Poker Hand Precedence

Poker Hand Precedence

In the event that two players show identical winning hands and therefore split the ‘relevant pot' (or, in the case of a split pot poker variant as described in rule 9.2, split the high half of the ‘relevant pot'), any bounty awarded will be divided equally between the winners. Now you can run ProPokerTools on your desktop! Download the Odds Oracle 2.30 Now. There's a seemingly endless list of nicknames used for hands in poker. The list seems to get bigger and bigger all the time too, as players are often coming up with new ones. Some of them are obvious, some of them amusing, and many of them are really quite tenuous.
Poker Hand Precedence
Poker Hand Order Of Precedence
Poker Hand Precedence
OBJECTIVE: To become a winner you should make up the highest possible poker hand of five cards, using the two initially dealt cards and the five community cards.
NUMBER OF PLAYERS: 2-10 players
NUMBER OF CARDS: 52- deck cards
RANK OF CARDS: A-K-Q-J-10-9-8-7-6-5-4-3-2
THE DEAL: Every player is dealt two cards face down which is commonly called ‘hole cards'.

TYPE OF GAME: Casino
AUDIENCE: Adults
Introduction to Texas Hold ‘EmNo Limit Texas Hold'em. Sometimes called the cadillac of Poker, Texas Hold ‘em is a fairly easy game to learn but can take years to master.
How to PlayTo begin every player gets two pocket cards. A deck of cards is placed in the middle of the table and these are known as community deck and these are the cards that the flop will be dealt from.
Once all players have been dealt their initial two cards players will be asked to place their first bid. Once all players have placed their first bid a second round of bidding occurs.
Once all players have placed their final bids, the dealer will deal the flop. The dealer will flip over the first 3 cards, known as the 'flop', from the community deck. The goal is to make the best 5 card had you can with the three cards from the community deck and the two in your hand.
Once the first three cards have been flipped over, player will have the option to bid again or fold. After all players have had a chance to bid or fold, the dealer will flip over a fourth card known as a 'turn' card.

The players still remaining will have the option to once again fold or bid. Now the dealer will flip the 5th and final card over, known as the 'river'card.
Once all five cards have been flipped by the dealer, players will have one last chance to raise the bid or fold. Once all bids and count bids have been made it's time for the players to reveal their hands and determine a winner.
First Round Betting: The Pre-FlopWhen playing Texas hold ‘em a round flat chip or 'disk' is used to represent the position of the dealer. This disk is placed in front of the dealer to indicate their status. The person sitting to dealer left is known as the small blind and the person sitting to the left of the small blind is known as the big blind.
When betting, both blinds are required to post a bet before receiving any cards. The big blind is required to post the equivalent or higher of the bet placed by the small blind. Once both blinds have posted their bids two cards are dealt to each player and remaining players can choose to fold, call, or raise. After the end of the game the dealer button is moved to the left so that every player takes on the blind position at some point to maintain the fairness of the game.
Fold – The action of surrendering your cards to the dealer and sitting out the hand. If one folds their cards in the first round of betting, they lose no money.
Call – The action of matching the table bet, which is the most recent bet that has been placed on the table.
Raise – The action of doubling the amount of the most recent bet.
The small and the big blind have the option to fold, call, or raise before the first round of betting ends. If either of them choose to fold, they will lose the blind bet that they initially placed.
Second Round Betting: The FlopAfter the first round of betting ends the dealer will proceed to deal the flop. Once the flop has been dealt, players will access the strength of their hands. Again, the player to the left of the dealer is the first to act.
Since there is no compulsory bet on the table, the first player has the option to to take the three previous options discussed, call, fold, raise, as well as the option to check. To check, a player taps his hand twice on the table, this allows the player to pass the option to make the first bet on to the player to his left. All players have the option to check until a bet has been placed on the table. Once a bet has been placed, players must choose to either fold, call, or raise.
Third & Fourth Round Betting: The Turn & The RiverAfter the second round of betting closes, the dealer will deal the fourth card of the flop, known as the turn card. The player to dealer left has the option to check or place a bet. The player that opens the bet closes the bet, after all other players have chosen to fold, raise, or call.
The dealer will then add the bets to the existing pot and deal a fifth card known as 'The River'. Once this card has been dealt, the remaining players have the option to check,fold, call, or raise. Lets say all players decide to check. If that is the case it is time for all remaining players to reveal there cards and determine the winner. The player with the highest ranking hand is the winner. They receive the full pot and a new game begins.
TiesIn the chance of a tie between hands the following tie-breakers are used:
Poker Hand PrecedencePairs– if two players are tied for highest pairs a 'kicker' or the next highest-ranking card is used to determine the winner. You continue until one player has a higher-ranking card or both are determined to have the same exact hand, in which case the pot is split.
Two pairs– in this tie, the higher ranked pair wins, if top pairs are equal in rank you move to the next pair, then move to kickers if necessary.
Three of a kind – higher ranking card takes the pot. 
Straights – the straight with the highest-ranking card wins; if both straights are the same the pot is split.
Flush – The flush with the highest-ranking card wins, if the same you move to the next card till a winner is found or hands are the same. If hands are the same split the pot.
Full house – the hand with the higher ranking three cards wins. 
Four of a kind – the higher ranking set of four wins.
Straight flush – ties are broken the same as a regular straight.

Royal Flush – split the pot.
Hand Ranking2. Pair – Two of the same the same card (9,9,6,4,7)
3. Two pair – Two pairs of the same card (K,K,9,9,J)
4. Three of a kind – Three cards of the same ( 7,7,7,10,2)
6. Flush – Five cards of the same suit
7. Full House – Three card of a kind and a pair (A,A,A,5,5)
9. Straight Flush – Five cards in order all of the same suit (4,5,6,7,8 – same suit)
10. Royal Flush – Five cards in order of the same suit 10- A (10,J,Q,K,A)
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. Ironman slot roll download.
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.
Poker Hand Order Of Precedence

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
Poker HandDefinition
1Royal FlushA, K, Q, J, 10, all in the same suit
2Straight FlushFive consecutive cards,
all in the same suit
3Four of a KindFour cards of the same rank,
one card of another rank
4Full HouseThree of a kind with a pair
5FlushFive cards of the same suit,
not in consecutive order
6StraightFive consecutive cards,
not of the same suit
7Three of a KindThree cards of the same rank,
2 cards of two other ranks
8Two PairTwo cards of the same rank,
two cards of another rank,
one card of a third rank
9One PairThree cards of the same rank,
3 cards of three other ranks
10High CardIf 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?
Poker Hand PrecedenceFlush
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 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

TYPE OF GAME: Casino
AUDIENCE: Adults
Introduction to Texas Hold ‘EmNo Limit Texas Hold'em. Sometimes called the cadillac of Poker, Texas Hold ‘em is a fairly easy game to learn but can take years to master.
How to PlayTo begin every player gets two pocket cards. A deck of cards is placed in the middle of the table and these are known as community deck and these are the cards that the flop will be dealt from.
Once all players have been dealt their initial two cards players will be asked to place their first bid. Once all players have placed their first bid a second round of bidding occurs.
Once all players have placed their final bids, the dealer will deal the flop. The dealer will flip over the first 3 cards, known as the 'flop', from the community deck. The goal is to make the best 5 card had you can with the three cards from the community deck and the two in your hand.
Once the first three cards have been flipped over, player will have the option to bid again or fold. After all players have had a chance to bid or fold, the dealer will flip over a fourth card known as a 'turn' card.
The players still remaining will have the option to once again fold or bid. Now the dealer will flip the 5th and final card over, known as the 'river'card.
Once all five cards have been flipped by the dealer, players will have one last chance to raise the bid or fold. Once all bids and count bids have been made it's time for the players to reveal their hands and determine a winner.
First Round Betting: The Pre-FlopWhen playing Texas hold ‘em a round flat chip or 'disk' is used to represent the position of the dealer. This disk is placed in front of the dealer to indicate their status. The person sitting to dealer left is known as the small blind and the person sitting to the left of the small blind is known as the big blind.
When betting, both blinds are required to post a bet before receiving any cards. The big blind is required to post the equivalent or higher of the bet placed by the small blind. Once both blinds have posted their bids two cards are dealt to each player and remaining players can choose to fold, call, or raise. After the end of the game the dealer button is moved to the left so that every player takes on the blind position at some point to maintain the fairness of the game.
Fold – The action of surrendering your cards to the dealer and sitting out the hand. If one folds their cards in the first round of betting, they lose no money.
Call – The action of matching the table bet, which is the most recent bet that has been placed on the table.
Raise – The action of doubling the amount of the most recent bet.
The small and the big blind have the option to fold, call, or raise before the first round of betting ends. If either of them choose to fold, they will lose the blind bet that they initially placed.
Second Round Betting: The FlopAfter the first round of betting ends the dealer will proceed to deal the flop. Once the flop has been dealt, players will access the strength of their hands. Again, the player to the left of the dealer is the first to act.
Since there is no compulsory bet on the table, the first player has the option to to take the three previous options discussed, call, fold, raise, as well as the option to check. To check, a player taps his hand twice on the table, this allows the player to pass the option to make the first bet on to the player to his left. All players have the option to check until a bet has been placed on the table. Once a bet has been placed, players must choose to either fold, call, or raise.
Third & Fourth Round Betting: The Turn & The RiverAfter the second round of betting closes, the dealer will deal the fourth card of the flop, known as the turn card. The player to dealer left has the option to check or place a bet. The player that opens the bet closes the bet, after all other players have chosen to fold, raise, or call.
The dealer will then add the bets to the existing pot and deal a fifth card known as 'The River'. Once this card has been dealt, the remaining players have the option to check,fold, call, or raise. Lets say all players decide to check. If that is the case it is time for all remaining players to reveal there cards and determine the winner. The player with the highest ranking hand is the winner. They receive the full pot and a new game begins.
TiesIn the chance of a tie between hands the following tie-breakers are used:
Poker Hand PrecedencePairs– if two players are tied for highest pairs a 'kicker' or the next highest-ranking card is used to determine the winner. You continue until one player has a higher-ranking card or both are determined to have the same exact hand, in which case the pot is split.
Two pairs– in this tie, the higher ranked pair wins, if top pairs are equal in rank you move to the next pair, then move to kickers if necessary.
Three of a kind – higher ranking card takes the pot. 
Straights – the straight with the highest-ranking card wins; if both straights are the same the pot is split.
Flush – The flush with the highest-ranking card wins, if the same you move to the next card till a winner is found or hands are the same. If hands are the same split the pot.
Full house – the hand with the higher ranking three cards wins. 
Four of a kind – the higher ranking set of four wins.
Straight flush – ties are broken the same as a regular straight.
Royal Flush – split the pot.
Hand Ranking2. Pair – Two of the same the same card (9,9,6,4,7)
3. Two pair – Two pairs of the same card (K,K,9,9,J)
4. Three of a kind – Three cards of the same ( 7,7,7,10,2)
6. Flush – Five cards of the same suit
7. Full House – Three card of a kind and a pair (A,A,A,5,5)
9. Straight Flush – Five cards in order all of the same suit (4,5,6,7,8 – same suit)
10. Royal Flush – Five cards in order of the same suit 10- A (10,J,Q,K,A)
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. Ironman slot roll download.
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.
Poker Hand Order Of PrecedenceThe 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
Poker HandDefinition
1Royal FlushA, K, Q, J, 10, all in the same suit
2Straight FlushFive consecutive cards,
all in the same suit
3Four of a KindFour cards of the same rank,
one card of another rank
4Full HouseThree of a kind with a pair
5FlushFive cards of the same suit,
not in consecutive order
6StraightFive consecutive cards,
not of the same suit
7Three of a KindThree cards of the same rank,
2 cards of two other ranks
8Two PairTwo cards of the same rank,
two cards of another rank,
one card of a third rank
9One PairThree cards of the same rank,
3 cards of three other ranks
10High CardIf 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?
Poker Hand PrecedenceFlush
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 HandCountProbability
2Straight Flush400.0000154
3Four of a Kind6240.0002401
4Full House3,7440.0014406
5Flush5,1080.0019654
6Straight10,2000.0039246
7Three of a Kind54,9120.0211285
8Two Pair123,5520.0475390
9One Pair1,098,2400.4225690
10High Card1,302,5400.5011774
Total2,598,9601.0000000
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 2017 – Dan Ma

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