Below is the complete guide for determining how to rank various poker hands. This article covers all poker hands, from hands in standard games of poker, to lowball, to playing with a variety of wild cards. Scroll to the end to find an in-depth ranking of suits for several countries, including many European countries and North American continental standards.

High Card is the worst possible hand on the poker hand rankings list. It consists of no pair or any other hand type – just a high card. The words “High Card” should have you thinking straight away about a hand with the highest card. One chooses the highest ranked 5-card poker hand among the 6 cards and values the hand based on the 5-card hand. The types of 5-card poker hands in decreasing rank are straight flush 4-of-a-kind full house flush straight 3-of-a-kind two pairs a pair high card The total number of 6-card poker hands is. No matching cards. A Two Pair is ranked based on the value of the highest pair in the hand. For example, J-J-2-2-5 beats 10-10-9-9-A. In case two or more players have the same high pair, the tie is.

Standard Poker Rankings

A standard deck of cards has 52 in a pack. Individually cards rank, high to low:

Ace, King, Queen, Jack, 10, 9, 8, 7, 6, 5, 4, 3, 2

In standard poker (in North America) there is no suit ranking. A poker hand has 5 cards total. Higher ranked hands beat lower ones, and within the same kind of hand higher value cards beat lower value cards.

#1 Straight Flush

In games without wild cards, this is the highest ranking hand. It consists of five cards in sequence of the same suit. When comparing flushes, the hand with the highest value high card wins. Example: 5-6-7-8-9, all spades, is a straight flush. A-K-Q-J-10 is the highest ranking straight flush and is called a Royal Flush. Flushes are not permitted to turn the corner, for example, 3-2-A-K-Q is not a straight flush.

#2 Four of a Kind (Quads)

A four of a kind is four cards of equal rank, for example, four jacks. The kicker, the fifth card, may be any other card. When comparing two four of a kinds, the highest value set wins. For example, 5-5-5-5-J is beat by 10-10-10-10-2. If two players happen to have a four of a kind of equal value, the player with the highest ranking kicker wins.

#3 Full House (Boat)

A full house consists of 3 cards of one rank and 2 cards of another. The three cards value determines rank within Full Houses, the player with the highest rank 3 cards wins. If the three cards are equal rank the pairs decide. Example: Q-Q-Q-3-3 beats 10-10-10-A-A BUT 10-10-10-A-A would beat 10-10-10-J-J.

#4 Flush

Any five cards of the same suit. The highest card in a flush determines its rank between other flushes. If those are equal, continue comparing the next highest cards until a winner can be determined.

#5 Straight

Five cards in sequence from different suits. The hand with the highest ranking top card wins within straights. Ace can either be a high card or low card, but not both. The wheel, or the lowest straight, is 5-4-3-2-A, where the top card is five.

#6 Three of a Kind (Triplets/Trips)

A three of a kind is three card of equal rank and two other cards (not of equal rank). The three of a kind with the highest rank wins, in the event they are equal, the high card of the two remaining cards determines the winner.

#7 Two Pairs

A pair is two cards that are equal in rank. A hand with two pairs consists of two separate pairs of different ranks. For example, K-K-3-3-6, where 6 is the odd card. The hand with the highest pair wins if there are multiple two pairs regardless of the other cards in hand. To demonstrate, K-K-5-5-2 beats Q-Q-10-10-9 because K > Q, despite 10 > 5.

#8 Pair

A hand with a single pair has two cards of equal rank and three other cards of any rank (as long as none are the same.) When comparing pairs, the one with highest value cards wins. If they are equal, compare the highest value oddball cards, if those are equal continue comparing until a win can be determined. An example hand would be: 10-10-6-3-2

#9 High Card (Nothing/No Pair)

If your hand does not conform to any of the criterion mentioned above, does not form any sort of sequence, and are at least two different suits, this hand is called high card. The highest value card, when comparing these hands, determines the winning hand.

Low Poker Hand Ranking

In Lowball or high-low games, or other poker games which lowest ranking hand wins, they are ranked accordingly.

A low hand with no combination is named by it’s highest ranking card. For example, a hand with 10-6-5-3-2 is described as “10-down” or “10-low.”

Ace to Five

The most common system for ranking low hands. Aces are always low card and straights and flushes do not count. Under Ace-to-5, 5-4-3-2-A is the best hand. As with standard poker, hands compared by the high card. So, 6-4-3-2-A beats 6-5-3-2-A AND beats 7-4-3-2-A. This is because 4 < 5 and 6 < 7.

The best hand with a pair is A-A-4-3-2, this is often referred to as California Lowball. In high-low games of poker, there is often a conditioned employed called “eight or better” which qualifies players to win part of the pot. Their hand must have an 8 or lower to be considered. The worst hand under this condition would be 8-7-6-5-4.

Duece to Seven

The hands under this system rank almost the same as in standard poker. It includes straights and flushes, lowest hand wins. However, this system always considers aces as high cards (A-2-3-4-5 is not a straight.) Under this system, the best hand is 7-5-4-3-2 (in mixed suits), a reference to its namesake. As always, highest card is compared first. In duece-to-7, the best hand with a pair is 2-2-5-4-3, although is beat by A-K-Q-J-9, the worst hand with high cards. This is sometimes referred to as “Kansas City Lowball.”

Ace to Six

This is the system often used in home poker games, straights and flushes count, and aces are low cards. Under Ace-to-6, 5-4-3-2-A is a bad hand because it is a straight. The best low hand is 6-4-3-2-A. Since aces are low, A-K-Q-J-10 is not a straight and is considered king-down (or king-low). Ace is low card so K-Q-J-10-A is lower than K-Q-J-10-2. A pair of aces also beats a pair of twos.

In games with more than five cards, players can choose to not use their highest value cards in order to assemble the lowest hand possible.

Hand Rankings with Wild Cards

Wild cards may be used to substitute any card a player may need to make a particular hand. Jokers are often used as wild cards and are added to the deck (making the game played with 54 as opposed to 52 cards). If players choose to stick with a standard deck, 1+ cards may be determined at the start as wild cards. For example, all the twos in the deck (deuces wild) or the “one-eyed jacks” (the jacks of hearts and spades).

Wild cards can be used to:

• substitute any card not in a player’s hand OR
• make a special “five of a kind”

Five of a Kind

Five of a Kind is the highest hand of all and beats a Royal Flush. When comparing five of a kinds, the highest value five cards win. Aces are the highest card of all.

The Bug

Some poker games, most notably five card draw, are played with the bug. The bug is an added joker which functions as a limited wild card. It may only be used as an ace or a card needed to complete a straight or a flush. Under this system, the highest hand is a five of a kind of aces, but no other five of a kind is legal. In a hand, with any other four of a kind the joker counts as an ace kicker.

Wild Cards – Low Poker

During a low poker game, the wild card is a “fitter,” a card used to complete a hand which is of lowest value in the low hand ranking system used. In standard poker, 6-5-3-2-joker would be considered 6-6-5-3-2. In ace-to-five, the wild card would be an ace, and deuce-to-seven the wild card would be a 7.

Lowest Card Wild

Home poker games may play with player’s lowest, or lowest concealed card, as a wild card. This applies to the card of lowest value during the showdown. Aces are considered high and two low under this variant.

Double Ace Flush

This variant allows the wild card to be ANY card, including one already held by a player. This allows for the opportunity to have a double ace flush.

Natural Hand v. Wild Hand

There is a house rule which says a “natural hand” beats a hand that is equal to it with wild cards. Hands with more wild cards may be considered “more wild” and therefore beat by a less wild hand with only one wild card. This rule must be agreed upon before the deal begins.

Incomplete Hands

If you are comparing hands in a variant of poker which there are less than five cards, there are no straights, flushes, or full houses. There is only four of a kind, three of a kind, pairs (2 pairs and single pairs), and high card. If the hand has an even number of cards there may not be a kicker.

Examples of scoring incomplete hands:

10-10-K beats 10-10-6-2 because K > 6. However, 10-10-6 is beat by 10-10-6-2 because of the fourth card. Also, a 10 alone will beat 9-6. But, 9-6 beats 9-5-3, and that beats 9-5, which beats 9.

Ranking Suits

In standard poker, suits are NOT ranked. If there are equal hands the pot is split. However, depending on the variant of poker, there are situations when cards must be ranked by suits. For example:

• Drawing cards to pick player’s seats
• Determining the first better in stud poker
• In the event an uneven pot is to be split, determining who gets the odd chip.

Typically in North America (or for English speakers), suits are ranked in reverse alphabetical order.

2 Card Poker Free

• Spades (highest suit), Hearts, Diamonds, Clubs (lowest suit)

Suits are ranked differently in other countries/ parts of the world:

• Spades (high suit), Diamonds, Clubs, Hearts (low suit)
• Hearts (high suit), Spades, Diamonds, Clubs (low suit) – Greece and Turkey
• Hearts (high suit), Diamonds, Spades, Clubs (low suit) – Austria and Sweden
• Hearts (high suit), Diamonds, Clubs, Spades (low suit) – Italy
• Diamonds (high suit), Spades, Hearts, Clubs (low suit) – Brazil
• Clubs (high suit), Spades, Hearts, Diamonds (low suit) – Germany

REFERENCES:

http://www.cardplayer.com/rules-of-poker/hand-rankings

https://www.pagat.com/poker/rules/ranking.html

https://www.partypoker.com/how-to-play/hand-rankings.html

Brian Alspach

18 January 2000

Abstract:

One of the most popular poker games is 7-card stud. The way hands areranked is to choose the highest ranked 5-card hand contained amongst the7 cards. People frequently encounter difficulty in counting 7-card handsbecause a given set of 7 cards may contain several different types of5-card hands. This means duplicate counting can be troublesome as canomission of certain hands. The types of 5-card poker hands in decreasingrank are

• straight flush
• 4-of-a-kind
• full house
• flush
• straight
• 3-of-a-kind
• two pairs
• a pair
• high card

The total number of 7-card poker hands is .

We shall count straight flushes using the largest card in the straightflush. This enables us to pick up 6- and 7-card straight flushes. Whenthe largest card in the straight flush is an ace, then the 2 other cardsmay be any 2 of the 47 remaining cards. This gives us straight flushes in which the largest card is an ace.

If the largest card is any of the remaining 36 possible largest cards ina straight flush, then we may choose any 2 cards other than theimmediate successor card of the particular suit. This gives usstraight flushes of the second type, and41,584 straight flushes altogether.

In forming a 4-of-a-kind hand, there are 13 choices for the rank ofthe quads, 1 choice for the 4 cards of the given rank, and choices for the remaining 3 cards. This implies there are 4-of-a-kind hands.

There are 3 ways to get a full house and we count them separately. Oneway of obtaining a full house is for the 6-card hand to contain 2 setsof triples and a singleton. There are ways tochoose the 2 ranks, 4 ways to choose each of the triples, and 44 ways tochoose the singleton. This gives us fullhouses of this type. A second way of getting a full houseis for the 7-card hand to contain a triple and 2 pairs. There are 13ways to choose the rank of the triple, ways tochoose the ranks of the pairs, 4 ways to choose the triple of the givenrank, and 6 ways to choose the pairs of each of the given ranks. Thisproduces full house of the secondkind. The third way to get a full house is for the 7-card hand tocontain a triple, a pair and 2 singletons of distinct ranks. There are13 choices for the rank of the triple, 12 choices for the rank of thepair, choices for the ranks of the singletons,4 choices for the triple, 6 choices for the pair, and 4 choices for eachof the singletons. We obtain full houses of the last kind. Adding the 3 numbers gives us3,473,184 full houses.

To count the number of flushes, we first obtain some useful informationon sets of ranks. The number of ways of choosing 7 distinct ranks from13 is .We want to remove the sets of rankswhich include 5 consecutive ranks (that is, we are removing straightpossibilities). There are 8 rank sets of the form .Another form to eliminate is ,where y is neither x-1 nor x+6. If x is ace or 9, thereare 6 choices for y. If x is any of the other 7 possibilities, thereare 5 possibilities for y. This produces sets with 6 consecutive ranks. Finally, the remaining form to eliminateis ,where neither y nor z is allowed totake on the values x-1 or x+5. If x is either ace or 10, theny,z are being chosen from a 7-subset. If x is any of the other 8possible values, then y,z are being chosen from a 6-set. Hence, thenumber of rank sets being excluded in this case is .In total, we remove 217 sets of ranks ending upwith 1,499 sets of 7 ranks which do not include 5 consecutive ranks.Thus, there are flushes having all 7 cards in thesame suit.

Now suppose we have 6 cards in the same suit. Again there are 1,716sets of 6 ranks for these cards in the same suit. We must excludesets of ranks of the form of which thereare 9. We also must exclude sets of ranks of the form ,where y is neither x-1 nor x+5. So if x is aceor 10, y can be any of 7 values; whereas, if x is any of the other8 possible values, y can be any of 6 values. This excludes 14 + 48= 62 more sets. Altogether 71 sets have been excluded leaving 1,645sets of ranks for the 6 suited cards not producing a straight flush.The remaining card may be any of the 39 cards from the other 3 suits.This gives us flushes with 6 suitedcards.

Finally, suppose we have 5 cards in the same suit. The remaining 2cards cannot possibly give us a hand better than a flush so all we needdo here is count flushes with 5 cards in the same suit. There arechoices for 5 ranks in the same suit. We mustremove the 10 sets of ranks producing straight flushes leaving us with1,277 sets of ranks. The remaining 2 cards can be any 2 cards from theother 3 suits so that there are choices for them.Then there are flushes of this lasttype. Adding the numbers of flushes of the 3 types produces 4,047,644flushes.

We saw above that there are 217 sets of 7 distinct ranks which include5 consecutive ranks. For any such set of ranks, each card may be anyof 4 cards except we must remove those which correspond to flushes.There are 4 ways to choose all of them in the same suit. There areways to choose 6 of them in the same suit. For 5of them in the same suit, there are ways to choosewhich 5 will be in the same suit, 4 ways to choose the suit of the 5cards, and 3 independent choices for the suits of each of the 2 remainingcards. This gives choices with 5 in the samesuit. We remove the 844 flushes from the 4⁷ = 16,384 choices of cardsfor the given rank set leaving 15,540 choices which produce straights.We then obtain straights when the 7-cardhand has 7 distinct ranks.

We now move to hands with 6 distinct ranks. One possible form is,where x can be any of 9 ranks. The otherpossible form is ,where y is neither x-1nor x+5. When x is ace or 10, then there are 7 choices for y.When x is between 2 and 9, inclusive, there are 6 choices for y.This implies there are sets of 6 distinctranks corresponding to straights. Note this means there must be a pairin such a hand. We have to ensure we do not count any flushes.

As we just saw, there are 71 choices for the set of 6 ranks. Thereare 6 choices for which rank will have a pair and there are 6 choicesfor a pair of that rank. Each of the remaining 5 cards can be chosenin any of 4 ways. Now we remove flushes. If all 5 cards were chosenin the same suit, we would have a flush so we remove the 4 ways ofchoosing all 5 in the same suit. In addition, we cannot choose 4 ofthem in either suit of the pair. There are 5 ways to choose 4 cardsto be in the same suit, 2 choices for that suit and 3 choices for thesuit of the remaining card. So there are choices which give a flush. This means there are 4⁵ - 34 = 990choices not producing a flush. Hence, there are straights of this form.

We also can have a set of 5 distinct ranks producing a straight whichmeans the corresponding 7-card hand must contain either 2 pairs or3-of-a-kind as well. The set of ranks must have the formand there are 10 such sets. First we supposethe hand also contains 3-of-a-kind. There are 5 choices for the rankof the trips, and 4 choices for trips of that rank. The cards of theremaining 4 ranks each can be chosen in any of 4 ways. This gives4⁴ = 256 choices for the 4 cards. We must remove the 3 choices for whichall 4 cards are in the same suit as one of the cards in the 3-of-a-kind.So we have straights which alsocontain 3-of-a-kind.

Next we suppose the hand also contains 2 pairs. There are choices for the 2 ranks which will be paired. There are 6choices for each of the pairs giving us 36 ways to choose the 2 pairs.We have to break down these 36 ways of getting 2 pairs because differentsuit patterns for the pairs allow different possibilities for flushesupon choosing the remaining 3 cards. Now 6 of the ways of getting the2 pairs have the same suits represented for the 2 pairs, 24 of themhave exactly 1 suit in common between the 2 pairs, and 6 of them haveno suit in common between the 2 pairs.

There are 4³ = 64 choices for the suits of the remaining 3 cards.In the case of the 6 ways of getting 2 pairs with the same suits, 2of the 64 choices must be eliminated as they would produce a flush(straight flush actually). In the case of the 24 ways of getting 2pairs with exactly 1 suit in common, only 1 of the 64 choices need beeliminated. When the 2 pairs have no suit in common, all 64 choicesare allowed since a flush is impossible. Altogether we obtain

Poker 2 Pair High Card Game

straights which alsocontain 2 pairs. Adding all the numbers together gives us 6,180,020straights.

A hand which is a 3-of-a-kind hand must consist of 5 distinct ranks.There are sets of 5 distinct ranks fromwhich we must remove the 10 sets corresponding to straights. Thisleaves 1,277 sets of 5 ranks qualifying for a 3-of-a-kind hand. Thereare 5 choices for the rank of the triple and 4 choices for the tripleof the chosen rank. The remaining 4 cards can be assigned any of 4suits except not all 4 can be in the same suit as the suit of one ofcards of the triple. Thus, the 4 cards may be assigned suits in 4⁴-3=253 ways. Thus, we obtain 3-of-a-kind hands.

Next we consider two pairs hands. Such a hand may contain either 3pairs plus a singleton, or two pairs plus 3 remaining cards of distinctranks. We evaluate these 2 types of hands separately. If the hand has3 pairs, there are ways to choose the ranks ofthe pairs, 6 ways to choose each of the pairs, and 40 ways to choosethe singleton. This produces 7-card hands with 3 pairs.

The other kind of two pairs hand must consist of 5 distinct ranks andas we saw above, there are 1,277 sets of ranks qualifying for a twopairs hand. There are choices for the two ranksof the pairs and 6 choices for each of the pairs. The remaining cardsof the other 3 ranks may be assigned any of 4 suits, but we must removeassignments which result in flushes. This results in exactly thesame consideration for the overlap of the suits of the two pairs asin the final case for flushes above. We then obtain

Does High Card Count In 2 Pair

hands of two pairs of the second type. Adding the two gives 31,433,4007-card hands with two pairs.

Now we count the number of hands with a pair. Such a hand must have6 distinct ranks. We saw above there are 1,645 sets of 6 ranks whichpreclude straights. There are 6 choices for the rank of the pair and6 choices for the pair of the given rank. The remaining 5 ranks canhave any of 4 suits assigned to them, but again we must remove thosewhich produce a flush. We cannot choose all 5 to be in the same suitfor this results in a flush. This can happen in 4 ways. Also, wecannot choose 4 of them to be in the same suit as the suit of eitherof the cards forming the pair. This can happen in ways. Hence, there are 4⁵-34 = 990 choices for the remaining 4 cards.This gives us hands with a 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 133,784,560 which will serve as a check on our arithmetic.

A high card hand has 7 distinct ranks, but does not include straights.So we must eliminate sets of ranks which have 5 consecutive ranks.Above we determined there are 1,499 sets of 7 ranks not containing 5consecutive ranks, that is, there are no straights. Now the card ofeach rank may be assigned any of 4 suits giving 4⁷ = 16,384 assignmentsof suits to the ranks. We must eliminate those which resulkt in flushes.There are 4 ways to assign all 7 cards the same suit. There are 7choices for 6 cards to get the same suit, 4 choices of the suit to beassigned to the 6 cards, and 3 choices for the suit of the other card.This gives assignments in which 6 cards end upwith the same suit. Finally, there are choices for5 cards to get the same suit, 4 choices for that suit, and 3 independentchoices for each of the remaining 2 cards. This gives assignments producing 5 cards in the same suit. Altogether wemust remove 4 + 84 + 756 = 844 assignments resulting in flushes. Thus,the number of high card hands is 1,499(16,384 - 844)=23,294,460.

If we sum the preceding numbers, we obtain 133,784,560 and we can beconfident the numbers are correct.

Here is a table summarizing the number of 7-card poker hands. Theprobability is the probability of having the hand dealt to you whendealt 7 cards.

How Does 2 Pair Work In Poker

hand	number	Probability
straight flush	41,584	.00031
4-of-a-kind	224,848	.0017
full house	3,473,184	.026
flush	4,047,644	.030
straight	6,180,020	.046
3-of-a-kind	6,461,620	.048
two pairs	31,433,400	.235
pair	58,627,800	.438
high card	23,294,460	.174

You will observe that you are less likely to be dealt a hand withno pair (or better) than to be dealt a hand with one pair. Thishas caused some people to query the ranking of these two hands.In fact, if you were ranking 7-card hands based on 7 cards, theorder of the last 2 would switch. However, you are basing the rankingon 5 cards so that if you were to rank a high card hand higher than a handwith a single pair, people would choose to ignore the pair in a7-card hand with a single pair and call it a high card hand. Thiswould have the effect of creating the following distortion. Thereare 81,922,260 7-card hands in the last two categories containing5 cards which are high card hands. Of these 81,922,260 hands,58,627,800 also contain 5-card hands which have a pair. Thus, thelatter hands are more special and should be ranked higher (as theyindeed are) but would not be under the scheme being discussed inthis paragraph.

2 Card Poker Game