Possible Poker Hands

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 lowest possible Straight Flush that you can form is 2, 3, 4, 5, 6. The highest possible Straight Flush you can form is 9, 10, Jack, Queen, King. You can form a straight flush through a combination of pocket cards and the board, and only a royal flush hand can beat this.
• The composition of the community poker cards will determine how many strong potential hands are in play. If you hold three of a kind, but there are four cards to a flush and four cards to a straight, your poker combination strength goes down.

The order of the hands in poker from strongest to weakest are as follows. Royal flush, straight flush, four of a kind, full house, flush, straight, three of a kind, two pair, one pair, high card. Question 4: How are poker hands constructed? In most variants of poker, it is necessary to use exactly five cards to make a hand. At the begging of each round of Texas Hold 'Em poker, you are dealt two cards. These are your hole cards or starting hand. Those hole cards can eventually be used with the cards revealed in the flop, turn and river to assemble a (hopefully) winning hand. After you are dealt your starting cards, there is. Print out this free poker hand rankings chart – and always know the best winning poker hands. Poker hands are ranked in order from best to worst. Royal Flush An ace high straight flush. Straight Flush Five consecutive cards in the same suit. Four of a Kind Four cards of the same rank.

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

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2017 – Dan Ma

Table Of Contents

Do you want to know what beats what in poker? Use the official poker hands rankings chart and seem them from best to worst!

Whether you play live at your local casino or card room, you have your home game going, or you prefer the online action at websites like PokerStars, 888Poker, or partypoker, you need to learn the order of poker hands from best to worse.

Use the list of poker hands below to know what beats what in poker.

Commit this poker hands ranking list to memory today and print it if you need it (there's a button for it at the bottom). Knowing the correct poker hands rank is key to start making winning poker hands.

Poker Hands From Best To Worst

Poker Hands From Best To Worst

Not Sure What Beats What in Poker?

Many consider poker less of a gambling game than other casino games. For that to be true, players need to improve their understanding of game play and the strategy required to be a winning player.

The first step toward learning how to play poker is to learn the poker hand rankings.

Most poker players have these rankings memorized, which allows them to think about other things at the table when deciding the best way to play their hands.

The good news is these hand rankings tend to be the same among a wide variety of poker variants, whether it is Texas Hold'em, Omaha, seven-card stud, or other games.

All of those games use the same traditional poker hand rankings that were first developed way back in the 19th century when five-card draw first started to be played.

On this page, you find a complete list of poker hand rankings going from the highest possible hand (the Royal Flush), down to the lowest hand in which there is no pair among the five cards.

Hand rankings in poker correspond to the likelihood of making such hands.

A royal flush, consisting of the cards ranked ace through ten all being the same suit, is extremely rare — in fact, some players go their entire lives without making a royal flush.

A regular straight flush with any five consecutive cards of the same suit is a little less rare, four of a kind occurs slightly more frequently, and so on.

Notice that a full house is ranked higher than a flush.

That's because a full house comes just a little less frequently than a flush, thereby making it the higher-ranked hand of the two.

Additional readings for beginners:

• Poker Tips: A collection of tips 'to bring your game from 'meh' to amazing' created to help beginners become better players.
• Texas Hold'em Strategy: a complete manual to read as soon as you start to remember what beats what in poker.
• Poker starting hands chart: the only article you need to read to learn how to use your cards to the fullest.

Understanding Winning Poker Hands

Players new to the game of Texas hold'em often struggle, at least at first, with what the best poker hands are.

Once they have read this easy-to-digest guide that will no longer be the case.

The aim of Texas hold'em is to make the best five-card poker hand at showdown.

You can win without having to show your cards if you force someone to fold before the river. Nonetheless, for the purpose of this article, we'll pretend that we've gone to showdown and need to know what beats what in poker.

Winning Poker Hands: What Are The Best Hands In Poker?

First up is the weakest possible holding you can make in poker, a hand that can still win you the pot, although the likelihood of that happening decreases in a pot involving multiple players.

We are of course talking about high card.

As the name suggests, you don't even hold a pair here and instead are using the highest card among the five you are playing.

Example:

You have and the board has come .

Your best five-card hand would be where you would hold queen-high.

Next up is one pair, one of the more common Texas hold'em hands and one that will win you plenty of pots.

Example:

You have and the board comes .

Your five-card hand is — you have a pair of aces. Nice poker hand!

One place higher up on the poker hands chart is two pair.

Example:

You have and the five community cards are .

Your best five-card hand at showdown is or two pair, tens and nines.

One note of warning on this specific poker hand: if you are verbally declaring your hand, try to announce the higher pair first as to help avoid confusion.

Good Poker Hands

Now we're getting into the realm of the best poker hands because once you make three-of-a-kind (sometimes called a set or trips), you are much more likely to win the pot than with any of the previously mentioned hands.

Example:

Your five-card poker hand is — you have three-of-a-kind kings, often a very powerful hand in hold'em.

To beat three-of-a-kind you're going to need at least a straight.

A straight is five consecutive cards where at least one of them is a different suit from the others.

Example:
Should your hand read you would hold a six-high straight.

If someone held a seven-high straight, then that player would win the hand.

There are two straights that have nicknames that are worth remembering.

A wheel is a straight that runs from ace-to-five, and a Broadway straight — the strongest straight — runs from ten-to-ace.

A flush is one of the most powerful Texas hold'em hands because it is only beaten by a handful of others.

Any hand that that has five cards of the same suit is a flush.

Aces are always high when it comes to flushes, which means a hand such as beats .

There are few hands that can beat a flush — one that does is a full house. Also called a 'boat,' a full house is when your five-card hand is made up of three of a kind plus a pair.

Possible Poker Hands 52-card Deck

Example:

With you have kings full of deuces, while is fives full of queens.

When it comes to full houses, the higher three of a kind determines which hand wins, so in this case 'kings full' would beat 'fives full.'

The Stronger Hands in Poker

The next three holdings are so rare that if you hold them, you can almost guarantee that they are winning poker hands.

Four of a kind is the minimum holding you'll need to beat someone with a full house.

Again, as the name suggests, four of a kind means having four cards of the same rank.

Example:

is four-of-a-kind tens and an extremely powerful holding.

Your only way to beat four of a kind, or 'quads' as they are often called, is to hold either a straight flush or a Royal Flush.

The former is five consecutive cards all of the same suit, so would be an eight-high straight flush and practically unbeatable.

If you manage to make (or the same holding in any of the other three suits), you have a Royal Flush and the only way to lose the hand would be to fold by accident!

Poker Hands Probability

If you are into numbers (most poker players are), you might be wondering about the probability of poker hands.

We said that she platers might go entire lives without ever getting the highest hand in poker but, looking at the numbers, what are the odds of a Royal Flush?

In this section of our complete analysis of the poker hand ranking and what beats what in poker, you get a clear overview of the probability of poker hands.

How to calculate the probability of poker hands?

When you know that there are 52 cards in play and 2,598,960 possible combinations, the calculation is easy.

You just need to divide the number of possibilities to build a specific poker hand by the number of total poker hands.

Let's run a few examples:

What are the odds of a Royal Flush? 0.000,001,539
(4/2,598,960)

What are the odds of a Straight Flush? 0.000,015,39
(40/2,598,960)

Use the table below to calculate the probabilities of all poker hands.

Absolute Value vs. Relative Value of Poker Hands

It should be noted also that while poker hand rankings never change, sometimes circumstances can make a good hand less valuable and a poor hand more valuable.

In other words, when it comes to poker hands there's a difference between absolute value (reflected in the list of poker hands above) and relative value.

For instance, in a game of Texas hold'em, if you have two pair that might seem like a good hand.

But if your opponent keeps betting into you and it's possible he could have a straight or flush, your two pair is no longer looking so good.

Meanwhile, if you have just one pair but your opponent keeps checking to give you a free play at the pot, you might well have the strongest hand and should bet your hand.

The 'absolute' value of your hand may not be great, but in that case the 'relative' value very well could be.

Also worth mentioning is the fact that in some games like razz, deuce-to-seven triple draw, Badugi, and others you might encounter when playing online poker, the hand rankings listed below do not apply.

These hand rankings are for regular or 'high-card' games, not 'lowball' games with alternate hand rankings.

Poker Hand Rankings F.A.Q.

What is the order of poker hands?

As shown in the poker hand rankings chart, the order of poker rankings (from the highest to the lowest) is: Royal Flush, Straight Flush, Four-of-a-Kind, Full House, Flush, Straight, Three-of-a-Kind, Two Pair, One Pair, High Card.

What is the best hand in poker?

The Royal Flush is the best hand in poker. To have a Royal Flush, you need an Ace, a King, a Queen, a Jack, and a 10. All the cards that compose the hand need to be of the same suit.

What beats what in poker?

As you can see in our poker hand rankings chart, the hands in poker follow a clear hierarchy.

In a game of poker, the hand rankings work as follows:

• a pair beats a high card;
• a two pair beats a one pair;
• a three-of-a-kind beats a two pair;
• a straight beats a three-of-a-kind;
• a flush beats a straight;
• a full house beats a flush;
• a four-of-a-kind beats a full house;
• a straight flush beats a four-of-a-kind;
• a Royal Flush beats a straight flush.

The Royal Flush is the best hand in poker, so no one other hands beat this one.

What is a straight in poker?

You have a straight when all the five cards that compose your poker hand are consecutive ones. E.g. 5-6-7-8-9.

If the cards are of the same suit, you have a straight flush, which is a considerably stronger hand compare d to the simple straight.

What beats a straight in poker?

Although many see the straight as a stronger hand, there are many other poker hands that beat it.

The list of hands that beat a straight includes:

• a flush;
• a full house;
• a four-of-a-kind;
• a straight flush;
• a Royal Flush.

What beats a flush in poker?

The list of hands that beat a flush includes:

• a full house;
• a four-of-a-kind;
• a straight flush;
• a Royal Flush.

What beats a full house in poker?

The list of hands that beat a full house includes:

• a four-of-a-kind;
• a straight flush;
• a Royal Flush.

What is the highest suit in poker?

All the suits in poker have the same value. In some games, different suits can be assigned different values.

When that happens, the value is as follow (from the lowest to the highest): clubs, diamonds, hearts, spades. In that case, spades is the highest suit.

How many poker hands are there?

The total number of poker hands in a game of poker is 2,598,960. Since a game of poker uses a 52-card deck of French cards, there are 2,598,960 different possible combinations (aka. poker hands).

What hands to play in poker?

The type of hands to play in a poker game depends on the game you play and other factors like your position in the hand, your stack, and the action at the table.

In a famous poker strategy article, professional player Jonathan Little shared which hands to play in poker and how to play marginal hands.

Can you make three pairs?

Although it is possible to hold a pair in your hand and then have another two pair appear among the five community cards, you can only use a total of five cards to make your poker hand, so you don't win anything for three pairs.

Which is better, a set or trips?

They are both essentially the same hand because they are both three of a kind.

The terminology 'set' is used when you have a pair as your hole cards and then catch another one of those cards on the board.

'Trips' is when there is a pair on the board and you have another of those cards as one of your hole cards.

Sets are easier to disguise than trips so many consider them to be a better hand, although they both rank the same.

What is a chopped or split pot?

If you and an opponent have the same five-card poker hand, then the pot is divided equally between you.

Say you have and your opponent has , and the board comes .

You both would be playing the same five-card hands in terms of their value (A-J-T-8-3), and so would split the pot.

If there is four of a kind on the board, who wins?

Because the aim is to make a five-card poker hand, whoever has the highest fifth card in this case wins.

Best Poker Hand Possible

If the board reads and you have in your hand and your opponent has , then you win because you hand is 7-7-7-7-A and your opponent's is 7-7-7-7-K.

You would also win even if your opponent holding was in this example.

Are the suits ranked in Texas hold'em?

No, they are not. Some poker variants have different ranks for suits, but hold'em is not one of them.

Why did my 4-4-4-T-T lose to my opponent's 7-7-7-8-8?

As mentioned earlier, it is the three-of-a-kind element of a full house that dictates the winner.

If you're new to the game and want a reference of all of Texas hold'em hands, you can keep this page open or you could always download and print our poker hands ranking chart and keep it next to you while you're playing poker.

Possible 5 Card Poker Hands

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