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3 Card Poker Hand Frequency

Frequency of Hands in 3 Card Poker

The table below lists the frequency and probability by percentage for the different hand ranks in Three Card Poker.

RankFrequencyProbability (%)
Straight Flush480.2172
Three of a Kind520.2353
Straight7203.2579
Flush10964.9593
Pair374416.9412
Nothing1644074.3891
Total22100100.0000

Calculating Frequency of 3-Card Poker Hands

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 (combine 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

Related Pages

3 card poker strategy differs from all other types of poker. Most poker hands are based on 5 cards regardless of how many are dealt. Even though 3 card poker uses the same poker hand hierarchy, it is difficult for many players, beginner and pro alike, to reconcile them into only 3 cards. We have created this 3 card poker hand frequency page to give you a quick look at all of the hands and their likely outcomes while you play. It isn't necessary to memorize the hands of 3 card poker or to remember their stats. You can bookmark this page and use it as you play. The best way to develop skills in any poker variety including 3 card poker is to play.

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