|
In some popular variations of poker, a player
uses the best five-card poker hand out of seven
cards. The frequencies are calculated in a
manner similar to that shown for 5-card hands,
except additional complications arise due to the
extra two cards in the 7-card poker hand. The
total number of distinct 7-card hands is . It is
notable that the probability of a no-pair hand
is less than the probability of a one-pair or
two-pair hand. (The frequencies given are exact;
the probabilities and odds are approximate.)
-
|
Hand |
Frequency |
Probability |
Cumulative |
Odds |
|
Straight flush |
41,584 |
0.0311% |
0.0311% |
3,216 : 1 |
|
Four of a kind |
224,848 |
0.168% |
0.199% |
594 : 1 |
|
Full house |
3,473,184 |
2.60% |
2.80% |
37.5 : 1 |
|
Flush |
4,047,644 |
3.03% |
5.82% |
32.1 : 1 |
|
Straight |
6,180,020 |
4.62% |
10.4% |
20.6 : 1 |
|
Three of a kind |
6,461,620 |
4.83% |
15.3% |
19.7 : 1 |
|
Two pair |
31,433,400 |
23.5% |
38.8% |
3.26 : 1 |
|
One pair |
58,627,800 |
43.8% |
82.6% |
1.28 : 1 |
|
No pair |
23,294,460 |
17.4% |
100% |
4.74 : 1 |
| Total |
133,784,560 |
100% |
100% |
0 : 1 |
Since suits have no relative value in poker, two
hands can be considered identical if one hand
can be transformed into the other by swapping
suits. Eliminating identical hands that ignore
relative suit values leaves 6,009,159 distinct
7-card hands.
The number of distinct 5-card poker hands that
are possible from 7 cards is 4,824. Perhaps
surprisingly, this is less than the number of
5-card poker hands from 5 cards because some
5-card hands are impossible with 7 cards (e.g.
7-high).
|
