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Surely 4 of a kind in your hand has very very little chance of winning the high or low pot in Omaha High Low, right?
Correct. It would be possible, but highly unlikely to win the high half of the pot, with one pair, two pair or a full house.
You cannot win the low half at all, as one pair does not qualify for a low hand in most split pot games such as Omaha-8 or Stud-8.
Required, but never shown