The ranking of poker hands based on probability starting from the highest are shown below.
There are 2,598,960 possible combinations of cards in a poker hand you can be dealt. In brackets next to the ranking of hands, are 1st the number of possible hands of that rank in 2,598,960 possible combinations, and 2nd your chances of getting one in percentage probability:
Royal Flush: This is the daddy of all hands and even if you play often, you will rarely see one. It's similar to a hole in one in golf. It is made of up all of the same suite, ten through Ace. It is a straight and a flush and the royal part comes from it being made up of the highest cards too.
4 possible hands in 2,598,960. Chance to get one: 0.000154%
Straight Flush: While not as magical as the royal straight flush, the straight flush still is a rariety. It is made up of 5 cards of the same suite ranked in succession. For example 6-10, or A-5 (Ace can play both high and low in straights).

36 possible hands in 2,598,960. Chance to get one: 0.00139%
Four of a Kind: This is self-explanatory. A four of a kind ocurrs when you have all the cards of one type.

624 possible hands in 2,598,960. Chance to get one: 0.0240%
Full House: A full house happens when you have both three of a kind and also a pair. To determine if one full house higher ranked then another, first look at the three cards of the same kind. The one that is larger wins. If they both are the same then you'll have to compare the two cards. For example: Jacks full of fours (JJJ, 44) beats 9s full of Aces (999, AA) Jacks full of tens (JJJ, TT) beats Jacks full of nines (JJJ, 99) Full houses in texas hold'em are nice hands and you will most likely see someone show one down everytime you play.

3744 possible hands in 2,598,960. Chance to get one: 0.144%
Flush: A flush occurs when you have five of the same suite. If the cards were also in succession (like a straight), then it would be a straight flush. To determine which flush wins if there are more then one in a hand, then the person with the highest card in their hand wins. In the example to the right, the person has a ten high flush. This would beat someone with a nine high flush and below. Flushes are pretty common in hold'em.

5108 possible hands in 2,598,960. Chance to get one: 0.197%
Straight: A straight occurs when a player has five cards in ranked succession. Note that an Ace can play both as a high card or a low card. Note the two examples to the right. Straights are also very common in hold'em.

10,200 possible hands in 2,598,960. Chance to get one: 0.392%
Three of a Kind: Three of a kind is a nice hand. There are two different names for three of a kind hands and it depends on whether you have two of them on the board, or a pair in your hand. They both rank the same but to be a savy player you should know the difference. If you have a pocket pair and hit one on the flop then it is called a "set". If you have two cards on the flop and only one in your hand then it is called three of a kind.

54912 possible hands in 2,598,960. Chance to get one: 2.11%
Two Pair: Two pair is when your best five cards create a pair twice. That seems easy enough right? When comparing two hands both with two pair then the larger one always wins.

123,552 possible hands in 2,598,960. Chance to get one: 4.75%
Pair: One pair is the hand you'll be getting the most and
trying to win with the most. Top pair is usually the hand you'll be betting
and trying to win some pots with. When more then one person has the same pair,
then the "kickers" come in to play. Remember texas hold'em
uses the best five cards so the following is true: Ah, Ac, Jc, 6d, 4d would
lose to
Ad, As, Jd, 6c, 5d Notice how the 5 beats the 4 (best five cards makes a hand).

1,098,240 possible hands in 2,598,960. Chance to get one: 42.26%
High Card: The high card hand is the lowest non pair hand. Sometimes Ace high can win, but in the low limit games it is very rare. In the example to the right, the high card is K. So you would have "king high". You would beat someone if they had "queen high" or below but even a pair of deuces would beat you!

1,302,540 possible hands in 2,598,960. Chance to get one: 50.12%
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