Poker Hands Rank Chart
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
The poker hand ranking charts are based on the probability for each distinct hand rank. More unlikely combinations are ranked higher. Those are the probabilities and odds for all 5-card poker hands: Poker Hand Odds for Texas Hold’em. Poker Starting Hand Chart (6-max Cash, 100bb): Hand Chart Notation Getting to know which hands to play and in which positions is even more important than the actual hand. This 6-max Cash Hand Chart details the hands you should play and the position. Poker Hand Rank #3 - Four of a kind. Four of a kind means four cards of the same value and any other card. If there are two hands with Four of a kind in the same game, the highest ranking Four of a kind wins i.e. Four Ks beats four 9s.
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:
Poker Hands Rank Chart
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
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.
Poker Hands Rank Chart 2020
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
For beginner poker players, memorizing the poker hand rankings can seem overwhelming. There are a lot of moving parts in a poker hand and trying to remember if a straight beats a flush can be confusing.
Don't panic, though. What seems confusing at first will become second nature very quickly. As an added benefit, poker hand rankings for all standard 'high hand' poker games - Texas Hold'em, Omaha, 7-Card Stud, etc - are always the same.
Poker Starting Hands Ranking Chart
A Royal Flush will always be the best hand you can get. A full house will always beat a flush. And a set will always beat two pair.
There are some poker hand ranking situations that will arise where you might need a little help - we've identified and explained a few of those below the hand ranking chart below.
Trust us - you'll get it! And soon you'll be the expert explaining to your friend at your home game why his two pair is the losing hand. Bookmark this page to keep our poker hand ranking chart as an easy reference guide - and check back for a downloadable Poker Hand Ranking PDF to come soon!
Official Poker Hand Rankings
Poker Hand Ranking FAQ
Which is higher a flush or a straight?
Always the flush is higher! This is one of the bigger misconceptions of poker hand rankings.
Despite it seeming to some that a straight is more difficult to get, a flush – meaning five cards of the same suit – is actually less likely of a hand to put together. Therefore the Flush is ranked higher than the Straight.
This applies in every situation – even if the Straight has more high cards (or the highest card) between the two hands. A Straight Flush, which is a straight with all of the cards of the same suit (eg. 4h-5h-6-h-7h-8h), is higher than both of those hands.
Which is higher, three-of-a-kind or two pair?
This is another common poker hand ranking confusion. A “set” or “trips” or 3 of a kind ALWAYS beats two pair.
Again it doesn’t matter if it’s a set of 2s and the two pair are Aces and Kings – the set always wins.
How do you know which two pair hand is higher?
The ranking of your two-pair hand is NEVER the sum of your two pairs. So, for example, two pair of Aces and 2s is ALWAYS higher than two pairs of Kings and Queens. The face cards look more powerful, sure, but it is only the HIGHEST single pair of the two pair that determines the winner.
If both of the high pairs are the same then the second pair will determine the winner. If both pairs are exactly the same the higher 5th card – aka “the kicker” decides the winner.
How do you know which Flush is higher?
If two players both have a Flush the hand with the highest card is the winning Flush. This means any Flush with an Ace is it will win over any other Flush. Much like two pair the combined total of the Flush is not relevant – only the single highest card determines the winning hand.
So: Ah-9h-7h-5h-2h beats Kh-Qh-Jh-Th-8h
If the top card of the Flush is the same in both hands (ie it’s from the shared community cards), the next highest Flush that’s not shared determines the winner. If the Flush is entirely on the board and neither player has a card of the same suit in their hole cards, it’s a split pot as long as neither player folds.
What is a kicker in poker?
A kicker is an unmatched card that's not part of a made hand that determines who wins when two players have the same ranked hand.
For example if both player have a single pair of aces, the next highest card in each of their hands are matched against each other to see which is highest. Eg.
- Player 1 has A-A-Q-6-2
- Player 2 has A-A-9-7-6
Player 1 is the winner as the Queen 'kicker' is higher than the 9 kicker. If the first kicker cards are the same, eg AAQ and AAQ, the next kicker card is then used to determine the winner.
If players both have the exact same two-pairs, the remaining fifth card is the kicker. If players have the exact same three-of-a-kind, the remaining two cards are kickers. If both hands have just a single high card all cards are considered the kickers
What does it mean to 'play the board?'
Playing the board means the 5 shared community cards in the middle of the table are the five cards that make up a player's best possible five card hand.
For example if the board cards are:
A-K-Q-J-T of different suits and a player's hole cards are the 6-7 of hearts, that player's best possible 5-card hand is the Broadway straight and his or her hole cards are inconsequential to the hand.
If all players left in the hand are 'playing the board,' the pot is split evenly among them. A player must make it all the way to the showdown to play the board.
Do Aces count as high or low?
In a standard 'high' poker game like Texas Hold'em aces can be played as either high or low. An ace can be used, for example, to complete the bottom end of the straight A-2-3-4-5. This is called a 'wheel' is is the lowest possible straight.
It can also of course be used as a high card as as the high end of a straight eg A-K-Q-J-T. It cannot, however, be 'wrapped around.' So Q-K-A-2-3 is NOT a straight.
In Lowball games Aces can be either high or low; it depends on the game variation. For specific poker hand rankings for lowball games, check our rules pages below.
Is 'Three Pair' a hand?
Three pair is not a hand. Your best poker hand is made up of 5 cards and 5 cards only. You can never have three pair.
Which poker suit is the highest?
In standard 'high hand' poker games like Texas Hold'em and Omaha, suits are not ranked compared to each other. Meaning no one suit is ranked higher and suits are not used to determine the winning hand. Only the card rankings matter
In other card games, however, suits can be ranked and come into play when determining betting order or winning hands. Typically suits are ranked in reverse alphabetical order from lowest to highest.
The only place where suit can come into play in poker is in 7-Card Stud, when the player with the lowest card showing has to pay the 'bring in' bet in the first betting round. If two players have the same ranked card, suits can be used to break the tie.
Are all red cards or all black cards a good hand?
Unless the suits are the same, five cards all of the same color are not a poker hand. A Flush by definition will have all red or black cards but all the cards must be diamonds or hearts or clubs or spades for it to be a Flush.
More Poker Games Rules
Further Reading: