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In poker games, a hand is a set of 5 cards drawn from the deck of 52 cards in 4 suits.
Hand ranking is a set of rules to determine which hand has a higher rank between 2 hands.
Rule 1: A hand in a stronger hand category ranks higher.
Below is a list of hand categories starting from the strongest.
- Straight Flush - 5 cards are of the same suit and have sequential values, such as Q♣ J♣ 10♣ 9♣ 8♣,
A♦ K♦ Q♦ J♦ 10♦, or 5♠4♠3♠2♠A♠.
Note that Ace (A) can be used as value 13 or 1.
The probability of "Straight Flush" is about 0.0015%.
- Four of a Kind - 4 of 5 cards have the same value, such as 9♣ 9♠9♦ 9♥ J♥.
The probability of "Four of a Kind" is about 0.0240%.
- Full House - 3 of 5 cards have the same value and the other 2 cards also have the same value, such as 7♥ 7♦ 7♠4♠4♣.
The probability of "Full House" is about 0.1441%.
- Flush - 5 cards are of the same suit, but not in sequence, such as Q♣ 10♣ 7♣ 6♣ 4♣.
The probability of "Flush" is about 0.1960%.
- Straight - 5 cards have sequencial numers, such as A♣ K♣ Q♠J♠10♠, or 5♥ 4♦ 3♦ 2♥ A♥.
Note that Ace (A) can be used as value 13 or 1.
The probability of "Flush" is about 0.3900%.
- Three of a Kind - 3 of 5 cards have the same value and the other 2 have different values, such as 2♦ 2♥ 2♣ K♠6♠.
The probability of "Flush" is about 2.1100%.
- Two Pair - 2 cards share same value and another 2 have a different value, such as 8♥ 8♣ 4♠4♣ 10♠.
The probability of "Two Pair" is about 4.7500%.
- One Pair - 2 cards share same value and the other 3 have different values, such as 4♥ 4♦ K♠10♣ 5♠.
The probability of "Two Pair" is about 42.2600%.
- High Card - 5 cards are not of the same suit, not have sequential values, and not share any values, such as K♥ J♥ 8♦ 7♣ 4♠.
The probability of "High Card" is about 50.1100%.
Rule 2: Two hands of the same category are ranked using the following rules in order:
- The hand with higher "Four of a Kind" value ranks higher.
For example, 7♣ 7♠7♦ 7♥ J♥ ranks higher than 5♣ 5♠5♦ 5♥ K♣.
- The hand with higher "Three of a Kind" value ranks higher.
For example, Q♠Q♥ Q♦ 7♠4♣ ranks higher than J♠J♣ J♦ A♦ K♣.
- The hand with higher "Pair" value ranks higher.
For example, 10♠10♣ 8♥ 8♣ 4♠ranks higher than
10♥ 10♦ 4♥ 4♣ Q♣.
- The hand with higher "Card" value ranks higher.
For example, Q♣ J♠10♠9♥ 8♥ ranks higher than 10♣ 9♦ 8♠7♣ 6♠.