Five-card poker hand probabilities: the full table and how each is counted
· 7 min read
Straight flush
Five consecutive ranks, all of one suit (the ace may count high or low).
0.0015%
1 in 64,974
40 hands
Four of a kind
Four cards of one rank plus one other card.
0.0240%
1 in 4,165
624 hands
Full house
Three cards of one rank and two of another.
0.1441%
1 in 694
3,744 hands
Flush
Five cards of one suit that are not consecutive.
0.1965%
1 in 509
5,108 hands
Straight
Five consecutive ranks that are not all of one suit.
0.3925%
1 in 255
10,200 hands
Three of a kind
Three cards of one rank and two unmatched cards.
2.11%
1 in 47
54,912 hands
Two pair
Two different pairs plus one unmatched card.
4.75%
1 in 21
123,552 hands
One pair
Exactly two cards of one rank and three unmatched cards.
42.26%
1 in 2
1,098,240 hands
No pattern (high card)
None of the above: all ranks differ, not consecutive, not all one suit.
50.12%
1 in 2
1,302,540 hands
The table
Out of 2,598,960 possible five-card hands, here is how many belong to each type. A royal flush is counted inside straight flush. The ace counts high or low in a straight, but a straight cannot wrap around (Q-K-A-2-3 is not one).
- Straight flush: 40 hands, about 0.0015%
- Four of a kind: 624 hands, about 0.024%
- Full house: 3,744 hands, about 0.144%
- Flush: 5,108 hands, about 0.197%
- Straight: 10,200 hands, about 0.392%
- Three of a kind: 54,912 hands, about 2.11%
- Two pair: 123,552 hands, about 4.75%
- One pair: 1,098,240 hands, about 42.26%
- No pattern: 1,302,540 hands, about 50.12%
How the four rarest are counted
Four of a kind: choose the rank (13 ways) and the fifth card (48 ways) for 13 × 48 = 624. Full house: choose the rank of the triple (13), three of its four suits (4), the rank of the pair (12), and two of its four suits (6): 13 × 4 × 12 × 6 = 3,744.
Straight flush: there are 10 possible runs of five ranks and 4 suits, so 40. Flush: any five cards of one suit is C(13, 5) = 1,287 per suit, times 4 suits is 5,148, and subtracting the 40 straight flushes leaves 5,108.
How the common ones are counted
One pair: 13 ranks × C(4, 2) = 6 suit choices × C(12, 3) = 220 ways to pick the three other ranks × 4³ = 64 suit choices for them, which gives 1,098,240. Two pair: C(13, 2) × 6 × 6 × 11 × 4 = 123,552.
13 × 6 × 220 × 64 = 1,098,240 (one pair)What the table teaches
Every individual hand is equally likely, yet the types differ enormously in size. The table is a demonstration of counting, and you can check it yourself by simulating thousands of random hands and watching the frequencies approach these exact values.