This term refers to when a player's hole cards consist of an Ace and a Three.
SoundPoker Says: This term comes from combining the pronunciation of Ace and Three. By saying Ace as "ash" and Three as "trey" you come to "ashtray".
Overall this is a mediocre starting hand because of the relatively weak 3 as a kicker. In looser games a suited combination of these cards is descent due to the flush and straight draws.
See Also: Draw, Flush, Hand, Hole Cards, Loose, Pocket Cards, Rank, Straight, Weak