Seven Card Poker Hands

Robert S. Wilson

Type of Hand

Computation

Number

4 of a kind and 3 of a kind

13 x C(4,4) x 12 x C(4,3)

624

4 of a kind and a pair

13 x C(4,4) x 12 x C(4,2) x 44

41,184

4 of a kind

13 x C(4,4) x C(12,3) x 43

183,040

2 3 of a kinds

C(13, 2) x C(4,3)2 x 44

54,912

3 of a kind and 2 pairs

13 x C(4,3) x C(12,2) x C(4,2)2

123,552

3 of a kind and 1 pair

13 x C(4,3) x 12 x C(4,2) x C(11,2) x 42

3,294,720

3 of a kind

13 x C(4,3) x C(12,4) x 44

6,589,440

3 pairs

C(13,3) x C(4,2)3 x 40

2,471,040

2 pairs

C(13,2) x C(4,2)2 x C(11,3) x 43

29,652,480

1 pair

13x C(4,2) x C(12,5) x 45

63,258,624

no pairs

C(13,7) x 47

28,114,944

Totals

C(52,7)

133,784,560

5 card hands

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