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Basic Texas Hold'em Poker Hand Mathematics

Texas Hold'em poker is perhaps the most popular poker variant today. This may be because of the large space it gives for strategic analysis, and especially mathematical analysis. Having that space means that players rely less on luck - on having good hands - and focus largely on skill. One of the most overlooked components of strategy by beginners is poker hand mathematics.

The main idea behind computing for the probability of Texas Hold'em poker hands is that a player could properly assess the strength of one's hand. This is done through knowing the probability of what other players' hands are.

Because only two cards consists a hand of each player in Texas Hold'em poker, it is relatively easy to compute the starting hands. The first card dealt is any of the 52 cards in the deck and the second any of the 51 other cards. Since the order of the cards is not important, then the computations could be divided by the two possible orders of cards.

This means that there are (52 x 51) / 2 = 1,326 possible hands, gained through poker hand mathematics. This number can also be relatively reduced because suits in poker have no value. Therefore, two cards with the same poker hand rankings can be reduced into one. For example, an Ace of Diamonds-Ace of Spades may be a different combination from Ace of Hearts-Ace of Clubs, they have the same value.

This reduces the strategic possibility of combinations to 169 possibilities. There could be three different groupings of hands: hands with pair, suited hands, and unsuited hands.

Through poker hand mathematics, one could see that there are 13 pocket pairs, from 2 to Ace. There are also 78 suited hands and 78 unsuited hands, of which the combinations would be as follows: 12 probable hands that contain an Ace, 11 probable hands that have no Ace but have a King, and 10 probable hands that have no Ace or King but have a Queen, 9 probable hands that have no Ace, King, or Queen but have a Jack, and so on and so forth.

Skilled players use these poker hand mathematics to assess their situation pre- and post-flop. This is especially valuable for players who intend to bluff, since a successful bluff requires that other players would not hold extremely strong hands.

Another important thing to remember is that a probability of a hand appearing is more probable as more players engage the game. This means that as the number of players decrease, the probability of holding a certain hand also decrease.

By knowing the hand probabilities in Texas Hold'em through poker hand mathematics, players could effectively assess their situation. This is done by knowing the probability of what other players' hands are. Poker mathematics, along with other strong poker strategies, would most likely help you conquer the table.


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