With few exceptions, all poker games place hands on the same
scale from high- to low-value. Poker hands are ranked depending
on their likelihood. The least-likely hands are the
highest-ranked; the most common hands are the lowest-ranked.
Identical poker hands are ranked by which hands holds cards of
the highest value.

Hold’em, Omaha, Seven Card Stud and Five Card Draw all use the traditional ‘high’ poker rankings. Omaha Hi/Lo, Razz and Stud Hi/Lo use the ‘Ace to Five’ (‘California’) low hand rankings for low hands. 2-7 Single Draw and 2-7 Triple Draw use the ‘Deuce to Seven’ (‘Kansas City’) lowball rankings for low hands. Use our poker hands reference chart until you are 100% certain of hand rankings. Poker hands from strongest to weakest Royal Flush: Five card sequence from 10 to the Ace in the same suit (10,J,Q,K,A). The standard ranking of poker hands is below, listed from highest to lowest. All standard poker hands are made up of exactly five cards (no more, no less). The top five cards in a single suit: 10, J, Q, K, A all of the same suit. Really, a Royal Flush is just the best possible straight flush. There can be no ties in a hand with royal flush, as there is only one card of a number and same suit.

Poker Hand Rank

Here is the standard hand rank, from highest to lowest:

Poker Hands Ranking Suits One Piece

A royal flush is a hand where all the cards are of the same suit and the 5 highest cards in consecutive order (10, J, Q, K, A). This hand is the best hand that you can get in the game of Texas Hold’em.

A straight flush is a hand where all the cards are of the same suit and are in consecutive order. For example, a 23456, all of hearts, is a straight flush. In the event of a tie, the straight flush with the highest card wins.

A 4 of a kind is a hand where 4 of the 5 cards are of the same ranking. An example of a hand with a 4 of a kind might have KKKK2. That would be the 2 in every suit–clubs, diamonds, hearts, and spades. In the event of a tie, the 4 of a kind with the highest hand ranking wins.

A full house is a hand that consists of 3 cards of one rank and 2 cards of another rank. An example of a full house might look like this: KKKQQ. In the event of a tie, the hand with the higher cards in the 3 cards is the winner.

A flush is a hand that consists of 5 cards of the same suit—clubs, diamonds, hearts, or spades. In the event of a tie, the flush with the highest card is the winner.

A straight is a hand where all 5 cards of consecutive ranks. 23456 is an example of a straight. In the event of a tie, the straight with the highest card is the winner.

2 pairs is a hand where you have 2 cards of one rank and 2 cards of another rank along with a final card of another rank. An example of 2 pairs might look like this: AAKK7.In the event of a tie, the hand with the highest pair wins.

1 pair is a hand where you 2 cards of one rank and 3 cards with different ranks. An example of a pair might look like this: JJ278. In the event of a tie, the higher ranked pair wins.

High card means a hand where none of the other hand rankings apply. If no one still in the hand can make a pair or better, the player with the highest card in his hand wins the pot.

Playing a live game of poker requires that you know this
hierarchy. For new players, this may seem a little daunting.
After all, here you have nine pieces of complex information to
remember in precise order.

A Word About Mnemonic Devices

I learned the order of poker hands using a mnemonic. I think
anyone can use this simple method to learn the hierarchy in a
matter of minutes. Mnemonics are popular memory devices used by
students, teachers, and people of all stripes for hundreds of
years in order to remember complex information.

You probably used a mnemonic device to remember the order of
the planets in our solar system. I remember learning the
sentence: “My very excellent mother just served us nine pizzas.”
The first letter of each of the words in that sentence will help
you remember that the planets go in this order – Mercury, Venus,
Earth, Mars, Jupiter, Saturn, Uranus, Neptune, Pluto. I’ll
probably never forget that fact, thanks to the mnemonic device I
was taught.

The trouble is, it’s hard to convert hand rankings into
words. Besides that, I don’t think you learn much about poker by
simply memorizing the order of hands. You should use the
opportunity of needing to learn proper hand hierarchy to improve
your understanding of poker strategy.

The tips below will help you understand the proper order of
poker hands better and introduce you to some basic poker
concepts to help you improve your overall game.

Low-Value Poker Hands

To remember the order of the four lowest-value hands, just
remember the number series “0, 1, 2, 3.”

• 0 means “high card.” Having nothing in your hand means
  the value of your hand depends on the value of your highest
  card. Remember – in poker, aces rank high, while 2’s rank
  low.
• 1 means “one pair.” Any hand that contains just a single
  pair of cards and nothing else valuable is a 1.
• 2 means “two pair.” This is a hand that contains two
  pairs of cards.
• 3 means “three-of-a-kind.” It’s the most valuable of the
  low-value hands.

High-Value Poker Hands

For the purpose of this post, I’m calling every hand above a
three-of-a-kind a “high-value hand,” but lots of poker
strategists would consider a straight to be a low-value hand.
This is really a difference in philosophy and a language issue
more than anything else.

For that reason, and for simplicity’s sake, I like to think
of straight as a “/” symbol in my mnemonic. That means our
current mnemonic string goes: “0, 1, 2, 3, /.”

It’s easier to memorize the order of the other high-ranking
hands if you count the number of letters in the hand’s name.
It’s made all the easier to remember by the fact that the number
of letters increases as you move up the scale.

Here’s how I break it down:

• 5 – The word flush contains five letters.
• 9 – The words full house contain nine letters.
• 11 – The words four of a kind contain eleven letters.
• 13 – The words straight flush contain thirteen letters.
• 18 – The words royal straight flush contain eighteen
  letters.

Putting them all together, our mnemonic is: “0 – 1 – 2 – 3 /
5 – 9 – 11 – 13 – 18.”

Other Ways to Memorize Hand Hierarchy

I’m not going to pretend that the method I used to learn hand
hierarchy is the only one that will work. The three ideas below
are the most popular tactics on the Web besides the use of
mnemonics, based on my research. You can use any of the four
methods described on this post to keep track of what hand beats
what other hand. That way, you’ll be able to plan your tactics
ahead of time and make smart bidding decisions.

Rote Memorization

Some people learn best by repeated drilling of the material
to be memorized. I’ve heard of actors reading their scripts over
and over, playing tapes of the script in their sleep, and
learning their lines by rote. I can’t think of any reason why
you shouldn’t try this method.

Hand Evaluation Diagrams

Various poker trainer programs and strategy gurus have put
together diagrams to help you analyze your hand. You can use
these in poker rooms, and obviously you can use them online, so
long as you don’t care about the other guys at the table making
fun of you. They’re available for free with a simple Google
search.

Frequent Exposure

The more rounds of poker you play, the more you’ll become
familiar with all the rules, including the rules of hand
ranking. You may lose a bunch on the way there, because of your
lack of familiarity with hand ranks, but, by God, you’ll get it
eventually.

Conclusion

Remember that some poker variations assign different values
to cards and hands. Some games are totally reversed, rewarding
the lowest-value hand instead of the highest-value one. Other
games may consider an Ace to be low, or use Jokers, which throws
off the hierarchy and strategy a bit.

I hope that this page helped you learn about the value of the
cards you’re dealt. I believe the best way to practice your
newfound understanding of hand hierarchy is to get out there and
play a bunch of poker. If you’re still new to the game and not
yet comfortable with your understanding of hand rankings, you
can always play in free-to-play apps or use play-money at your
favorite online poker room.

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

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

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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 Hands Ranking Suits Against

Poker Hands Ranking Suits 2019

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2017 – Dan Ma