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Probability and Poker
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Poker Hand Ranks

The rank of poker hands is generally the same across all poker games. This is because the value of a hand is based on the probability of a player acquiring a specific hand.

1. The best hand in poker is the royal flush. This is composed of the 10, jack, queen , king , ace, all cards in the same suit. The chances of getting this hand are quite remote.

2. Next down the list of hands is the straight flush. Actually the royal flush is simply a subset of the straight flush. The straight flush is comprised of any five cards in a row, all of the same suit. The ace may serve as the high card of the flush, or the low card (below the 2).

3. Four of a kind is a tremendous hand. It is composed of all four of any particular type card from all four suits. The types of cards are ranked ace-high, king, queen, jack, 10, 9, 8, 7, 6, 5, 4, 3, 2.

4. The full house is still a very reliable hand to bet on. Three of a kind, plus two of a kind together make a full house. The name probably signifies that all the cards of the hand are important, and one can imagine a couple of queens and a few jacks in a hand looking like the photos of children, nieces and nephews stuffed in a bettor's wallet.

5. A flush is a fistful of cards all of the same suit. Naturally, they rank better or worse based on the highest card in the hand. If this should tie, then the next two cards would be compared, and so on through the last card. The flush has pulled in many a pot.

6. A straight is five cards in a row (ex: 5,6,7,8,9) of mixed suits. As in a flush, the highest ranking card in the hand determines the winner. In cases where wild cards are used natural cards take precedence. Here again, the ace may serve as the lower or higher end anchor of the hand. However, the hand may NOT go around the ace as in (3,2,A,K,Q).

7. Three of a kind can be a fairly good betting hand, but care should be used in assessing its value. It is basically, three cards, all of the same rank. Sometimes 3 kings is called a Christmas hand because of the symbolism of the three kings as well as the gifts such a hand may deliver. It is impossible to have two hands of three of a kind with the same ranked cards.

8. Two pair is basically two sets of two of a kind. This hand becomes even riskier to bet on, but depending on the game can often be a winner. Between two hands containing two pair, the highest pair is first considered, then the second pair, then the extra card.

9. A single pair is a fairly frequent phenomenon. It is dealt out (in five-card games) about one in every five hands. Between two single pair hands, the highest pair takes the pot. In cases of equal pairs, the highest unmatched card is considered, then the next highest and so on.

10. The fact is that almost any hand may win. Lack of one of the more desirable hands leaves the player declaring that he has merely a high card. A high card hand is, of course, dependent on the rank of the highest card in the hand. It is beaten by all of the hands mentioned above. Any ties between the high card require the players to match the next highest cards, and so on.

According to Hoyle, ties are possible. Any two hands that are exactly alike in ranked cards split the pot. The suit of the cards is never considered.

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