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The Frequencies of Starting Hands

In Texas Hold'em, each poker player is dealt with two starting cards. These two cards are called pocket cards or personal cards. And these two cards are combined with three of the community cards. The community cards are up cards that will be shared with other poker players. To win in the Texas Hold'em poker, the player must have strong pocket cards. But how often do strong starting cards end up in ones hands?

Here is how the frequencies of starting hands are computed. With 52 cards in one deck, mathematicians have calculated that there will be 1,326 two-card combinations. But in Texas Hold'em, the suits are considered equal in rank. This significantly reduces the number of unique starting hands. In Texas Hold'em, there will only be 169 different starting hands. But these 169 starting hands do not have the same frequency.

Thus, it will useful to classify the 169 starting hands into five different groups. The five groups are pairs, straight-flush draws, straight draws, flush draws, and no draws.

A "pair" is a combination of two cards which are of the same rank. For example, two Aces is a pair and two Fours is a pair. The former is a high pair and the latter is a low pair. In one deck of cards, there will be 13 pairs. This means that the frequency of such pairs is only 5.9%.

A "straight-flush draw" is a combination of two cards which are of the same suit, making them parts of a flush. At the same time, these two cards can be part of a straight. For example, a straight-flush draw can be a 10 and an 8 of Diamonds. If three of the community cards are diamonds, the poker player can definitely form a flush. And if three of the community cards are 9, Jack, and Queen of Diamonds, then the poker player forms a very strong hand, which is a straight-flush. In one deck of cards, there will be 46 combinations. This means that there is a surprisingly higher frequency of getting straight-flush draws, 13.9%.

"Straight draws" is a two-card combination which can form part of a straight, but not a flush. One example is a 10 of Hearts and a 9 of Spades. After the flop, the only possible combination for these cards is a straight. The frequency of getting this starting pair is 41.6%

A "flush draw" is composed of two cards that are suited. At whatever point in the game after the flop, these two cards can only form a flush. They cannot form a straight. For example, a Jack and a Four of Hearts can form a flush. The frequency of getting a flush draw is only 9.7%, a figure which is slightly higher than a pair, but infinitely lower than a straight.

And the last group of two-cards is the "no draws" in which no straight nor flush can be formed. The frequency of getting such cards is 28.8%.

 
 
 

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