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?
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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.