Total Possible Poker Hands
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*Total Possible Poker Hands Against
*Possible Poker Hand CombinationsA pair of aces is the best pre-flop hand in Texas Hold’em Poker
Poker Hand Rankings Quiz. Put your knowledge of poker hands to the test with the quiz below. Each of the 2,598,960 possible hands of poker is equally likely when dealt 5 cards from a standard poker deck. Because of this, one can use probability by outcomes to compute the probabilities of each classification of poker hand. The binomial coefficient can be used to calculate certain combinations of cards.
In the poker game of Texas hold ’em, a starting hand consists of two hole cards, which belong solely to the player and remain hidden from the other players. Five community cards are also dealt into play. Betting begins before any of the community cards are exposed, and continues throughout the hand. The player’s ’playing hand’, which will be compared against that of each competing player, is the best 5-card poker hand available from his two hole cards and the five community cards. Unless otherwise specified, here the term hand applies to the player’s two hole cards, or starting hand.Essentials[edit]
There are 1326 distinct possible combinations of two hole cards from a standard 52-card deck in hold ’em, but since suits have no relative value in this poker variant, many of these hands are identical in value before the flop. For example, A♥J♥ and A♠J♠ are identical in value, because each is a hand consisting of an ace and a jack of the same suit.
Therefore, there are 169 non-equivalent starting hands in hold ’em, which is the sum total of : 13 pocket pairs, 13 × 12 / 2 = 78 suited hands and 78 unsuited hands (13 + 78 + 78 = 169).
Card hand possible. Other variations include the use of jokers and wild cards. In this paper I will derive the probabilities of being dealt one of the given hands in five-card stud poker and how those probabilities change when jokers and wild cards are included. I will also analyze Texas Hold em and derive the probability of a given hand winning. An ace-high straight flush, commonly known as a royal flush, is the best possible hand in many variants of poker. In poker, players form sets of five playing cards, called hands, according to the rules of the game. However, let’s look at these hands by comparing the total combinations for each hand: AA = 6 combinations (21.5%) KK = 6 combinations (21.5%) AK = 16 combinations (57%) There are more AK hands in a range of AA, KK, AK than there are AA and KK hands combined. So out of 28 possible combinations made up from AA, KK and AK, 16 of them come from AK.
These 169 hands are not equally likely. Hold ’em hands are sometimes classified as having one of three ’shapes’:
*Pairs, (or ’pocket pairs’), which consist of two cards of the same rank (e.g. 9♠9♣). One hand in 17 will be a pair, each occurring with individual probability 1/221 (P(pair) = 3/51 = 1/17).Alternative means of making this calculationFirst StepAs confirmed above.There are 1326 possible combination of opening hand.Second StepTotal Possible Poker Hands AgainstThere are 6 different combos of each pair. 9h9c, 9h9s, 9h9d, 9c9s, 9c9d, 9d9s. Therefore, there are 78 possible combinations of pocket pairs (6 multiplied by 13 i.e. 22-AA)To calculate the odds of being dealt a pair78 (the number of any particular pair being dealt. As above) divided by 1326 (possible opening hands)78/1326 = 0.058 or 5.8%Possible Poker Hand Combinations
*Suited hands, which contain two cards of the same suit (e.g. A♣6♣). 23.5% of all starting hands are suited.
Probability of first card is 1.0 (any of the 52 cards)Probability of second hand suit matching the first:There are 13 cards per suit, and one is in your hand leaving 12 remaining of the 51 cards remaining in the deck. 12/51=.2353 or 23.5%
*Offsuit hands, which contain two cards of a different suit and rank (e.g. K♠J♥). 70.6% of all hands are offsuit hands
Offsuit pairs = 78Other offsuit hands = 936
It is typical to abbreviate suited hands in hold ’em by affixing an ’s’ to the hand, as well as to abbreviate non-suited hands with an ’o’ (for offsuit). That is,QQ represents any pair of queens,KQ represents any king and queen,AKo represents any ace and king of different suits, andJTs represents any jack and ten of the same suit.Limit hand rankings[edit]
Some notable theorists and players have created systems to rank the value of starting hands in limit Texas hold’em. These rankings do not apply to no limit play.Sklansky hand groups[edit]
David Sklansky and Mason Malmuth[1] assigned in 1999 each hand to a group, and proposed all hands in the group could normally be played similarly. Stronger starting hands are identified by a lower number. Hands without a number are the weakest starting hands. As a general rule, books on Texas hold’em present hand strengths starting with the assumption of a nine or ten person table. The table below illustrates the concept:Chen formula[edit]
The ’Chen Formula’ is a way to compute the ’power ratings’ of starting hands that was originally developed by Bill Chen.[2]Highest CardBased on the highest card, assign points as follows:Ace = 10 points, K = 8 points, Q = 7 points, J = 6 points.10 through 2, half of face value (10 = 5 points, 9 = 4.5 points, etc.)PairsFor pairs, multiply the points by 2 (AA=20, KK=16, etc.), with a minimum of 5 points for any pair. 55 is given an extra point (i.e., 6).SuitedAdd 2 points for suited cards.ClosenessSubtract 1 point for 1 gappers (AQ, J9)2 points for 2 gappers (J8, AJ).4 points for 3 gappers (J7, 73).5 points for larger gappers, including A2 A3 A4Add an extra point if connected or 1-gap and your highest card is lower than Q (since you then can make all higher straights)Phil Hellmuth’s: ’Play Poker Like the Pros’[edit]
Phil Hellmuth’s ’Play Poker Like the Pros’ book published in 2003.TierHandsCategory1AA, KK, AKs, QQ, AKTop 12 Hands2JJ, TT, 99388, 77, AQs, AQ466, 55, 44, 33, 22, AJs, ATs, A9s, A8sMajority Play Hands5A7s, A6s, A5s, A4s, A3s, A2s, KQs, KQ6QJs, JTs, T9s, 98s, 87s, 76s, 65sSuited ConnectorsStatistics based on real online play[edit]
Statistics based on real play with their associated actual value in real bets.[3]TierHandsExpected Value1AA, KK, QQ, JJ, AKs2.32 - 0.782AQs, TT, AK, AJs, KQs, 990.59 - 0.383ATs, AQ, KJs, 88, KTs, QJs0.32 - 0.204A9s, AJ, QTs, KQ, 77, JTs0.19 - 0.155A8s, K9s, AT, A5s, A7s0.10 - 0.086KJ, 66, T9s, A4s, Q9s0.08 - 0.057J9s, QJ, A6s, 55, A3s, K8s, KT0.04 - 0.01898s, T8s, K7s, A2s0.00987s, QT, Q8s, 44, A9, J8s, 76s, JT(-) 0.02 - 0.03Nicknames for starting hands[edit]
In poker communities, it is common for hole cards to be given nicknames. While most combinations have a nickname, stronger handed nicknames are generally more recognized, the most notable probably being the ’Big Slick’ - Ace and King of the same suit, although an Ace-King of any suit combination is less occasionally referred to as an Anna Kournikova, derived from the initials AK and because it ’looks really good but rarely wins.’[4][5] Hands can be named according to their shapes (e.g., paired aces look like ’rockets’, paired jacks look like ’fish hooks’); a historic event (e.g., A’s and 8’s - dead man’s hand, representing the hand held by Wild Bill Hickok when he was fatally shot in the back by Jack McCall in 1876); many other reasons like animal names, alliteration and rhyming are also used in nicknames.Notes[edit]
*^David Sklansky and Mason Malmuth (1999). Hold ’em Poker for Advanced Players. Two Plus Two Publications. ISBN1-880685-22-1
*^Hold’em Excellence: From Beginner to Winner by Lou Krieger, Chapter 5, pages 39 - 43, Second Edition
*^http://www.pokerroom.com/poker/poker-school/ev-stats/total-stats-by-card/[dead link]
*^Aspden, Peter (2007-05-19). ’FT Weekend Magazine - Non-fiction: Stakes and chips Las Vegas and the internet have helped poker become the biggest game in town’. Financial Times. Retrieved 2010-01-10.
*^Martain, Tim (2007-07-15). ’A little luck helps out’. Sunday Tasmanian. Retrieved 2010-01-10.Retrieved from ’https://en.wikipedia.org/w/index.php?title=Texas_hold_%27em_starting_hands&oldid=989142522’Brian Alspach13 January 2000Abstract:
Weird poker hands. The types of 3-card poker hands are
*straight flush
*3-of-a-kind
*straight
*flush
*a pair
*high card
The total number of 3-card poker hands is .
A straight flush is completely determined once the smallest card in thestraight flush is known. There are 48 cards eligible to be the smallestcard in a straight flush. Hence, there are 48 straight flushes.
Casino sites uk no deposit bonus. In forming a 3-of-a-kind hand, there are 13 choices for the rank and4 choices for the 3 cards of the given rank. This implies there are3-of-a-kind hands.
The ranks of the cards in a straight have the form x,x+1,x+2, wherex can be any of 12 ranks. There are then 4 choices for each card ofthe given ranks. This yields total choices. However,this count includes the straight flushes. Removing the 48 straightflushes leaves us with 720 straights.
To count the number of flushes, we obtain choicesfor 3 cards in the same suit. Of these, 12 are straight flushes whoseremoval leaves 274 flushes of a given suit. Multiplying by 4 produces1,096 flushes.
Now we count the number of hands with a pair. There are 13 choices forthe rank of the pair, and pairs of the chosen rank.The non-pair card can be any of the remaining 48. Thus, thereare 3-card hands with a single pair.
We could determine the number of high card hands by removing the handswhich have already been counted in one of the previous categories.Instead, let us count them independently and see if the numbers sumto 22,100 which will serve as a check on our arithmetic.
A high card hand has 3 distinct ranks, but does not allow ranks of theform x,x+1,x+2 as that would constitute a straight. Thus, there arepossible sets of ranks from which we remove the12 sets of the form .This leaves 274 sets of ranks.For a given set of ranks, there are 4 choices for each cardexcept we cannot choose all in the same suit. Hence, there are274(43-4) = 16,440 high card hands.
If we sum the preceding numbers, we obtain 22,100 and we can be confidentthe numbers are correct.
Here is a table summarizing the number of 3-card poker hands. Theprobability is the probability of having the hand dealt to you whendealt 3 cards.handnumberProbabilitystraight flush48.00223-of-a-kind52.0024straight720.0326flush1,096.0496pair3,744.1694high card16,440.7439Home |Publications |Preprints |MITACS |Poker Digest |Graph Theory Workshop |Poker Computations |Feedbackwebsite by the Centre for Systems Science
last updated 13 January 2000
Register here: http://gg.gg/oforh
https://diarynote-jp.indered.space
*Total Possible Poker Hands Against
*Possible Poker Hand CombinationsA pair of aces is the best pre-flop hand in Texas Hold’em Poker
Poker Hand Rankings Quiz. Put your knowledge of poker hands to the test with the quiz below. Each of the 2,598,960 possible hands of poker is equally likely when dealt 5 cards from a standard poker deck. Because of this, one can use probability by outcomes to compute the probabilities of each classification of poker hand. The binomial coefficient can be used to calculate certain combinations of cards.
In the poker game of Texas hold ’em, a starting hand consists of two hole cards, which belong solely to the player and remain hidden from the other players. Five community cards are also dealt into play. Betting begins before any of the community cards are exposed, and continues throughout the hand. The player’s ’playing hand’, which will be compared against that of each competing player, is the best 5-card poker hand available from his two hole cards and the five community cards. Unless otherwise specified, here the term hand applies to the player’s two hole cards, or starting hand.Essentials[edit]
There are 1326 distinct possible combinations of two hole cards from a standard 52-card deck in hold ’em, but since suits have no relative value in this poker variant, many of these hands are identical in value before the flop. For example, A♥J♥ and A♠J♠ are identical in value, because each is a hand consisting of an ace and a jack of the same suit.
Therefore, there are 169 non-equivalent starting hands in hold ’em, which is the sum total of : 13 pocket pairs, 13 × 12 / 2 = 78 suited hands and 78 unsuited hands (13 + 78 + 78 = 169).
Card hand possible. Other variations include the use of jokers and wild cards. In this paper I will derive the probabilities of being dealt one of the given hands in five-card stud poker and how those probabilities change when jokers and wild cards are included. I will also analyze Texas Hold em and derive the probability of a given hand winning. An ace-high straight flush, commonly known as a royal flush, is the best possible hand in many variants of poker. In poker, players form sets of five playing cards, called hands, according to the rules of the game. However, let’s look at these hands by comparing the total combinations for each hand: AA = 6 combinations (21.5%) KK = 6 combinations (21.5%) AK = 16 combinations (57%) There are more AK hands in a range of AA, KK, AK than there are AA and KK hands combined. So out of 28 possible combinations made up from AA, KK and AK, 16 of them come from AK.
These 169 hands are not equally likely. Hold ’em hands are sometimes classified as having one of three ’shapes’:
*Pairs, (or ’pocket pairs’), which consist of two cards of the same rank (e.g. 9♠9♣). One hand in 17 will be a pair, each occurring with individual probability 1/221 (P(pair) = 3/51 = 1/17).Alternative means of making this calculationFirst StepAs confirmed above.There are 1326 possible combination of opening hand.Second StepTotal Possible Poker Hands AgainstThere are 6 different combos of each pair. 9h9c, 9h9s, 9h9d, 9c9s, 9c9d, 9d9s. Therefore, there are 78 possible combinations of pocket pairs (6 multiplied by 13 i.e. 22-AA)To calculate the odds of being dealt a pair78 (the number of any particular pair being dealt. As above) divided by 1326 (possible opening hands)78/1326 = 0.058 or 5.8%Possible Poker Hand Combinations
*Suited hands, which contain two cards of the same suit (e.g. A♣6♣). 23.5% of all starting hands are suited.
Probability of first card is 1.0 (any of the 52 cards)Probability of second hand suit matching the first:There are 13 cards per suit, and one is in your hand leaving 12 remaining of the 51 cards remaining in the deck. 12/51=.2353 or 23.5%
*Offsuit hands, which contain two cards of a different suit and rank (e.g. K♠J♥). 70.6% of all hands are offsuit hands
Offsuit pairs = 78Other offsuit hands = 936
It is typical to abbreviate suited hands in hold ’em by affixing an ’s’ to the hand, as well as to abbreviate non-suited hands with an ’o’ (for offsuit). That is,QQ represents any pair of queens,KQ represents any king and queen,AKo represents any ace and king of different suits, andJTs represents any jack and ten of the same suit.Limit hand rankings[edit]
Some notable theorists and players have created systems to rank the value of starting hands in limit Texas hold’em. These rankings do not apply to no limit play.Sklansky hand groups[edit]
David Sklansky and Mason Malmuth[1] assigned in 1999 each hand to a group, and proposed all hands in the group could normally be played similarly. Stronger starting hands are identified by a lower number. Hands without a number are the weakest starting hands. As a general rule, books on Texas hold’em present hand strengths starting with the assumption of a nine or ten person table. The table below illustrates the concept:Chen formula[edit]
The ’Chen Formula’ is a way to compute the ’power ratings’ of starting hands that was originally developed by Bill Chen.[2]Highest CardBased on the highest card, assign points as follows:Ace = 10 points, K = 8 points, Q = 7 points, J = 6 points.10 through 2, half of face value (10 = 5 points, 9 = 4.5 points, etc.)PairsFor pairs, multiply the points by 2 (AA=20, KK=16, etc.), with a minimum of 5 points for any pair. 55 is given an extra point (i.e., 6).SuitedAdd 2 points for suited cards.ClosenessSubtract 1 point for 1 gappers (AQ, J9)2 points for 2 gappers (J8, AJ).4 points for 3 gappers (J7, 73).5 points for larger gappers, including A2 A3 A4Add an extra point if connected or 1-gap and your highest card is lower than Q (since you then can make all higher straights)Phil Hellmuth’s: ’Play Poker Like the Pros’[edit]
Phil Hellmuth’s ’Play Poker Like the Pros’ book published in 2003.TierHandsCategory1AA, KK, AKs, QQ, AKTop 12 Hands2JJ, TT, 99388, 77, AQs, AQ466, 55, 44, 33, 22, AJs, ATs, A9s, A8sMajority Play Hands5A7s, A6s, A5s, A4s, A3s, A2s, KQs, KQ6QJs, JTs, T9s, 98s, 87s, 76s, 65sSuited ConnectorsStatistics based on real online play[edit]
Statistics based on real play with their associated actual value in real bets.[3]TierHandsExpected Value1AA, KK, QQ, JJ, AKs2.32 - 0.782AQs, TT, AK, AJs, KQs, 990.59 - 0.383ATs, AQ, KJs, 88, KTs, QJs0.32 - 0.204A9s, AJ, QTs, KQ, 77, JTs0.19 - 0.155A8s, K9s, AT, A5s, A7s0.10 - 0.086KJ, 66, T9s, A4s, Q9s0.08 - 0.057J9s, QJ, A6s, 55, A3s, K8s, KT0.04 - 0.01898s, T8s, K7s, A2s0.00987s, QT, Q8s, 44, A9, J8s, 76s, JT(-) 0.02 - 0.03Nicknames for starting hands[edit]
In poker communities, it is common for hole cards to be given nicknames. While most combinations have a nickname, stronger handed nicknames are generally more recognized, the most notable probably being the ’Big Slick’ - Ace and King of the same suit, although an Ace-King of any suit combination is less occasionally referred to as an Anna Kournikova, derived from the initials AK and because it ’looks really good but rarely wins.’[4][5] Hands can be named according to their shapes (e.g., paired aces look like ’rockets’, paired jacks look like ’fish hooks’); a historic event (e.g., A’s and 8’s - dead man’s hand, representing the hand held by Wild Bill Hickok when he was fatally shot in the back by Jack McCall in 1876); many other reasons like animal names, alliteration and rhyming are also used in nicknames.Notes[edit]
*^David Sklansky and Mason Malmuth (1999). Hold ’em Poker for Advanced Players. Two Plus Two Publications. ISBN1-880685-22-1
*^Hold’em Excellence: From Beginner to Winner by Lou Krieger, Chapter 5, pages 39 - 43, Second Edition
*^http://www.pokerroom.com/poker/poker-school/ev-stats/total-stats-by-card/[dead link]
*^Aspden, Peter (2007-05-19). ’FT Weekend Magazine - Non-fiction: Stakes and chips Las Vegas and the internet have helped poker become the biggest game in town’. Financial Times. Retrieved 2010-01-10.
*^Martain, Tim (2007-07-15). ’A little luck helps out’. Sunday Tasmanian. Retrieved 2010-01-10.Retrieved from ’https://en.wikipedia.org/w/index.php?title=Texas_hold_%27em_starting_hands&oldid=989142522’Brian Alspach13 January 2000Abstract:
Weird poker hands. The types of 3-card poker hands are
*straight flush
*3-of-a-kind
*straight
*flush
*a pair
*high card
The total number of 3-card poker hands is .
A straight flush is completely determined once the smallest card in thestraight flush is known. There are 48 cards eligible to be the smallestcard in a straight flush. Hence, there are 48 straight flushes.
Casino sites uk no deposit bonus. In forming a 3-of-a-kind hand, there are 13 choices for the rank and4 choices for the 3 cards of the given rank. This implies there are3-of-a-kind hands.
The ranks of the cards in a straight have the form x,x+1,x+2, wherex can be any of 12 ranks. There are then 4 choices for each card ofthe given ranks. This yields total choices. However,this count includes the straight flushes. Removing the 48 straightflushes leaves us with 720 straights.
To count the number of flushes, we obtain choicesfor 3 cards in the same suit. Of these, 12 are straight flushes whoseremoval leaves 274 flushes of a given suit. Multiplying by 4 produces1,096 flushes.
Now we count the number of hands with a pair. There are 13 choices forthe rank of the pair, and pairs of the chosen rank.The non-pair card can be any of the remaining 48. Thus, thereare 3-card hands with a single pair.
We could determine the number of high card hands by removing the handswhich have already been counted in one of the previous categories.Instead, let us count them independently and see if the numbers sumto 22,100 which will serve as a check on our arithmetic.
A high card hand has 3 distinct ranks, but does not allow ranks of theform x,x+1,x+2 as that would constitute a straight. Thus, there arepossible sets of ranks from which we remove the12 sets of the form .This leaves 274 sets of ranks.For a given set of ranks, there are 4 choices for each cardexcept we cannot choose all in the same suit. Hence, there are274(43-4) = 16,440 high card hands.
If we sum the preceding numbers, we obtain 22,100 and we can be confidentthe numbers are correct.
Here is a table summarizing the number of 3-card poker hands. Theprobability is the probability of having the hand dealt to you whendealt 3 cards.handnumberProbabilitystraight flush48.00223-of-a-kind52.0024straight720.0326flush1,096.0496pair3,744.1694high card16,440.7439Home |Publications |Preprints |MITACS |Poker Digest |Graph Theory Workshop |Poker Computations |Feedbackwebsite by the Centre for Systems Science
last updated 13 January 2000
Register here: http://gg.gg/oforh
https://diarynote-jp.indered.space
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