The question might be paraphrased:
Complete the pattern with a word that played a parallel historical role:
- count: three, two, one, zero
- rank: third, second, first, zeroth
- dice: trey, deuce, ace, ____
Briefly, there is no exact fit because historically, dice didn't have 0 until perhaps as late as the mid-20th century, ditto playing cards, etc. etc.
However, some candidates for near matches:
- "nought" / "naught" -- Old English word meaning "nothing" that came to mean "zero" sometime in the 15th century. Featured in games such as Noughts and Crosses, so nought / ace / deuce....
- "love" -- tennis word for zero, and tennis is a medieval French that emerged in the 15th century and uses the the words ace and deuce, so there you have it. Etymological theories are that the term "love" either means "no money" or that it is a corruption of the French word for egg (l'œuf), indicateing an egg-shaped zero (also termed a "goose-egg").
- "joker" -- a specially named card (like the "ace") with no numerical marking (so perhaps like zero). A counterargument is that the origin of the joker is relatively recent (19th century), even if it might be modeled on the Fool tarot, and furthermore that the joker's origin and gameplay use puts it closer to meaning "infinity" (an uber-trump) than to "zero".