List of poker hands
In the card game of poker, the term describes the best five-card hand that can take advantage of a player. The ranking of the individual cards combinations in all game modes same, only their probability varies. The most important change is a deck with one Joker represents the best achievable hand is in such a deck, a quintuplet, while the best hand is a normal French Journal of the Royal Flush.
- 4.1 Royal Flush
- 4.2 Straight Flush
- 4.3 Vierling
- 4.4 Full House
- 4.5 flush
- 4.6 Straight
- 4.7 Drilling
- 4.8 Two pairs
- 4.9 A pair of
- 4:10 High Card
General rules
- If an equality of rank of the hand there, usually decides the amount of each card. The following, in decreasing order applies: Ace - King - Queen - Jack - 10-9 - 8-7 - 6 - 5 - 4 - 3 - 2 Is such a card key, the affected player has the better kicker.
- A hand always consists of five cards. Therefore, it is not possible that the kicker decides in two equal straights, as these already consist of five cards.
- Cards are ranked first by the rank of the hand and only then on the amount of cards involved: Two pairs of twos and threes are therefore better than a pair of aces.
- There is no hierarchy of symbols with influence on the rank of the hand, the strength of a flush is not dependent on which of the four symbols include the five suited cards.
Influence of game variations to the probabilities of the hands
The information on the probabilities of the different hands are dependent on the version of the game; are therefore dependent on whether there are community cards are exchanged (eg, Texas Hold'em ) or maps (eg, Draw Poker ) can.
The different game modes are characterized by the fact that there is in each case different ways to achieve a hand of five cards. The total number of combinations thus changes from game to game variant variant. When pure drawing five cards from a poker hand of 52 cards, there are 2,598,960 combinations in seven cards of 52 (Texas Hold'em ), there are already 133 784 560 combinations.
In general: If you divide the number of combinations for a hand by the total number of combinations, so this gives the chance to get this hand in this game variant. So applies (with exceptions) mostly the rule: every hand is all the more valuable the fewer combinations to match.
Both the possibility to exchange cards and the community cards to choose from usually affect the probabilities rather favor of more valuable hands. Thus, in the game variant Texas Hold'em, for example, the couple is more likely than high card, but still ranked higher because mind you the ranking of each hand remains unchanged.
In the case of the card exchange, it comes naturally to the player selected by the strategy, such as the probabilities are influenced in detail. A valid regardless of the player strategy calculation is not possible, and to the determination of a potentially optimal exchange strategy can not be discussed here.
Even in the case of community cards, the probabilities are much more complicated to calculate than for the case of 5 52 For 7 out of 52 (Texas Hold'em ), therefore, the hands are here only as an example a pair and high card compared.
Combinations in five of 52 cards
Taking five cards from a poker hand of 52 cards, 2,598,960 combinations are possible:
The following table gives for each hand the number of ways to make it 5 out of 52 cards; in other variants ( for example, addition of wild cards or mixing several complete card ), there would be other values. In the next column we find the resultant from this number probability of obtaining such a sheet in the random drawing of five cards; Variants with strategic behavior or choices are therefore not considered here. These restrictions also compare the influence of the section game variations to the probabilities. The next column " as the ratio " gives the probability for such a leaf on not as a percentage, but in terms of odds. The cumulative probability indicates finally, how likely is it to draw at least looked at the combination. The table is one of the extremely rare royal flush with the Straight Flush, which is justified insofar as it is without being specifically naming the highest among the Straight Flushes.
Royal Flush
This hand is actually a straight flush, is her role as the best hand in poker, and their rarity but considered separately. A royal flush, such as A ♣ K ♣ Q ♣ J ♣ 10 ♣ is a straight flush with the ace high, so that is the highest straight flush.
This hand is so rare that it has so far been seen only three times in a poker broadcast on German television. In the very unlikely event that eg when Draw Poker, two players hold a royal flush, the pot is split. The Hold'em variants, in which played with community cards, such a situation is only possible if the Royal Flush completely open on the table, so the Royal Flush show the five community cards ( board) for the variation of Omaha Hold 'em up in which there are community cards, such a situation is not possible.
Examples:
- A ♣ K ♣ Q ♣ J ♣ 10 ♣ K ♣ Q ♣ J proposes ♣ ♣ 9 ♣ 10
A split pot is only possible if the board of A ♣ K ♣ Q ♣ J ♣ 10 ♣ (or other color). In this case, all players play the Royal Flush from the board.
Number of possible combinations,
There is a possible highest card ( ace ) and four different colors:
Straight Flush
The different straight flushes ( for: Monochrome roads, including the Royal Flush s, o ) are the best possible card combinations. An example is a hand like Q ♠ J ♠ 10 ♠ 9 ♠ 8 ♠, which contains five cards in succession in the same color. Two competing Straight Flushes are valued at their highest card, similar to a straight. The probability of occurrence of straight flushes is still less than that of four cards of the same rank (eg, four boys ), so the straight flush is the second highest -evaluated all poker hands. Here are straights with 5 as the highest card possible, such as 5 ♦ 4 ♦ 3 ♦ 2 ♦ A ♦. This hand is also known as steel wheel.
Examples:
- 7 ♥ 6 ♥ 5 ♥ 4 ♥ 3 ♥ 5 ♠ 4 ♠ beats 3 ♠ 2 ♠ A ♠
- J ♣ 10 ♣ 9 ♣ 8 ♣ 7 ♣ " splits " J ♦ 10 ♦ 9 ♦ 8 ♦ 7 ♦ ( split pot )
Number of possible combinations (excluding Royal Flush )
There are (excluding Ace) nine different possible high cards and four different colors:
Quadruplet
Four of a kind, or poker, also known in English four of a kind or quads, is another poker hand. One example is 9 ♣ 9 ♠ 9 ♦ 9 ♥ J ♥. A four contains four cards of the same value. The Vierling is above the full house and below a straight flush. It determines the height of the quadruplet. If there is already a four of a kind among the community cards, so that all remaining players can use this Vierling, decides the rank of the kicker, in case of equality, there is a split pot
Examples:
Number of possible combinations,
Each of the thirteen values may evolve into a four of a kind. Stay ( 52-4 ) = 48 remaining cards, which serve as a kicker:
Another approach is - equivalent to twin and triplet - assuming that each of the thirteen values can form a quadruplet. Included are four of the four colors of a value. The remaining card can be one of the twelve remaining values in four different colors have:
Full House
A full house to full house German, sometimes called full boat corresponds to a hand such as 3 ♣ 3 ♠ 3 ♦ 6 ♣ 6 ♥. A full house thus consists of three of a kind and a pair. To keep the hand in the valence is below a four of a kind and a flush. The height of the triplet decides. Can two players together with the community cards a full house with the same triplet, decides the level of the pair, in case of equality, there is a split pot
Examples:
Number of possible combinations,
The drilling can be of thirteen values and three different colors. The pair may be one of the remaining twelve values, and is composed of two of the four colors:
Flush
A flush is a hand such as Q ♣ 10 ♣ 7 ♣ 6 ♣ 4 ♣, which consists of five cards of the same color. Two flushes are valued at their highest card. Is this tied, the second highest, then the third highest card, and so on. A flush must not be formed from successive cards. But is this the case, one speaks of a straight flush. The color of the flushes plays no role in the order.
Examples:
- A ♥ Q ♥ 10 ♥ 5 ♥ 3 ♥ K ♠ Q ♠ J beats ♠ 9 ♠ 6 ♠ ( ace high flush wins)
- A ♦ K ♦ 7 ♦ 6 ♦ 2 ♦ A ♥ Q ♥ proposes 10 ♥ 5 ♥ 3 ♥ ( flush, ace king high wins)
- Q ♥ 10 ♥ 9 ♥ 5 ♥ 2 ♥ " splits " Q ♠ 10 ♠ 9 ♠ 5 ♠ 2 ♠ ( split pot )
Number of possible combinations,
The Flush consists of five cards of the same color. From each color there are thirteen cards. There are four different colors. From the figure we draw the 36 possible straight flushes and from the four possible royal flushes, which are each separately counted:
Straight
A straight, in German also street, is a hand such as Q ♣ J ♠ 10 ♠ 9 ♥ 8 ♥, which is formed from five consecutive cards of different colors. Are the colors of the five cards, however, are identical, it is called a straight flush. The hand is stronger than a triple and weaker than a flush. If two straights in circulation will be counted the highest card. Is this the same, there is a split pot straights with five as the highest number, so A - 2 - 3 - 4 - 5, are allowed, straights as K - A - 2 - 3 - 4 ( round the corner straight) but not if not expressly agreed. Other variants, such as skip straight (3 - 5 - 7 - 9 - J) should be agreed before the start of the turn, if necessary, including its assessment.
Examples:
- 8 ♠ 7 ♠ 6 ♥ 5 ♥ 4 ♠ 6 ♦ 5 ♠ 4 proposes ♦ 3 ♥ 2 ♣ (eight high straight )
- 8 ♠ 7 ♠ 6 ♥ 5 ♥ 4 ♠ " splits " 8 ♥ 7 ♦ 6 ♣ 5 ♣ 4 ♥ ( split pot )
Number of possible combinations,
A straight consists of five cards. It consists of one of ten possible highest cards. Each card can have any of the four colors. As with the flushs the 36 straight flushs and the four royal flushs deducted:
Triplet
Drilling, also called in English, three of a kind or trips, is a hand such as 2 ♦ 2 ♠ 2 ♥ K ♠ 6 ♠, which contains three cards of the same rank and two other cards. There is disposed above the two pairs and the straight. Can two players from the community cards form an equal Drilling, determines the height of the first kickers, in case of equality of the second kicker.
Examples:
- 8 ♠ 8 ♥ 8 ♦ 5 ♠ 3 ♣ 5 ♣ 5 ♥ 5 suggests ♦ Q ♦ 10 ♣ (three eights wins)
- 8 ♠ 8 ♥ 8 ♦ A ♣ 2 ♦ 8 ♣ 8 ♥ 8 suggests ♦ 5 ♠ 3 ♣
Although evaluation technically identical, resulting in community card games two fundamentally different game situations.
- A set is three of a kind, which originated from a pocket pair, which is a very strong hand, especially since it is difficult to read for the opponent.
- Trips is a triplet with a map of the starting hand and an open pair. This combination can never be the nuts.
Number of possible combinations,
Each of the thirteen values can form a kind. Includes three of the four colors of a value. The other two cards must have two of the twelve remaining values and can be in four different colors:
Two pairs of
A hand such as J ♥ J ♣ 4 ♣ 4 ♠ 9 ♠, called Two couples, Eng. two pair. Often, couples are also called, such as two pairs, aces and eights. It consists of two pairs, and another map. If there are several duplicate pairs, the higher pair, then the second highest, and where appropriate, the kicker decides. The hand is positioned below the drilling and the pair.
Examples:
- K ♥ K ♦ 2 ♣ 2 ♦ J ♥ J ♦ J ♠ beats 10 ♠ 10 ♣ 9 ♠ (kings up wins)
- 4 ♠ 4 ♣ 3 ♠ 3 ♥ K ♦ ( fours and threes king, kicker ) beats 4 ♥ 4 ♦ 3 ♦ 3 ♣ 10 ♠
Number of possible combinations,
Each of the two pairs may have one of the thirteen values and two of the four colors. The kicker may have one of the eleven remaining values and any color:
A pair
A couple, engl. One pair is a hand, in which a value is present twice, such as 4 K ♥ 4 ♠ ♠ 10 ♦ ♠ 5 which additionally contains other three cards. The hand is less than two pairs, and better than the so-called High Card. Can two players have the same boast high pairs, decide the height of the first kickers, in case of equality of the second and possibly the third kicker.
Examples:
Number of possible combinations,
A couple can thirteen values and two of four different colors have. The remaining three cards can have twelve different values and four colors:
High Card
A High Card, also known as no pair, it means none of the above combinations. One example is K ♥ J ♣ 8 ♣ 7 ♦ 3 ♠. When two competing high cards of football, in case of equality of the second kicker and so on counts.
Examples:
- A ♦ 10 ♦ 9 ♠ 5 ♣ 4 ♣ K ♣ Q ♦ J proposes ♣ 8 ♥ 7 ♥
- A ♦ 10 ♦ 9 ♠ 5 ♣ 4 ♣ A ♣ 9 ♦ 8 beats ♥ 5 ♠ 4 ♠
Number of possible combinations,
The number is derived from the difference in the number of all possible hands, and the sum of the pair of hands to those listed above Royal Flush:
Another approach is to look at values and colors independently of each other:
- It must happen five different values , while they may not of that - considering only the values and lets the colors outside before - make ten streets.
- The colors may not form the four flushes, with analog only color is viewed and the values are left out.
These two numbers are multiplied together:
Combinations in 7 of 52 cards (Texas Hold'em )
Royal Flush
There are four ways of five cards to make a Royal Flush. With the remaining two cards, there are now ways for each royal flush. Overall, there are therefore
Since there is a total different (Poker ) combinations, the probability will be about 0.00323 %.
Straight Flush
In five cards, there are 9 ways (no royal flush ) with four colors for a straight flush. The remaining cards are distributed among the remaining 46 cards ( with the next higher card of the same color, a higher straight flush would form ). There are then
The probability is about 0.0279 %.
Quadruplet
Thus, from the seven cards four of a kind can be formed, four equal values must occur, a straight flush is therefore not to be considered.
There are 13 different quadruplets. Since four cards are already permanently assigned thus still remain three cards that can be combined from the remaining 48 cards. This results in
Different combinations.
Dividing by the possibilities of a whole, so yields a probability of about 0.168 % to be able to form a quadruplet as the best hand in Texas Hold'em.
Full House
There are three different ways to make a full house:
Three of a kind, a couple and two kickers
Three of a kind and two pairs
Two Triplets and a kicker
Overall, there is therefore possible combinations for a full house.
This gives a probability of approximately 2.60%.
Flush
There are three ways for a flush: exactly five suited cards, exactly six suited cards, exactly seven cards of the same color. The five, six or seven cards of the flushes are first distributed to the 13 different heights rank of the cards. Then, the number of combinations that would make a straight flush, creating a higher ranking hand would arise deducted. Now there are four different colors in which may be the flush. The remaining cards are now distributed to the 39 cards that would not form a flush with more same-colored cards. obtained
The probability is about 3.03%.
Straight
There are 10 different levels of roads. It may be a street on three independent paths form:
A road and two kickers
One of the two remaining cards together with a map of the road a couple
Both remaining cards form with one or two cards of the road two pair or three of a kind
Overall, there is therefore possible combinations for the poker hand straight.
This gives a probability of about 4.62%.
Triplet
In addition to the drilling, there must be no further pairs, triplets or quadruplets, because this higher ranking combinations would arise. The Drilling and the four kickers are first distributed to 13 different heights rank of the cards. Then the number of combinations must be removed, which would form a line. In addition, there are five ways in which the drilling and the kicker can be located ( according to the ranking level of the cards). There are four possibilities for the triple ( colors) at the same rank level. For the kicker, there are respective ways, although three have to be subtracted, since they would form a flush. There are then
The probability is about 4.83%.
Two pairs of
There are two ways in which two pairs can be formed: two couples and three kickers, three couples and a kicker. For the first case, the two couples and the three kickers are first distributed to the 13 rank ups of the cards. The number of combinations that form a road is taken off. There are ways where the couples and the kicker are located (Rank height). Then, even with the number of possible combinations of the kicker (there should be no flush form ) multiplied. For the second case, the three pairs are first distributed back to the 13 rank ups. For each pair, there are six possibilities ( colors). The kicker can now even fall to 40 different cards. There are
The probability is about 23.5%.
A pair
Thus, from the seven cards a couple ( but no better ) can be formed, six different values must occur, of which a double, but no road. Prohibitions are here ten streets in combination with another value with 13-5 options; However, here are nine " six- streets " deducted twice.
This results in the values
Different combinations.
With regard to the colors you have for forming the pair cards choose two of four colors while everything is allowed in the other cards except the four same color with one of the two colors observed also in the couple or otherwise same five colors.
This results in
Different color combinations.
The total combinations arise as a product, ie
Combinations.
Dividing by the possibilities of a whole, so yields a probability of about 43.8 percent, to form a pair as the best hand in Texas Hold'em.
High Card
Thus, from the seven cards no valuable combination can be formed, but seven different values must occur, including any road. According to the principle of inclusion and exclusion are removed, the combinations of ten streets with two other values , then add the double drawn combinations of nine six- roads with a different value. The eight - seven roads will be deducted three times in the five - streets and added twice in the six- streets, and are therefore hereby been correctly deducted.
This results in
Value combinations.
The stand
Color combinations over.
Again, as a product arising
Combinations only to achieve a whole and thus a probability of only about 17.4 percent, with Texas Hold'em High Card.