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In no-limit or pot-limit poker, a player's M-ratio (also called "M number", "M factor" [1] or just "M") is a measure of the health of a player's chip stack as a function of the cost to play each round. In simple terms, a player can sit passively in the game, making only compulsory bets, for M laps of
In poker, the Independent Chip Model (ICM), also known as the Malmuth–Harville method, [1] 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; [2] in 1987, Mason Malmuth independently rediscovered it for poker. [3]
In some popular variations of poker such as Texas hold 'em, the most widespread poker variant overall, [3] a player uses the best five-card poker hand out of seven cards. The frequencies are calculated in a manner similar to that shown for 5-card hands, [ 4 ] except additional complications arise due to the extra two cards in the 7-card poker hand.
Poker calculators are algorithms which through probabilistic or statistical means derive a player's chance of winning, losing, or tying a poker hand. [1] [2]Given the complexities of poker and the constantly changing rules, most poker calculators are statistical machines, probabilities and card counting is rarely used.
Pot odds are only useful if a player has enough equity.Equity is the chance a player has to win the hand at showdown.It is calculated as the fraction of remaining cards in the deck for each remaining street (sequential card being dealt, e.g. turn, river) that can give a player the winning hand.
The mathematics of gambling is a collection of probability applications encountered in games of chance and can get 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.
The player's "playing hand", which will be compared against that of each competing player, is the best 5-card poker hand available from his two hole cards and the five community cards. Unless otherwise specified, here the term hand applies to the player's two hole cards, or starting hand .
Probability of being dealt a four of a kind in poker 10 −3: Milli-(m) 1.3×10 −3: Gaussian distribution: probability of a value being more than 3 standard deviations from the mean on a specific side [17] 1.4×10 −3: Probability of a human birth giving triplets or higher-order multiples [18] Probability of being dealt a full house in poker ...