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Table 1. Playing situations Drawing hands probabilities Odds Percent Double wraparound straight draw e. Table 2 will hopefully increase that overview a bit.
In Texas Hold'em, common knowledge is that A-A is very big favorite against all other hands. Omaha Odds and Ranking for All Starting Hands Number of Hands: Examples for All Starting Hands Strong Hand:.
Notes On top you see the groups for Omaha starting hands. One Pair. Two Pair. Three to Straight. Poker Tools. Dead Cards. X Click on a card in the deck to deal it.
Get Started. Online Poker Bonus Offers. When calculating probabilities for a card game such as Omaha, there are two basic approaches.
Often, the key to determining probability is selecting the best approach for a given problem. This article uses both of these approaches, but relies primarily on enumeration.
The probability of being dealt various starting hands can be explicitly calculated. In Omaha, a player is dealt four down or hole cards.
The first card can be any one of 52 playing cards in the deck; the second card can be any one of the 51 remaining cards; the third and fourth any of the 50 and 49 remaining cards, respectively.
There are 4! Alternatively, the number of possible starting hands is represented as the binomial coefficient.
The , starting hands can be reduced for purposes of determining the probability of starting hands for Omaha—since suits have no relative value in poker, many of these hands are identical in value before the flop.
The only factors determining the strength of a starting hand are the ranks of the cards and whether cards in the hand share the same suit.
Of the , combinations, there are 16, distinct starting hands grouped into 16 shapes. Throughout this article, hand shape is indicated with the ranks denoted using uppercase letters and suits denoted using lower case letters.
For example, the hand shape XaXbYaYc is any hand containing two pair XX and YY that share one suit a , but not the other suits b and c.
The 16 hand shapes can be organized into the following five hand types based on the ranks of the cards. There are also five types of hands based on the suits of the cards that mirror the five rank types: aaaa , aaab , aabb , aabc , and abcd.
The following are the probabilities and odds of being dealt each suit type. Unlike the rank types, the suit types can be absolutely ranked in terms of starting hand value because suits in poker hands only factor in flushes and straight flushes.
From best to worst starting hand value the suit types are: aabb , aabc , aaab , aaaa , and abcd. The relative probability of being dealt a hand of each given shape is different.
The following shows the probabilities and odds of being dealt each shape of starting hand. In addition to the rank type and suit type of a starting hand, each starting hand also has a sequence type that is useful for estimating the possibility of improving to a straight or straight flush.
The sequence type is based on the sequential proximity of the ranks in the hand—the number of different ranks in the hand that can be combined to fill a straight on the board.
The ace is a special case in the sequence type because it can be either high or low, and is also both the high and low card in the rank sequence from which straights are formed: AJ-Q-K-A.
The sequence type of the hand is only relevant in determining the probability of making a straight or straight flush. In order to make a straight, exactly three community cards must be combined with exactly two cards from the starting hand.
Thus the sequence shape of a hand is the number of different combinations of three cards that can make a straight when combined with two cards from the hand.
There are 20 different sequence shapes ranging from hands like K that can't make a straight 0 straight combinations to hands like J that can make a straight with 20 different combinations of three ranks , , , , , , J , , J , J , Q , Q , 8-J-Q , Q , 9-J-Q , 9-Q-K , J-Q , Q-K , J-Q-K , Q-K-A.
The 20 sequence shapes can be organized by the number of ranks in the starting hand. This is similar to the rank type of the hand, the only difference being that both the rank types two pair XXYY and three of a kind XXXY have two ranks.
The following table shows the four sequence types based on the number of distinct ranks in the starting hand.
Note that the table above shows 36 sequence shapes because although there are only 20 different sequence shapes, the sequence shapes overlap with the sequence types.
For example, the sequence shape where two different combinations of three cards can make a straight occurs for hands with two ranks e.
The relative probability of being dealt a hand of each sequence shape is different. The following shows the probabilities and odds of being dealt starting hands of each sequence shape.
As the table indicates, there is a The set of starting hands that can make a straight flush are a subset of the intersection of the set of hands that can make a straight and the set of hands that can make a flush.
The hands that can make a straight flush can be organized similar to the parent superset of hands that can make a straight. The straight flush sequence shape of a hand is the number of different combinations of three cards that can make a straight flush when combined with two cards from the hand.
As with straights, the relative probability of being dealt a hand of each straight flush sequence shape is different. The following shows the probabilities and odds of being dealt starting hands of each straight flush sequence shape.
Omaha Hi-Low is a high-low split variant where the best qualifying low hand, if any, splits the pot with the high hand.
Different cards can be used to form the high and low hands, each using two cards from the player's hand and three from the board, and a single player can win both the high and low pots.
A less common variant of Omaha Hi-Lo uses a qualifying low hand of 9-high or lower or lower. Suits and cards higher than the maximum qualifying low hand do not factor into low hands and neither do straights and flushes.
Based on the ranks of cards, low starting hands in Omaha Hi-Lo are grouped into 12 different low-hand shapes, seven of which have the possibility of making a qualifying low hand.
The low hand shapes can be organized by the number of distinct low card ranks in the hand: 0 or 1 low ranks no low hand possible , 2 low ranks, 3 low ranks and 4 low ranks.
The number of distinct low hands depends on the low-hand qualifier. The preceding table shows that with an 8-high low qualifier, a random hand has an If r represents the low hand qualifier 8 or 9 , there are cards with a rank higher than the low hand qualifier 20 high cards in 8-high, 16 in 9-high.
The probability of making a low hand depends on the number of low card ranks in the hand. However, although both are important, the probability of having the lowest hand depends more on the ranks of the low cards than on the number of low cards.
Beginning hand selection is critical in Omaha. Exactly two hole cards are combined with three community cards to form a hand in Omaha. The most favorable hand shapes have two suits with two cards in each suit, giving the hand two flush draws; have card ranks that are consecutive, giving the hand straight possibilities; and have one or more pairs, giving the hand a pair , and draws to three of a kind , full house and four of a kind possibilities.
This makes the hands with the shape XaXbYaYb , with the ranks of X and Y adjacent, great starting hands in Omaha. Against one opponent, AaAbKaKb is the strongest starting hand in Omaha against multiple opponents, the strongest starting hand is AaAbJaTb , while in Omaha Hi-Low the best starting hand is AaAb2a3b , which gives A for making a low hand and straights, two suited aces for nut flushes, and a pair of aces for high.
Contrary to most poker variants, more is not necessarily better or the same in Omaha, because only two hole cards are used.
Because of this limitation, hands with more than two of the same suit or more than two of the same rank are weaker than the hand would be with exactly two of the suit or rank.
The extra cards of the same suit remove outs for the flush draw and the extra cards of the same rank remove valuable outs for three of a kind, a full house, and four of a kind.
The suit type aaaa is only about half as likely to make a flush as aabc. Paradoxically, the worst hand in Omaha hold 'em is four of a kind deuces twos , because this hand can only make a pair of deuces plus the community cards.
Some professional poker players have created point systems for evaluating starting hands in Omaha, with the decision to raise, fold or call based on the number of points assigned to the starting hand.
However, because of the necessary simplifications point systems make, there is disagreement regarding the value of particular point systems and point systems in general.
By the turn the total number of combinations has increased to. An Omaha poker hand consists of two cards from the player's hand and three cards from the board.
Therefore, there are. By contrast, in Texas hold 'em there are only and ways to form a poker hand on the flop, turn and river, respectively.
This increase in opportunities to make a hand means that the average strength of the winning hand in Omaha is higher than in Texas hold' em and other 7-card poker variants.