3 Card Poker Hands
Poker hands listed (Highest to Lowest) Royal Flush. Three of a Kind. What hands are rank highest in Poker. ABOUT CARDPLAYER, THE POKER AUTHORITY CardPlayer.com is the world's oldest and most well respected poker magazine and online poker guide.Since 1988.
The amount you win depends on what type of hand you are dealt. The 6 Card bonus looks at the three cards in your hand and the three cards in the dealer’s hand. If, after combining the 6 cards, you can make a poker hand of three of a kind or better, you win the 6 Card bonus wager. The following are the traditional rules for a game of Three-Card Poker: Play begins with the player making up to two wagers. The first is known as the Ante, and the second is known as the Pair Plus wager. Both of these are optional bets in some casinos, while others require the Ante wager to be made.
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.
| Rank | Frequency | Probability (%) |
|---|---|---|
| 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 |
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
All 3 Card Poker Hands
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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