The table below lists the number of combinations and frequency by percentage for the different hand ranks in Three Card Poker.
| Rank | Combinations | Frequency (%) |
|---|
| Straight Flush | 48 | 0.2172 |
| Three of a Kind | 52 | 0.2353 |
| Straight | 720 | 3.2579 |
| Flush | 1096 | 4.9593 |
| Pair | 3744 | 16.9412 |
| Nothing | 16440 | 74.3891 |
| Total | 22100 | 100.0000 |
The following describes a method for calculating the frequency of 3-card poker hands. The calculations make extensive use of the combinations without repetition formula (combin formula in Excel) nCr = n! / (r! x (n - r)!)
Any Hand : Total number of 3-card poker hands drawn from a 52 card standard deck.
52C3 = 22100
Straight Flush : There are 12 differently ranked straight flushes from A-2-3 up to Q-K-A in each of the 4 different suits.
12C1 x 4C1 = 48
Three of a Kind : There are 13 differently ranked three of a kinds using 3 of the 4 suits.
13C1 x 4C3 = 52
Straight : The are 12 differently ranked straights from A-2-3 up to Q-K-A. Each of the cards can be 1 of the 4 suits with the straight flushes being excluded.
12C1 x (4C1)3 - 48 = 720
Flush : A flush contains 3 of the 13 ranks, each card belonging to 1 of the 4 suits. The straight flushes are excluded.
13C3 x 4C1 - 48 = 1096
One Pair : There are 13 differently ranked pairs using 2 of 4 suits, the third card being 1 of the 12 remaining ranks using 1 of the 4 suits.
13C1 x 4C2 x 12C1 x 4C1 = 3744
Nothing : Any hand not being one of the above type of hands.
52C3 - 48 - 52 - 720 - 1096 - 3744 = 16440
