- In low games, like razz, the lowest-ranking hands win. In high-low split games, both the highest-ranking and lowest-ranking hands win, though different rules are used to rank the high and low hands. Each hand belongs to a category determined by the patterns formed by its cards. A hand in a higher-ranking category always ranks higher than a hand.
- Your starting hands need to work together, cards that work together tend to be winning poker hands! At showdown, the Omaha8 total pot will be divided by 2; half will go to the winning high hand(s), and half will go to the winning low hand(s) if there are qualifying low hands. To qualify for a high hand, standard NLHE or LHE (high poker) rules.
- What Is The Lowest Hand In Poker
- What Is The Lowest Possible Hand In Poker
- What Is The Highest Winning Hand In Poker
Against a hand of KJ87643, the ace-high hand would be the winning hand. If the king-high hand were up against KQT8542, the queen in this hand being the highest next card would beat the KJ87643. The winning hand would be read as; king high, high kicker. In Hi/Lo games, there is always an Eight qualifier for the low. In other words, to qualify as a low hand, you must have five different cards ranked Eight or below. Thus 8-7-6-5-4 qualifies as a low hand in Hi/Lo games, whereas 9-4-3-2-A and 4-3-3-2-A do not.
Poker Hands Has The Best Winning Poker Hands In Order
Poker Hands in Order Hand Rankings List and Poker Hierarchy Pictures Below. Keep the List Handy and Book Mark this Page so you can refer to our ultra easy to follow Poker Hands Order Listing of Winning Hands High to Low.
Very easy and quick to use and memorize Poker Hand Listings Ranked Below that should enable you to make the decisions needed to make good calls, raises, and all in decisions when you know what you can beat, and what you cant. Great for New Poker Players just starting out! Everyone's gotta learn some time!
Poker Hands Royal Flush Straight Flush Four of a Kind Full House Flush Straight Three of a Kind Two Pairs One Pair High Hand Winning Poker Hands in Order Rankings
Poker Hierarchy Listing of Winning Hands High to Low
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- Royal Flush AKQJ10 Of the same suit
- Straight Flush 5 cards in order of the same suit 65432 and up
- 4 of a Kind Any four cards the same from AAAA to 2222
- Full House Any 3 cards the same plus 2 different the same
- Flush Any 5 cards in the same suit
- Straight Any 5 cards in order not suited
- 3 of a Kind Any 3 cards the same
- 2 Pair Any 2 cards the same plus another 2 the same
- AA AA and 22 for 2 pair beat KK QQ 2 pair as the
- KK highest suit AA takes rank above all the others
- JJ
- 1010
- 99
- 88
- 77
- 66
- 55
- 44
- 33
- 22
- ACE HIGH
- KING HIGH
- QUEEN HIGH
- JACK HIGH 10, 9, 8, 7, 6, 5, 4, 3, 2
Try Out Your Texas Holdem Winning Hands at the Best Online Gambling Poker Sites in the Business
Keep in mind that common poker hands are often top pair with top kicker. Most poker players are looking to trap you by hitting two pair or better yet 3 of a kind aka 'trips'. These are often big hands paying out big pots when there are no flush or straight draws available that people may be fishing for.
Texas Holdem Poker Hand Rankings List of Poker Hands by Rank
[/sociallocker]
Winning Poker Hands and What Beats What Poker Hand Ranking
Royal Flush The Number One Hand Rank and Best Hand In Poker
Why would it be called a Royal Flush?
A Royal Flush is the same as a 5 card Straight flush only it ranks as a royal because of the fact that it contains the Jack, Queen, and King, which are symbols of Royalty from times long ago up until today. As royalty is the upper echelons of society so be it the upper class poker hand ranking.
What are the odds and probabilities of hitting a royal flush?
Slim to none, you might not ever see it in a lifetime whereas someone else may see it a few times. Your Poker Hand Man at Poker hands has been lucky enough to hit it 2 times. One time online and one time no word of a lie, playing strip poker.
Yup, I thought what a time to hit this hand, why could it not be in Vegas or on a Video Poker Machine. Probability of 0.000154% and odds of 649,739 : 1 So anyhow its somewhere around one hand out of over 650 000 thousand plus or minus a few thousand hands you will see a Royal Flush Holdem Poker Hand. Good Luck I hope you get one when it counts!
Royal Flush Poker Hand Rank #1
Poker Hands Royal Flush Highest Ranking Cards Ranked #1
Royal Flush Best Poker Winning Hands in all Four Card Suits Copyright : Sergii Telesh 123rf.com
What is a Royal Flush Poker Hand?
A Royal Flush is the Holy Grail of Poker Hands Ranked Number #1
How often do you get a Royal Flush? I mean What are the odds of a Royal Flush?
Not very often do you get a Royal Flush only one in approximately 400 thousand hands.
Is a Royal Flush the Highest Hand? Yes you can only tie it. But have never seen that ever.
Straight Flush Poker Hands Ranking #2
Straight Flush Winning Poker Hands Rank Suited in Hearts Copyright: www.123rf.com/profile_mackoflower
What is a Straight Flush Poker Hand?
It is 5 cards of the same suit, hearts, diamonds, clubs, or spades. This is the Flush Part of the Card Hand. The Straight part refers to the numbers all being in order with no missing cards from the order within the 5 card poker hand. Therefore you see above 45678 all ranked in order and all the same suit which is called a flush, together combined making the poker hand ranking of straight flush which is number 2 in the list of Poker Hand Rankings.
What does a Straight Flush Poker Hand Beat?
Everything but a royal flush. The only thing that can beat a straight flush hand is another straight flush hand that is higher. For example, if you had the 45678 of hearts as shown in the picture above and I had a straight flush in spades 34567 then you Beat Me. Your 5th high card in the straight flush is an 8 which is higher than my last card 7. Best free poker hud pokerstars.
What Beats a Straight Flush Poker Hand?
The Reverse Of the Hands Mentioned above which is a higher straight flush beats a straight flush and then a Royal Flush beats Any straight flush hand 9 10 J Q K or lower. Ip casino biloxi mississippi phone number.
What is a Flush Card Poker Hand?
A Flush is 5 cards all the same suit. It does not matter what card value as long as you have all 5 cards making up your hand all the same suit.
What Does a Flush Poker Hand Beat?
A flush Poker Hand Beats everything but a straight flush and royal flush. The only time a flush beats another flush is when 2 or more players at the same showdown hand have flushes. If so the one with the highest card overall in his flush hand wins. For example if you have ACE 3456 of any suit suited (Notice no 2 which would make it a straight flush) and I have King Jack 10 9 8 suited (Again notice no Queen which would make it a straight flush again.) You win! All my cards are higher than yours except the Ace which plays high and you win. Then it goes from there on to the 2nd card, 3rd card etc if need be, but rarely ever does. For example I had an Ace 2347 then I win because my ace matches your ace but my 7 out ranks your 6.
Poker HandsSuggests You Read about Poker History at our Texas Holdem Fun Filled Information page on the Rise of Texas Holdem Poker.Thanks for coming and join us and watch as this site grows into something wonderful for those interested in Poker Hands and all things Poker. Bookmark and link to Us for all your Poker Information. What we don't have now will be here eventually. So stay tuned and SHARE Us.
Thanks for coming and stay tuned for more at Pokerhands.poker and book mark us for all your PokerHand Ranking and Online Poker and Poker Tournament Information.
P>S> If Your Eager To Try Your PokerHand TexasHoldem Skills out in Online Poker look no further than below in the footer of this page for Ignition Poker for USA Residents and Party Poker and 888 Poker For Everyone Else. All three sites are Giants and Well Respected in the Online Poker World, offering easy ways to Deposit and Withdraw once you start crushing Tournaments, Sit n Goes and Hand Games. Go Get to Multi tabling with your Poker Hand skills and Rake it in! Here You can Find Information on all The Best Online Poker Sites and thanks for checking out and bookmarking our Poker Hands Order Hand Ranking Page!
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.
___________________________________________________________________________
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.
___________________________________________________________________________
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 |
___________________________________________________________________________
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.
What Is The Lowest Hand In Poker
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.
What Is The Lowest Possible Hand In Poker
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.
- JJ
- 1010
- 99
- 88
- 77
- 66
- 55
- 44
- 33
- 22
- ACE HIGH
- KING HIGH
- QUEEN HIGH
- JACK HIGH 10, 9, 8, 7, 6, 5, 4, 3, 2
Try Out Your Texas Holdem Winning Hands at the Best Online Gambling Poker Sites in the Business
Keep in mind that common poker hands are often top pair with top kicker. Most poker players are looking to trap you by hitting two pair or better yet 3 of a kind aka 'trips'. These are often big hands paying out big pots when there are no flush or straight draws available that people may be fishing for.
Texas Holdem Poker Hand Rankings List of Poker Hands by Rank
[/sociallocker]
Winning Poker Hands and What Beats What Poker Hand Ranking
Royal Flush The Number One Hand Rank and Best Hand In Poker
Why would it be called a Royal Flush?
A Royal Flush is the same as a 5 card Straight flush only it ranks as a royal because of the fact that it contains the Jack, Queen, and King, which are symbols of Royalty from times long ago up until today. As royalty is the upper echelons of society so be it the upper class poker hand ranking.
What are the odds and probabilities of hitting a royal flush?
Slim to none, you might not ever see it in a lifetime whereas someone else may see it a few times. Your Poker Hand Man at Poker hands has been lucky enough to hit it 2 times. One time online and one time no word of a lie, playing strip poker.
Yup, I thought what a time to hit this hand, why could it not be in Vegas or on a Video Poker Machine. Probability of 0.000154% and odds of 649,739 : 1 So anyhow its somewhere around one hand out of over 650 000 thousand plus or minus a few thousand hands you will see a Royal Flush Holdem Poker Hand. Good Luck I hope you get one when it counts!
Royal Flush Poker Hand Rank #1
Poker Hands Royal Flush Highest Ranking Cards Ranked #1
Royal Flush Best Poker Winning Hands in all Four Card Suits Copyright : Sergii Telesh 123rf.com
What is a Royal Flush Poker Hand?
A Royal Flush is the Holy Grail of Poker Hands Ranked Number #1
How often do you get a Royal Flush? I mean What are the odds of a Royal Flush?
Not very often do you get a Royal Flush only one in approximately 400 thousand hands.
Is a Royal Flush the Highest Hand? Yes you can only tie it. But have never seen that ever.
Straight Flush Poker Hands Ranking #2
Straight Flush Winning Poker Hands Rank Suited in Hearts Copyright: www.123rf.com/profile_mackoflower
What is a Straight Flush Poker Hand?
It is 5 cards of the same suit, hearts, diamonds, clubs, or spades. This is the Flush Part of the Card Hand. The Straight part refers to the numbers all being in order with no missing cards from the order within the 5 card poker hand. Therefore you see above 45678 all ranked in order and all the same suit which is called a flush, together combined making the poker hand ranking of straight flush which is number 2 in the list of Poker Hand Rankings.
What does a Straight Flush Poker Hand Beat?
Everything but a royal flush. The only thing that can beat a straight flush hand is another straight flush hand that is higher. For example, if you had the 45678 of hearts as shown in the picture above and I had a straight flush in spades 34567 then you Beat Me. Your 5th high card in the straight flush is an 8 which is higher than my last card 7. Best free poker hud pokerstars.
What Beats a Straight Flush Poker Hand?
The Reverse Of the Hands Mentioned above which is a higher straight flush beats a straight flush and then a Royal Flush beats Any straight flush hand 9 10 J Q K or lower. Ip casino biloxi mississippi phone number.
What is a Flush Card Poker Hand?
A Flush is 5 cards all the same suit. It does not matter what card value as long as you have all 5 cards making up your hand all the same suit.
What Does a Flush Poker Hand Beat?
A flush Poker Hand Beats everything but a straight flush and royal flush. The only time a flush beats another flush is when 2 or more players at the same showdown hand have flushes. If so the one with the highest card overall in his flush hand wins. For example if you have ACE 3456 of any suit suited (Notice no 2 which would make it a straight flush) and I have King Jack 10 9 8 suited (Again notice no Queen which would make it a straight flush again.) You win! All my cards are higher than yours except the Ace which plays high and you win. Then it goes from there on to the 2nd card, 3rd card etc if need be, but rarely ever does. For example I had an Ace 2347 then I win because my ace matches your ace but my 7 out ranks your 6.
Poker HandsSuggests You Read about Poker History at our Texas Holdem Fun Filled Information page on the Rise of Texas Holdem Poker.Thanks for coming and join us and watch as this site grows into something wonderful for those interested in Poker Hands and all things Poker. Bookmark and link to Us for all your Poker Information. What we don't have now will be here eventually. So stay tuned and SHARE Us.
Thanks for coming and stay tuned for more at Pokerhands.poker and book mark us for all your PokerHand Ranking and Online Poker and Poker Tournament Information.
P>S> If Your Eager To Try Your PokerHand TexasHoldem Skills out in Online Poker look no further than below in the footer of this page for Ignition Poker for USA Residents and Party Poker and 888 Poker For Everyone Else. All three sites are Giants and Well Respected in the Online Poker World, offering easy ways to Deposit and Withdraw once you start crushing Tournaments, Sit n Goes and Hand Games. Go Get to Multi tabling with your Poker Hand skills and Rake it in! Here You can Find Information on all The Best Online Poker Sites and thanks for checking out and bookmarking our Poker Hands Order Hand Ranking Page!
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.
___________________________________________________________________________
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.
___________________________________________________________________________
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 |
___________________________________________________________________________
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.
What Is The Lowest Hand In Poker
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.
What Is The Lowest Possible Hand In Poker
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
What Is The Highest Winning Hand In Poker
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 |
___________________________________________________________________________
2017 – Dan Ma