Also known as trips or a set, three of a kind is a poker hand that contains three cards of the same rank, plus two additional unpaired cards, for example Ah Ac As Ks Jc. Three of a kind is better than two pair, but worse than a straight. In comparing hands, the highest ranked.
- Hand Rankings in Three Card Poker. If you’re familiar with any form of poker like Hold’em or Five Card Draw, you’ll have a pretty good idea of how poker hands rankings work in 3 card poker. However, due to only three cards being dealt to the dealer and the players and no help from any community cards, hand strengths are somewhat different.
- 3-x COMBINATIONS. Ace-Ace (A-A) The best starting hand in poker has generated numerous names through the years. Bullets – Poker was played in the Old West and references to cowboys and gun fighting are numerous – and part of the fun. The look of the two letters (A) remind players of bullets and thus the name seems a natural.
- The term “three pair” may be confusing at first, since it appears to be describing an illegal poker hand. Hands in poker are typically constructed with 5 cards, so making 3 sets of pairs (6 cards) is technically impossible. Despite this, the term “three pair” is commonly used amongst Omaha players. So what does it mean?
Poker Hands 3 Pairs
This post works with 5-card Poker hands drawn from a standard deck of 52 cards. The discussion is mostly mathematical, using the Poker hands to illustrate counting techniques and calculation of probabilities
Working with poker hands is an excellent way to illustrate the counting techniques covered previously in this blog – multiplication principle, permutation and combination (also covered here). There are 2,598,960 many possible 5-card Poker hands. Thus the probability of obtaining any one specific hand is 1 in 2,598,960 (roughly 1 in 2.6 million). The probability of obtaining a given type of hands (e.g. three of a kind) is the number of possible hands for that type over 2,598,960. Thus this is primarily a counting exercise.
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Preliminary Calculation
Usually the order in which the cards are dealt is not important (except in the case of stud poker). Thus the following three examples point to the same poker hand. The only difference is the order in which the cards are dealt.
These are the same hand. Order is not important.
The number of possible 5-card poker hands would then be the same as the number of 5-element subsets of 52 objects. The following is the total number of 5-card poker hands drawn from a standard deck of 52 cards.
The notation is called the binomial coefficient and is pronounced “n choose r”, which is identical to the number of -element subsets of a set with objects. Other notations for are , and . Many calculators have a function for . Of course the calculation can also be done by definition by first calculating factorials.
Thus the probability of obtaining a specific hand (say, 2, 6, 10, K, A, all diamond) would be 1 in 2,598,960. If 5 cards are randomly drawn, what is the probability of getting a 5-card hand consisting of all diamond cards? It is
This is definitely a very rare event (less than 0.05% chance of happening). The numerator 1,287 is the number of hands consisting of all diamond cards, which is obtained by the following calculation.
The reasoning for the above calculation is that to draw a 5-card hand consisting of all diamond, we are drawing 5 cards from the 13 diamond cards and drawing zero cards from the other 39 cards. Since (there is only one way to draw nothing), is the number of hands with all diamonds.
If 5 cards are randomly drawn, what is the probability of getting a 5-card hand consisting of cards in one suit? The probability of getting all 5 cards in another suit (say heart) would also be 1287/2598960. So we have the following derivation.
Thus getting a hand with all cards in one suit is 4 times more likely than getting one with all diamond, but is still a rare event (with about a 0.2% chance of happening). Some of the higher ranked poker hands are in one suit but with additional strict requirements. They will be further discussed below.
Another example. What is the probability of obtaining a hand that has 3 diamonds and 2 hearts? The answer is 22308/2598960 = 0.008583433. The number of “3 diamond, 2 heart” hands is calculated as follows:
One theme that emerges is that the multiplication principle is behind the numerator of a poker hand probability. For example, we can think of the process to get a 5-card hand with 3 diamonds and 2 hearts in three steps. The first is to draw 3 cards from the 13 diamond cards, the second is to draw 2 cards from the 13 heart cards, and the third is to draw zero from the remaining 26 cards. The third step can be omitted since the number of ways of choosing zero is 1. In any case, the number of possible ways to carry out that 2-step (or 3-step) process is to multiply all the possibilities together.
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The Poker Hands
Worst Poker Pair
Here’s a ranking chart of the Poker hands.
The chart lists the rankings with an example for each ranking. The examples are a good reminder of the definitions. The highest ranking of them all is the royal flush, which consists of 5 consecutive cards in one suit with the highest card being Ace. There is only one such hand in each suit. Thus the chance for getting a royal flush is 4 in 2,598,960.
Royal flush is a specific example of a straight flush, which consists of 5 consecutive cards in one suit. There are 10 such hands in one suit. So there are 40 hands for straight flush in total. A flush is a hand with 5 cards in the same suit but not in consecutive order (or not in sequence). Thus the requirement for flush is considerably more relaxed than a straight flush. A straight is like a straight flush in that the 5 cards are in sequence but the 5 cards in a straight are not of the same suit. For a more in depth discussion on Poker hands, see the Wikipedia entry on Poker hands.
The counting for some of these hands is done in the next section. The definition of the hands can be inferred from the above chart. For the sake of completeness, the following table lists out the definition.
Definitions of Poker Hands
| Poker Hand | Definition | |
|---|---|---|
| 1 | Royal Flush | A, K, Q, J, 10, all in the same suit |
| 2 | Straight Flush | Five consecutive cards, |
| all in the same suit | ||
| 3 | Four of a Kind | Four cards of the same rank, |
| one card of another rank | ||
| 4 | Full House | Three of a kind with a pair |
| 5 | Flush | Five cards of the same suit, |
| not in consecutive order | ||
| 6 | Straight | Five consecutive cards, |
| not of the same suit | ||
| 7 | Three of a Kind | Three cards of the same rank, |
| 2 cards of two other ranks | ||
| 8 | Two Pair | Two cards of the same rank, |
| two cards of another rank, | ||
| one card of a third rank | ||
| 9 | One Pair | Three cards of the same rank, |
| 3 cards of three other ranks | ||
| 10 | High Card | If no one has any of the above hands, |
| the player with the highest card wins |
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Counting Poker Hands
Straight Flush
Counting from A-K-Q-J-10, K-Q-J-10-9, Q-J-10-9-8, …, 6-5-4-3-2 to 5-4-3-2-A, there are 10 hands that are in sequence in a given suit. So there are 40 straight flush hands all together.
Four of a Kind
There is only one way to have a four of a kind for a given rank. The fifth card can be any one of the remaining 48 cards. Thus there are 48 possibilities of a four of a kind in one rank. Thus there are 13 x 48 = 624 many four of a kind in total.
Full House
Let’s fix two ranks, say 2 and 8. How many ways can we have three of 2 and two of 8? We are choosing 3 cards out of the four 2’s and choosing 2 cards out of the four 8’s. That would be = 4 x 6 = 24. But the two ranks can be other ranks too. How many ways can we pick two ranks out of 13? That would be 13 x 12 = 156. So the total number of possibilities for Full House is
Note that the multiplication principle is at work here. When we pick two ranks, the number of ways is 13 x 12 = 156. Why did we not use = 78?
Flush
There are = 1,287 possible hands with all cards in the same suit. Recall that there are only 10 straight flush on a given suit. Thus of all the 5-card hands with all cards in a given suit, there are 1,287-10 = 1,277 hands that are not straight flush. Thus the total number of flush hands is 4 x 1277 = 5,108.
Straight
There are 10 five-consecutive sequences in 13 cards (as shown in the explanation for straight flush in this section). In each such sequence, there are 4 choices for each card (one for each suit). Thus the number of 5-card hands with 5 cards in sequence is . Then we need to subtract the number of straight flushes (40) from this number. Thus the number of straight is 10240 – 10 = 10,200.
Three of a Kind
There are 13 ranks (from A, K, …, to 2). We choose one of them to have 3 cards in that rank and two other ranks to have one card in each of those ranks. The following derivation reflects all the choosing in this process.
Two Pair and One Pair
These two are left as exercises.
High Card
The count is the complement that makes up 2,598,960.
The following table gives the counts of all the poker hands. The probability is the fraction of the 2,598,960 hands that meet the requirement of the type of hands in question. Note that royal flush is not listed. This is because it is included in the count for straight flush. Royal flush is omitted so that he counts add up to 2,598,960.
Probabilities of Poker Hands
| Poker Hand | Count | Probability | |
|---|---|---|---|
| 2 | Straight Flush | 40 | 0.0000154 |
| 3 | Four of a Kind | 624 | 0.0002401 |
| 4 | Full House | 3,744 | 0.0014406 |
| 5 | Flush | 5,108 | 0.0019654 |
| 6 | Straight | 10,200 | 0.0039246 |
| 7 | Three of a Kind | 54,912 | 0.0211285 |
| 8 | Two Pair | 123,552 | 0.0475390 |
| 9 | One Pair | 1,098,240 | 0.4225690 |
| 10 | High Card | 1,302,540 | 0.5011774 |
| Total | 2,598,960 | 1.0000000 |
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2017 – Dan Ma
There are many casino poker variants to choose from, but unquestionably, three card poker is among the most fast-paced and thrilling. This essential guide takes you through everything you need to know; we breakdown the rules of 3 card poker and explain how to play the game. Plus, we cover all the side bets, bonuses, and payouts; and reveal the perfect three-card poker strategy.
How to play three card poker
The important elements of creating great casino poker games are to firstly make the rules easy to understand, and secondly, the payouts have to be appealing to players. Derek Webb, the game’s inventor, combines these factors to a tee. Learning the basics of how to play three card poker only takes a minute or two.
Of course, you want to refine your play with a proven strategy, but we’ll get to that part later. For now, let’s explain 3 card poker rules and guide you through the gameplay.
Three card poker rules
Once you know the rules, you’ll be well on your way to being able to play 3 card poker online. The game is played with a standard 52-card deck. Here’s a step-by-step guide to a single round.
- To begin a round, the player must place an ante bet.
- The dealer then deals three cards to the player, which are face-up, and three cards to himself, which are face down.
- Based on the three cards, the player can either fold the hand or continue by placing a play bet.
- If the player folds, he loses the original ante bet wager.
- If he continues, the cost of the play bet is equal to the ante bet.
- Assuming the player continues, the dealer turns over his three cards.
- The dealer’s hand needs to be at least Queen high to qualify.
- If the dealer’s hand doesn’t qualify, the player wins even money (1:1) on the ante bet, but the play bet is pushed (returned).
- When the dealer does qualify; the player’s hand is compared to the dealer’s hand. The winner is determined according to the order of 3 card poker hand ranks.
- If the player’s hand wins, he gets paid 1:1 on both the ante bet and the play bet.
- If the dealer’s hand wins, both bets are lost.
- It is possible for the hands to tie. In which case, the ante and play bets are pushed.
- Regardless of the outcome of the round, if the player holds a straight or higher, he wins an ante bonus (as described below).
Poker hand ranks
There’s a slight alteration in the poker hand ranks for this game (compared to most other forms of poker). The reason is that you are less likely to hit a straight draw than you are to get a flush draw. This is the ranking order, starting with the highest three card poker hand at the top:
- Straight flush: 3 cards of the same suit in consecutive order.
- Three of a kind: 3 cards of equal face value.
- Straight: 3 cards of mixed suits in consecutive order.
- Flush: 3 cards from the same suit but not in consecutive order.
- Pair: two cards of equal face value.
- High card: none of the above hands, means you only have a high card.
Three card poker odds and payouts
We described the standard 1:1 payouts in the 3 card poker rules outlined above, but those are just one part of this game. The excitement jumps up a few notches because three card poker also includes an ante bet bonus. The ante bet bonus is based purely on the player’s three cards. Therefore, you can win this bet but still lose the round.
Ante bet bonus payouts:
- Straight flush: 5 times the ante bet
- Three of a kind: 4 times the ante bet
- Straight: 1 times the ante bet
Pair Plus bet
Before the start of a hand, players can also make a Pair Plus side bet. Again, this wager is independent of the outcome of your game against the dealer. It’s based on the 3 cards you are dealt.
Pair Plus bet payouts:
- Straight flush: 40 to 1
- Three of a kind: 30 to 1
- Straight: 6 to 1
- Flush: 4 to 1
- A pair: 1 to 1
Six Card bonus
The six card bonus is another optional side bet, but not all three card poker games offer this wager. It uses the three player cards and the three dealer cards from which you must form a five-card hand that is on the pay table to win.
Pair Plus bet payouts:
- Royal flush: 1000 to 1
- Straight flush: 200 to 1
- Four of a kind: 50 to 1
- Full house: 25 to 1
- Flush: 15 to 1
- Straight: 10 to 1
- Three of a kind: 5 to 1
These poker hand rankings are more traditional with a royal flush being the best possible hand, and the flush payout is valued higher than the straight.
3 card poker strategy
We can categorize casino card games into two types. The first are games of chance, such as baccarat and Dragon Tiger. The others are decision-based games like blackjack, Caribbean Stud, and Casino Hold’em. Three card poker drops into the second type because the player makes a decision after seeing his cards on whether he wants to fold or continue by making the play bet.
All of these decision-based games have an optimal strategy. However, some of these involve studying playing charts, which dilutes the entertainment value of the game when you first start playing. The 3 card poker strategy doesn’t bother with such complexities. In fact, you only need to remember 3 cards.
The optimal three card poker strategy for the ante and play bet is QUEEN – SIX – FOUR
This means if your hand is equal to, or stronger than, Q-6-4, you should always raise and make the play bet. What you need to remember is to look at each card separately.
- Start with your highest card. If it’s lower than a Queen – you fold the hand.
- If the highest card is a King or Ace – you raise.
- If the highest card is a Queen, you must look at the second highest card. If lower than 6 – you fold the hand. But, if higher than 6 – you raise.
- If the second highest card is 6, you move onto the third card. Lower than 4 means you fold. 4 or higher, and you raise.
House edge
When choosing what casino games to play, you should always consider the house edge. This is essentially the advantage the casino has. The good news is the three card poker house edge is competitive, which is why this game has grown in popularity.
- The house edge for the ante and play bet combination is 2.01% when using the Q-6-4 strategy described above.
- For the Pair Plus bet, the house edge is 2.32% based on the pay table used in our example. This is reasonable value for a side bet.
- The same cannot be said for the Six Card Bonus bet. It has a house edge of 14.36% using the pay table shown. Therefore, even though the royal flush pays 1000 to 1, this side bet will cripple your bankroll over the long-term.
New players should note that the term ‘house edge’ is rarely used these days. Instead, the theoretical return to player (RTP) percentage is given. The RTP can be calculated by: 100% – house edge. Therefore, the RTP for the ante – play bet is 97.99%.
Tips for playing 3 card poker
Using our experience, and from talking with other three card poker players, we’ve composed a few easy-to-follow tips to help you get more from this game.
- Follow the Q-6-4 strategy. It can be tempting to play J-10-8 because the cards are all reasonably high, but this is not smart, and you will end up losing more than you win.
- Check the pay tables before you play. Several software developers have created their own variants, and there is also live 3 card poker. Just because the title of the game is the same, it doesn’t mean the pay tables are. This has an impact on the RTP, and you want to play where you get the best value.
- Avoid the Six Card Bonus wager. The RTP for this bet is 85.64%. That means on average (over the long-term) for every $100 wagered, you win $85.64.
- Manage your bankroll. You don’t want to play $20 ante bets, and $20 play bets if you only have $100 in your casino account. Look to divide your budget so you can get 50 to 100 hands out of what you have.
- Practice by playing free three card poker games. Most online casinos, after you have registered, will allow you to play in demo mode. This allows you to practice your playing and betting strategy. Please note, you won’t be able to play live 3 card poker games for free.
Live three card poker
The award-winning Evolution Gaming, in partnership with Scientific Gaming, has created a spectacular live dealer three card poker game. This brings you all the authentic gameplay that you get in a land-based casino, but from the comfort of your own home.
It should be noted that there is usually a trade-off playing live games. Most of the time, the RTP is lower due to the extra costs involved in operating these tables. For instance, we’ve read reports that the ante bonus on Evolution’s live variant pays 5 to 1, but you need a mini royal flush to claim it.
This title also has the two side bets we talked about above. However, the pay table for Pairs Plus is not identical. Playing live, there is a maximum payout of 100 to 1 for a mini royal. This may appear more rewarding, but the payout for a straight is less, so the house edge ends up being higher. With that said, playing three card poker live is a great experience, and we think it’s worth trying even though the RTP is not as high.
Where to play online three card poker
Three card poker may not have the iconic status of roulette or blackjack, but it’s catching up in the popularity stakes. Thanks to there being both virtual RNG and live games, you can now find this poker variant in hundreds of online casinos around the world, including:
- 888casino
- PlayOJO
- Mr Green
- Ignition
The decision where to play three card poker depends on what you want from the casino. Each operator has its strengths and weaknesses. Some offer larger bonuses, while others have faster payouts or better mobile apps. If you’re looking for your first casino, we recommend checking out our online casino reviews section for an honest point of view. In terms of bonuses specific for 3 card poker; the truth is that there aren’t many. You can use a casino’s welcome bonus to play, but the wagering requirements combined with game weighting limitations means you are unlikely to score a profit from these offers.
Three card poker – F.A.Q.
To summarize the main points of this article, we’ve included this general three card poker FAQ.
Is there any strategy to 3 card poker?
Yes, and it’s very straightforward. The strategy is Queen – Six – Four. If your hand value is lower than that, you fold. If equal or higher, you make the play bet.
What is the highest hand in 3 card poker?
The highest hand is Ace – King – Queen of the same suit. This is known as a mini royal. There are no trump suits in three card poker.
Do I play against other players?
No, three card poker is a player vs dealer game. If you play live, you can play alongside other players although each of you has to take on the dealer.
Can I play free 3 card poker?
Yes, nearly all online casinos that offer an RNG version will allow you to play free 3 card poker in practice mode.