler with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poker
Poker is a family of comparing card games in which players wager over which hand is best according to that specific game's rules. It is played worldwide, however in some places the rules may vary. While the earliest known form of the game was played with just 20 cards, today it is usually played with a standard 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 dealt face up or face down, and the number shared by all players, but all have rules that involve one or more rounds of 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'' or ''ante''). In standard poker, each player bets according to the rank they believe their hand is worth as compared to the other players. The action then proceeds clockwise as each play ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sample Space
In probability theory, the sample space (also called sample description space, possibility space, or outcome space) of an experiment or random trial is the set of all possible outcomes or results of that experiment. A sample space is usually denoted using set notation, and the possible ordered outcomes, or sample points, are listed as elements in the set. It is common to refer to a sample space by the labels ''S'', Ω, or ''U'' (for "universal set"). The elements of a sample space may be numbers, words, letters, or symbols. They can also be finite, countably infinite, or uncountably infinite. A subset of the sample space is an event, denoted by E. If the outcome of an experiment is included in E, then event E has occurred. For example, if the experiment is tossing a single coin, the sample space is the set \, where the outcome H means that the coin is heads and the outcome T means that the coin is tails. The possible events are E=\, E = \, and E = \. For tossing two coins, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gaming Mathematics
Experiments, events and probability spaces The technical processes of a game stand for experiments that generate aleatory events. Here are a few examples: * Throwing the dice in craps is an experiment that generates events such as occurrences of certain numbers on the dice, obtaining a certain sum of the shown numbers, and obtaining numbers with certain properties (less than a specific number, higher than a specific number, even, uneven, and so on). The sample space of such an experiment is for rolling one die or for rolling two dice. The latter is a set of ordered pairs and counts 6 x 6 = 36 elements. The events can be identified with sets, namely parts of the sample space. For example, the event ''occurrence of an even number'' is represented by the following set in the experiment of rolling one die: . * Spinning the roulette wheel is an experiment whose generated events could be the occurrence of a certain number, of a certain color or a certain property of the numbers (low, hig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Complexity
Combinatorial game theory has several ways of measuring game complexity. This article describes five of them: state-space complexity, game tree size, decision complexity, game-tree complexity, and computational complexity. 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, meaning positions that can never arise in the course of a game. Game tree size The game tree size is the total number of possible games that can be played: the number of leaf nodes in the game tree rooted at the game's initial position. The game tree is typically vastly larger than the state space because the same positions can occur in many games by making moves in a different order (for example, in a tic-tac-toe game with two X and one O on the board, this position co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Event (probability Theory)
In probability theory, an event is a set 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 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 sample space is finite, any subset of the sample space is an event (that is, all e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Effective Hand Strength Algorithm
Effective Hand Strength (EHS) is a poker algorithm conceived by computer scientists 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 deteriorate (PPOT and NPOT): : EHS = HS \times (1 - NPOT) + (1-HS) \times PPOT where: * EHS is the Effective Hand Strength * HS is the current Hand Strength (i.e. not taking into account potential to improve or deteriorate, depending on upcoming table cards * NPO ... [...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. Study has been largely confined to two-player games that have a ''position'' that the players take turns changing in defined ways or ''moves'' to achieve a defined winning condition. Combinatorial game theory has not traditionally studied games of chance or those that use imperfect or incomplete information, favoring games that offer perfect information in which the state of the game and the set of available moves is always known by both players. However, as mathematical techniques advance, the types of game that can be mathematically analyzed expands, thus the boundaries of the field are ever changing. Scholars will generally define what they mean by a "game" at the beginning of a paper, and these definitions often vary as they are specific to the game being analyzed and are not meant to represent the entire scope of the field. C ... [...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 (mathematics), 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 as 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! ... [...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] |
Lowball (poker)
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. Some patterns of Tarot playing card are also used for divination, although bespoke cards for this use are more common. 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Texas Hold 'em
Texas hold 'em (also known as Texas holdem, hold 'em, and holdem) is one of the most popular variants 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 tw ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
