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The Probability of drawing a given hand is calculated by dividing the number of ways of drawing the hand (Frequency) by the total number of 5-card hands (the sample space; () =,,). For example, there are 4 different ways to draw a royal flush (one for each suit), so the probability is 4 / 2,598,960 , or one in 649,740.
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.
A hand pattern denotes the distribution of the thirteen cards in a hand over the four suits. In total 39 hand patterns are possible, but only 13 of them have an a priori probability exceeding 1%. The most likely pattern is the 4-4-3-2 pattern consisting of two four-card suits, a three-card suit and a doubleton.
is the current Hand Strength (i.e. not taking into account potential to improve or deteriorate, depending on upcoming table cards N P O T {\displaystyle NPOT} is the Negative POTential (i.e. the probability that our current hand, if the strongest, deteriorates and becomes a losing hand)
The underlying premise of LTC is that if a suit is evenly distributed, i.e. three players hold three cards in the suit and one player holds four, a maximum of three losers can be assumed in any one suit held by the partnership and, in turn, the maximum number of losers held by the partnership in all four suits is 24 (three in each of the four suits in each of two hands, i.e. 3 x 4 x 2 = 24).
W E ♠ K 10 3 ♥ A Q ♥ K J 9 4 ♦ K Q 3 2 ♦ A J ♣ A 4 3 ♣ 8 7 6 5 ♠ A Q J W E ♠ K 10 3 ♥ A Q 3 2 ♥ K J 9 4 ♦ K Q ♦ A J ♣ A 4 3 2 ♣ 8 7 6 5 Both East hands are exactly the same, and both West hands have the same shape, the same HCP count, and the same high cards. The only difference between the West hands is that two low red cards and one low black card have been ...
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.
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]