A three-card flush loses to both of those. Only in three-card poker variants does a three-card flush have any value, and even there it's less than three-of-a-kind; if it's being compared to two pair, then obviously the game isn't three-card hands and the three-card flush is a nothing hand. (Whether it would beat ONE pair is inconsequential for the sample puzzle, since there are no duplicate cards in the deck to make both hands simultaneously possible, but in Brag for example it would beat a pair.) - ZM