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Poker Hand Ranks and Probabilities

Royal Flush - 10, Jack, Queen, King, Ace, all of the same suit.

Straight Flush - Any five cards in succession, all of the same suit.  (ie. 8-9-10-Jack-Queen, all of hearts)

4 of a Kind - Four of the same card, ie. Ace-Ace-Ace-Ace.  The 5th card doesn't matter, and in case of 2 players with 4 of a kind, the higher ranking 4 of a kind wins the pot.  4 Aces beats 4 kings.

Full House - 3 of a kind plus a pair, as in King-King-King-5-5.  This would be expressed as “full house, kings over fives.“  On the other hand, 5-5-5-King-King would be expressed “full house, fives over kings.“  In the case of two or more players with full house, the winner is decided by who has the highest “3 of a kind“ portion of the hand.  10-10-10-2-2 would beat 8-8-8-Ace-Ace.  The pair means nothing, the 3 matching cards determine your rank, and in this example, 10 is obviously higher than 8.  Sometimes, a full house is called a “boat.“

Flush - Any 5 cards of the same suit.  A flush is referred to by its high card.  King-5-8-Jack-2 of hearts would be called a “flush, king high.“  In the case of two or more flushes at showdown, the flush with the highest ranking card wins.

Straight - 5 cards in succession, any suit.  In the case of two straights, the one with the highest ranking top card wins.  Straight, 10 through Ace beats any other straight.

3 of a Kind - 3 of any matching card,  7-7-7, etc.  The 4th and 5th cards are meaningless.  In the case of two of these hand at showdown, the higher ranking 3 of a kind wins.  3 of a kind is often referred to as “trips.“

2 Pair - Any 2 pair, with the rank determined by the top pair.  Kings and 2's beats Queens and Jacks.  In case of a tie, ( two players hold queens and jacks), then the winner is determined by the 5th card, called the “kicker.“  Whoever holds the higher ranking 5th card wins the pot.

1 Pair - One pair of any card.  In case of a tie (two players hold Aces), the winner is determined by who holds the highest kicker or kickers.  A pair of 8's queen kicker beats a pair of 8's, jack kicker.

High Card - In the case of no pairs, the player with the highest ranking card wins.

 

5 Card Probabilities

Your chance of being dealt one of the following hands in your first five cards are roughly:

Royal Flush - 1 in 650,000

Straight Flush - 1 in 72,200

4 of a Kind - 1 in 4200

Full House - 1 in 700

Flush - 1 in 510

Straight - 1 in 250

3 of a Kind - 1 in 48

2 Pair - 1 in 21

1 Pair - 1 in 2.4

 

7 Card Probabilities

Your chance of being dealt a ranked hand in 7 card stud are roughly:

Royal Flush - .0002%

Straight Flush - .0012%

4 of a Kind - .024%

Full House - .144%

Flush - .197%

Straight - .353%

3 of a Kind - 2.11%

2 Pair - 4.754%

1 Pair - 42%

The Moral?  Good cards are rare.  Wait on them, and then play them to the hilt!