Probability of making the nut low hand in Omaha hold 'em

:"See "Poker probability (Omaha)#Making low nuts" for a discussion of making low nut hands in Omaha hold 'em."

There are 165 different nut-low starting hand shapes that have the possibility of making a nut-low hand in Omaha hold 'em Hi-Lo. Combining the hand shapes into groups based on the factors that determine the probabilities for making the nut low hand and making low hands, the 165 different cases fall into 56 groupings.

The nut low hand shapes are denoted using the lower case letters x and y to represent qualifying low ranks higher than 5 (6–8 or 6–9 for 8- and 9-high qualifiers, respectively), and * to represent any high card. The following tables give the probability for select starting hands to make the nut low hand and make a non-nut low hand on the flop, turn and river. The hands in the table are listed in order of the probability of having the nut hand on the river, from highest probability to lowest. The tables also give the probability that the hand will make a nut low hand if at least three different low ranks are on the board, making a low hand possible. See "Poker probability (Omaha)#Making a low hand" for the probabilities of a low hand being possible and the probability of making or missing a low hand when one is possible.

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Note that while the probabilities are different between an 8-high and 9-high qualifier, the relative probabilities and the order of the probabilities for the hands making the nuts is the same for both qualifiers.

See also

* Binomial coefficient