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Four of a kind, also known as quads, is a hand that contains four cards of one rank and one card of another rank (the kicker), such as 8♣ 8♠ 8♦ 8♥ J♥ ("four of a kind, Eights"). It ranks below a straight flush and above a full house. Yes, Four of a kind (four cards of the same rank) beats a full house. If two or more players share the same four of a kind, then the fifth card kicker determines who is the winner.
Each four of a kind is ranked first by the rank of its quadruplet, and then by the rank of its kicker. For example, Q♠ Q♥ Q♣ Q♦ 3♥ranks higher than 8♥ 8♦ 8♠ 8♣ Q♥, which ranks higher than 8♥ 8♦ 8♠ 8♣ 10♠. Four of a kind hands that differ by suit alone, such as 6♣ 6♠ 6♦ 6♥ 9♣ and 6♣ 6♠ 6♦ 6♥ 9♦, are of equal rank
In a 52-card deck, there are 624 possible 4-of-a-Kind hand combinations and 156 distinct ranks of 4-of-a-Kind. As poker hands are made up of 5 cards, the kicker does come into play here.
For example, hand 5♥5♠5♦5♣10♦ would rank higher than 5♥5♠5♦5♣7♦.
However, hand K♥K♠K♦K♣2♦ ranks higher than Q♥Q♠Q♦Q♣A♦ even though the Quad Queens has an ace kicker and the Quad Kings has a two kicker.
When you play poker, In this hand ranking, you need to keep in mind that it’s the rank/denomination that is the most important. Four-of-a-Kind Aces will always beat 4-of-a-Kind Kings, and Quad Kings will always beat Quad Queens, and so forth.
This hand consists of four cards of one value, and a fifth card of a different value. There are 13 x 1 = 13 ways to choose the value for the quadruple. Then, among the of this value, there are 4 x 4 = 1 ways to choose the quadruple.
After this, there are 12 x 1 = 12 ways to choose a value for the single from the remaining values, and 4 x 1 = 4 ways to choose the single from the four cards of this value, for a grand total of (13/1) x (4/4) x (12/1) x (4/1) = 13 x 1 x 12 x 4 = 624.
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