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He thus has 9 outs for a flush out of 47 cards yet to be drawn, giving him a 9/47 chance to fill his flush on the turn. If he fails on the turn, he then has a 9/46 chance to fill on the river. Calculating the combined odds of filling on either the turn or river is more complicated: it is (1 - ((38/47) * (37/46))), or about 35%.
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.
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.
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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
PokerStove is a program that calculates hand equities (i.e., expected percentage of the time that each hand wins at showdown). [3] Since poker is a game of incomplete information, the calculator is designed to evaluate the equity of ranges of hands that players can hold, instead of individual hands. [4]
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