Within an ace of

from The Collaborative International Dictionary of English v.0.48
Ace \Ace\ ([=a]s), n.; pl. {Aces} ([=a]"s[e^]z). [OE. as, F. as,
   fr. L. as, assis, unity, copper coin, the unit of coinage.
   Cf. {As}.]
   [1913 Webster]
   1. A unit; a single point or spot on a card or die; the card
      or die so marked; as, the ace of diamonds.
      [1913 Webster]

   2. Hence: A very small quantity or degree; a particle; an
      atom; a jot.
      [1913 Webster]

            I 'll not wag an ace further.         --Dryden.
      [1913 Webster]

   3. (Sport) A single point won by a stroke, as in handball,
      rackets, etc.; in tennis, frequently, a point won by a
      service stroke.
      [Webster 1913 Suppl.]

   {To bate an ace}, to make the least abatement. [Obs.]

   {Within an ace of}, very near; on the point of. --W. Irving.
      [1913 Webster]