Poker Hands Two Pair
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*Poker Pair Crossword
*Two Pair Vs Two Pairs
*Two Pairs In Poker
*Poker Hands Does 2 Pair Beat 3 Of A Kind
*Poker Two Pair Beats What
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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The poker hand which is directly above Two Pair is Three of a Kind. The best possible Three of a Kind hand you can form is 3 x Aces. This is otherwise known as Trip Aces. When you form a Two Pair Poker Hand, there are two hands that are weaker than this – One Pair poker hand and a High Card hand. Since suits have no relative value in poker, two hands can be considered identical if one hand can be transformed into the other by swapping suits. Eliminating identical hands that ignore relative suit values leaves 6,009,159 distinct 7-card hands. The number of distinct 5-card poker hands that are possible from 7. One Pair in most variants of poker ranks under a Two Pair hand and above a hand with just a High Card. It is generally not a very strong hand and there are usually multiple players that make One. A - if two or more players are holding the same type of hand, the kicker card helps in determining the winner. For example – if player A has 10-5, B has 10-8 and the board comes 2-4-J-10-k, both players have a pair of 10s. In this situation, player B will win as the kicker card ‘8’ is higher than player A’s ‘5’. The term pocket pair is used in poker games such as Texas Hold’em where there are cards dealt to the players (hole cards) and cards dealt to the board (community cards). A pocket pair is when a player has a pair in their hole cards. Each one of the possible pairs has at least one nickname associated with it and many of them have several.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 HandsPoker HandDefinition1Royal FlushA, K, Q, J, 10, all in the same suit2Straight FlushFive consecutive cards,all in the same suit3Four of a KindFour cards of the same rank,one card of another rank4Full HouseThree of a kind with a pair5FlushFive cards of the same suit,not in consecutive order6StraightFive consecutive cards,not of the same suit7Three of a KindThree cards of the same rank,2 cards of two other ranks8Two PairTwo cards of the same rank,two cards of another rank,one card of a third rank9One PairThree cards of the same rank,3 cards of three other ranks10High CardIf no one has any of the above hands,the player with the highest card wins
___________________________________________________________________________Counting Poker Hands
Straight FlushCounting 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 KindThere 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 HouseLet’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?
FlushThere 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.
StraightThere 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 KindThere 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 PairThese two are left as exercises.
High CardThe 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 HandsPoker Pair CrosswordPoker HandCountProbability2Straight Flush400.00001543Four of a Kind6240.00024014Full House3,7440.00144065Flush5,1080.00196546Straight10,2000.00392467Three of a Kind54,9120.02112858Two Pair123,5520.04753909One Pair1,098,2400.422569010High Card1,302,5400.5011774Total2,598,9601.0000000
___________________________________________________________________________ 2017 – Dan Ma
This page describes the ranking of poker hands. This applies not only in the game of poker itself, but also in certain other card games such as Chinese Poker, Chicago, Poker Menteur and Pai Gow Poker.
*Low Poker Ranking: A-5, 2-7, A-6
*Hand probabilities and multiple decks - probability tablesStandard Poker Hand Ranking
There are 52 cards in the pack, and the ranking of the individual cards, from high to low, is ace, king, queen, jack, 10, 9, 8, 7, 6, 5, 4, 3, 2. In standard poker - that is to say in the formal casino and tournament game played internationally and the home game as normally played in North America - there is no ranking between the suits for the purpose of comparing hands - so for example the king of hearts and the king of spades are equal. (Note however that suit ranking is sometimes used for other purposes such as allocating seats, deciding who bets first, and allocating the odd chip when splitting a pot that can’t be equally divided. See ranking of suits for details.)
A poker hand consists of five cards. The categories of hand, from highest to lowest, are listed below. Any hand in a higher category beats any hand in a lower category (so for example any three of a kind beats any two pairs). Between hands in the same category the rank of the individual cards decides which is better, as described in more detail below.
In games where a player has more than five cards and selects five to form a poker hand, the remaining cards do not play any part in the ranking. Poker ranks are always based on five cards only, and if these cards are equal the hands are equal, irrespective of the ranks of any unused cards.
Some readers may wonder why one would ever need to compare (say) two threes of a kind of equal rank. This obviously cannot arise in basic draw poker, but such comparisons are needed in poker games using shared (community) cards, such as Texas Hold’em, in poker games with wild cards, and in other card games using poker combinations.1. Straight Flush
If there are no wild cards, this is the highest type of poker hand: five cards of the same suit in sequence - such as J-10-9-8-7. Between two straight flushes, the one containing the higher top card is higher. An ace can be counted as low, so 5-4-3-2-A is a straight flush, but its top card is the five, not the ace, so it is the lowest type of straight flush. The highest type of straight flush, A-K-Q-J-10 of a suit, is known as a Royal Flush. The cards in a straight flush cannot ’turn the corner’: 4-3-2-A-K is not valid. 2. Four of a kind
Four cards of the same rank - such as four queens. The fifth card, known as the kicker, can be anything. This combination is sometimes known as ’quads’, and in some parts of Europe it is called a ’poker’, though this term for it is unknown in English. Between two fours of a kind, the one with the higher set of four cards is higher - so 3-3-3-3-A is beaten by 4-4-4-4-2. If two or more players have four of a kind of the same rank, the rank of the kicker decides. For example in Texas Hold’em with J-J-J-J-9 on the table (available to all players), a player holding K-7 beats a player holding Q-10 since the king beats the queen. If one player holds 8-2 and another holds 6-5 they split the pot, since the 9 kicker makes the best hand for both of them. If one player holds A-2 and another holds A-K they also split the pot because both have an ace kicker.3. Full House
This combination, sometimes known as a boat, consists of three cards of one rank and two cards of another rank - for example three sevens and two tens (colloquially known as ’sevens full of tens’ or ’sevens on tens’). When comparing full houses, the rank of the three cards determines which is higher. For example 9-9-9-4-4 beats 8-8-8-A-A. If the threes of a kind are equal, the rank of the pairs decides.4. Flush
Five cards of the same suit. When comparing two flushes, the highest card determines which is higher. If the highest cards are equal then the second highest card is compared; if those are equal too, then the third highest card, and so on. For example K-J-9-3-2 beats K-J-7-6-5 because the nine beats the seven.If all five cards are equal, the flushes are equal.5. Straight
Five cards of mixed suits in sequence - for example Q-J-10-9-8. When comparing two sequences, the one with the higher ranking top card is better. Ace can count high or low in a straight, but not both at once, so A-K-Q-J-10 and 5-4-3-2-A are valid straights, but 2-A-K-Q-J is not. 5-4-3-2-A, known as a wheel, is the lowest kind of straight, the top card being the five.6. Three of a Kind
Three cards of the same rank plus two unequal cards. This combination is also known as Triplets or Trips. When comparing two threes of a kind the rank of the three equal cards determines which is higher. If the sets of three are of equal rank, then the higher of the two remaining cards in each hand are compared, and if those are equal, the lower odd card is compared.So for example 5-5-5-3-2 beats 4-4-4-K-5, which beats 4-4-4-Q-9, which beats 4-4-4-Q-8. 7. Two Pairs
A pair consists of two cards of equal rank. In a hand with two pairs, the two pairs are of different ranks (otherwise you would have four of a kind), and there is an odd card to make the hand up to five cards. When comparing hands with two pairs, the hand with the highest pair wins, irrespective of the rank of the other cards - so J-J-2-2-4 beats 10-10-9-9-8 because the jacks beat the tens. If the higher pairs are equal, the lower pairs are compared, so that for example 8-8-6-6-3 beats 8-8-5-5-K. Finally, if both pairs are the same, the odd cards are compared, so Q-Q-5-5-8 beats Q-Q-5-5-4.8. Pair
A hand with two cards of equal rank and three cards which are different from these and from each other. When comparing two such hands, the hand with the higher pair is better - so for example 6-6-4-3-2 beats 5-5-A-K-Q. If the pairs are equal, compare the highest ranking odd cards from each hand; if these are equal compare the second highest odd card, and if these are equal too compare the lowest odd cards. So J-J-A-9-3 beats J-J-A-8-7 because the 9 beats the 8.9. Nothing
Five cards which do not form any of the combinations listed above. This combination is often called High Card and sometimes No Pair. The cards must all be of different ranks, not consecutive, and contain at least two different suits. When comparing two such hands, the one with the better highest card wins. If the highest cards are equal the second cards are compared; if they are equal too the third cards are compared, and so on. So A-J-9-5-3 beats A-10-9-6-4 because the jack beats the ten.Hand Ranking in Low Poker
There are several poker variations in which the lowest hand wins: these are sometimes known as Lowball. There are also ’high-low’ variants in which the pot is split between the highest and the lowest hand. A low hand with no combination is normally described by naming its highest card - for example 8-6-5-4-2 would be described as ’8-down’ or ’8-low’.
It first sight it might be assumed that in low poker the hands rank in the reverse order to their ranking in normal (high) poker, but this is not quite the case. There are several different ways to rank low hands, depending on how aces are treated and whether straights and flushes are counted.Ace to Five
This seems to be the most popular system. Straights and flushes do not count, and Aces are always low. The best hand is therefore 5-4-3-2-A, even if the cards are all in one suit. Then comes 6-4-3-2-A, 6-5-3-2-A, 6-5-4-2-A, 6-5-4-3-A, 6-5-4-3-2, 7-4-3-2-A and so on. Note that when comparing hands, the highest card is compared first, just as in standard poker. So for example 6-5-4-3-2 is better than 7-4-3-2-A because the 6 is lower than the 7. The best hand containing a pair is A-A-4-3-2. This version is sometimes called ’California Lowball’.
When this form of low poker is played as part of a high-low split variant, there is sometimes a condition that a hand must be ’eight or better’ to qualify to win the low part of the pot. In this case a hand must consist of five unequal cards, all 8 or lower, to qualify for low. The worst such hand is 8-7-6-5-4.Deuce to Seven
The hands rank in almost the same order as in standard poker, with straights and flushes counting and the lowest hand wins. The difference from normal poker is that Aces are always high , so that A-2-3-4-5 is not a straight, but ranks between K-Q-J-10-8 and A-6-4-3-2. The best hand in this form is 7-5-4-3-2 in mixed suits, hence the name ’deuce to seven’. The next best is 7-6-4-3-2, then 7-6-5-3-2, 7-6-5-4-2, 8-5-4-3-2, 8-6-4-3-2, 8-6-5-3-2, 8-6-5-4-2, 8-6-5-4-3, 8-7-4-3-2, etc. The highest card is always compared first, so for example 8-6-5-4-3 is better than 8-7-4-3-2 even though the latter contains a 2, because the 6 is lower th
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*Poker Pair Crossword
*Two Pair Vs Two Pairs
*Two Pairs In Poker
*Poker Hands Does 2 Pair Beat 3 Of A Kind
*Poker Two Pair Beats What
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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The poker hand which is directly above Two Pair is Three of a Kind. The best possible Three of a Kind hand you can form is 3 x Aces. This is otherwise known as Trip Aces. When you form a Two Pair Poker Hand, there are two hands that are weaker than this – One Pair poker hand and a High Card hand. Since suits have no relative value in poker, two hands can be considered identical if one hand can be transformed into the other by swapping suits. Eliminating identical hands that ignore relative suit values leaves 6,009,159 distinct 7-card hands. The number of distinct 5-card poker hands that are possible from 7. One Pair in most variants of poker ranks under a Two Pair hand and above a hand with just a High Card. It is generally not a very strong hand and there are usually multiple players that make One. A - if two or more players are holding the same type of hand, the kicker card helps in determining the winner. For example – if player A has 10-5, B has 10-8 and the board comes 2-4-J-10-k, both players have a pair of 10s. In this situation, player B will win as the kicker card ‘8’ is higher than player A’s ‘5’. The term pocket pair is used in poker games such as Texas Hold’em where there are cards dealt to the players (hole cards) and cards dealt to the board (community cards). A pocket pair is when a player has a pair in their hole cards. Each one of the possible pairs has at least one nickname associated with it and many of them have several.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 HandsPoker HandDefinition1Royal FlushA, K, Q, J, 10, all in the same suit2Straight FlushFive consecutive cards,all in the same suit3Four of a KindFour cards of the same rank,one card of another rank4Full HouseThree of a kind with a pair5FlushFive cards of the same suit,not in consecutive order6StraightFive consecutive cards,not of the same suit7Three of a KindThree cards of the same rank,2 cards of two other ranks8Two PairTwo cards of the same rank,two cards of another rank,one card of a third rank9One PairThree cards of the same rank,3 cards of three other ranks10High CardIf no one has any of the above hands,the player with the highest card wins
___________________________________________________________________________Counting Poker Hands
Straight FlushCounting 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 KindThere 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 HouseLet’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?
FlushThere 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.
StraightThere 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 KindThere 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 PairThese two are left as exercises.
High CardThe 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 HandsPoker Pair CrosswordPoker HandCountProbability2Straight Flush400.00001543Four of a Kind6240.00024014Full House3,7440.00144065Flush5,1080.00196546Straight10,2000.00392467Three of a Kind54,9120.02112858Two Pair123,5520.04753909One Pair1,098,2400.422569010High Card1,302,5400.5011774Total2,598,9601.0000000
___________________________________________________________________________ 2017 – Dan Ma
This page describes the ranking of poker hands. This applies not only in the game of poker itself, but also in certain other card games such as Chinese Poker, Chicago, Poker Menteur and Pai Gow Poker.
*Low Poker Ranking: A-5, 2-7, A-6
*Hand probabilities and multiple decks - probability tablesStandard Poker Hand Ranking
There are 52 cards in the pack, and the ranking of the individual cards, from high to low, is ace, king, queen, jack, 10, 9, 8, 7, 6, 5, 4, 3, 2. In standard poker - that is to say in the formal casino and tournament game played internationally and the home game as normally played in North America - there is no ranking between the suits for the purpose of comparing hands - so for example the king of hearts and the king of spades are equal. (Note however that suit ranking is sometimes used for other purposes such as allocating seats, deciding who bets first, and allocating the odd chip when splitting a pot that can’t be equally divided. See ranking of suits for details.)
A poker hand consists of five cards. The categories of hand, from highest to lowest, are listed below. Any hand in a higher category beats any hand in a lower category (so for example any three of a kind beats any two pairs). Between hands in the same category the rank of the individual cards decides which is better, as described in more detail below.
In games where a player has more than five cards and selects five to form a poker hand, the remaining cards do not play any part in the ranking. Poker ranks are always based on five cards only, and if these cards are equal the hands are equal, irrespective of the ranks of any unused cards.
Some readers may wonder why one would ever need to compare (say) two threes of a kind of equal rank. This obviously cannot arise in basic draw poker, but such comparisons are needed in poker games using shared (community) cards, such as Texas Hold’em, in poker games with wild cards, and in other card games using poker combinations.1. Straight Flush
If there are no wild cards, this is the highest type of poker hand: five cards of the same suit in sequence - such as J-10-9-8-7. Between two straight flushes, the one containing the higher top card is higher. An ace can be counted as low, so 5-4-3-2-A is a straight flush, but its top card is the five, not the ace, so it is the lowest type of straight flush. The highest type of straight flush, A-K-Q-J-10 of a suit, is known as a Royal Flush. The cards in a straight flush cannot ’turn the corner’: 4-3-2-A-K is not valid. 2. Four of a kind
Four cards of the same rank - such as four queens. The fifth card, known as the kicker, can be anything. This combination is sometimes known as ’quads’, and in some parts of Europe it is called a ’poker’, though this term for it is unknown in English. Between two fours of a kind, the one with the higher set of four cards is higher - so 3-3-3-3-A is beaten by 4-4-4-4-2. If two or more players have four of a kind of the same rank, the rank of the kicker decides. For example in Texas Hold’em with J-J-J-J-9 on the table (available to all players), a player holding K-7 beats a player holding Q-10 since the king beats the queen. If one player holds 8-2 and another holds 6-5 they split the pot, since the 9 kicker makes the best hand for both of them. If one player holds A-2 and another holds A-K they also split the pot because both have an ace kicker.3. Full House
This combination, sometimes known as a boat, consists of three cards of one rank and two cards of another rank - for example three sevens and two tens (colloquially known as ’sevens full of tens’ or ’sevens on tens’). When comparing full houses, the rank of the three cards determines which is higher. For example 9-9-9-4-4 beats 8-8-8-A-A. If the threes of a kind are equal, the rank of the pairs decides.4. Flush
Five cards of the same suit. When comparing two flushes, the highest card determines which is higher. If the highest cards are equal then the second highest card is compared; if those are equal too, then the third highest card, and so on. For example K-J-9-3-2 beats K-J-7-6-5 because the nine beats the seven.If all five cards are equal, the flushes are equal.5. Straight
Five cards of mixed suits in sequence - for example Q-J-10-9-8. When comparing two sequences, the one with the higher ranking top card is better. Ace can count high or low in a straight, but not both at once, so A-K-Q-J-10 and 5-4-3-2-A are valid straights, but 2-A-K-Q-J is not. 5-4-3-2-A, known as a wheel, is the lowest kind of straight, the top card being the five.6. Three of a Kind
Three cards of the same rank plus two unequal cards. This combination is also known as Triplets or Trips. When comparing two threes of a kind the rank of the three equal cards determines which is higher. If the sets of three are of equal rank, then the higher of the two remaining cards in each hand are compared, and if those are equal, the lower odd card is compared.So for example 5-5-5-3-2 beats 4-4-4-K-5, which beats 4-4-4-Q-9, which beats 4-4-4-Q-8. 7. Two Pairs
A pair consists of two cards of equal rank. In a hand with two pairs, the two pairs are of different ranks (otherwise you would have four of a kind), and there is an odd card to make the hand up to five cards. When comparing hands with two pairs, the hand with the highest pair wins, irrespective of the rank of the other cards - so J-J-2-2-4 beats 10-10-9-9-8 because the jacks beat the tens. If the higher pairs are equal, the lower pairs are compared, so that for example 8-8-6-6-3 beats 8-8-5-5-K. Finally, if both pairs are the same, the odd cards are compared, so Q-Q-5-5-8 beats Q-Q-5-5-4.8. Pair
A hand with two cards of equal rank and three cards which are different from these and from each other. When comparing two such hands, the hand with the higher pair is better - so for example 6-6-4-3-2 beats 5-5-A-K-Q. If the pairs are equal, compare the highest ranking odd cards from each hand; if these are equal compare the second highest odd card, and if these are equal too compare the lowest odd cards. So J-J-A-9-3 beats J-J-A-8-7 because the 9 beats the 8.9. Nothing
Five cards which do not form any of the combinations listed above. This combination is often called High Card and sometimes No Pair. The cards must all be of different ranks, not consecutive, and contain at least two different suits. When comparing two such hands, the one with the better highest card wins. If the highest cards are equal the second cards are compared; if they are equal too the third cards are compared, and so on. So A-J-9-5-3 beats A-10-9-6-4 because the jack beats the ten.Hand Ranking in Low Poker
There are several poker variations in which the lowest hand wins: these are sometimes known as Lowball. There are also ’high-low’ variants in which the pot is split between the highest and the lowest hand. A low hand with no combination is normally described by naming its highest card - for example 8-6-5-4-2 would be described as ’8-down’ or ’8-low’.
It first sight it might be assumed that in low poker the hands rank in the reverse order to their ranking in normal (high) poker, but this is not quite the case. There are several different ways to rank low hands, depending on how aces are treated and whether straights and flushes are counted.Ace to Five
This seems to be the most popular system. Straights and flushes do not count, and Aces are always low. The best hand is therefore 5-4-3-2-A, even if the cards are all in one suit. Then comes 6-4-3-2-A, 6-5-3-2-A, 6-5-4-2-A, 6-5-4-3-A, 6-5-4-3-2, 7-4-3-2-A and so on. Note that when comparing hands, the highest card is compared first, just as in standard poker. So for example 6-5-4-3-2 is better than 7-4-3-2-A because the 6 is lower than the 7. The best hand containing a pair is A-A-4-3-2. This version is sometimes called ’California Lowball’.
When this form of low poker is played as part of a high-low split variant, there is sometimes a condition that a hand must be ’eight or better’ to qualify to win the low part of the pot. In this case a hand must consist of five unequal cards, all 8 or lower, to qualify for low. The worst such hand is 8-7-6-5-4.Deuce to Seven
The hands rank in almost the same order as in standard poker, with straights and flushes counting and the lowest hand wins. The difference from normal poker is that Aces are always high , so that A-2-3-4-5 is not a straight, but ranks between K-Q-J-10-8 and A-6-4-3-2. The best hand in this form is 7-5-4-3-2 in mixed suits, hence the name ’deuce to seven’. The next best is 7-6-4-3-2, then 7-6-5-3-2, 7-6-5-4-2, 8-5-4-3-2, 8-6-4-3-2, 8-6-5-3-2, 8-6-5-4-2, 8-6-5-4-3, 8-7-4-3-2, etc. The highest card is always compared first, so for example 8-6-5-4-3 is better than 8-7-4-3-2 even though the latter contains a 2, because the 6 is lower th
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