Green’s Dictionary of Slang

ambs-ace n.

also ames-ace
[SE ambs-ace, double ace or both aces; thus the lowest possible throw in dice]

1. [late 14C–18C] nothing, next to nothing.

2. [early 16C–18C] bad luck, misfortune, worthlessness.

In phrases

within ambs-ace of (also the ambs-ace of, within an aim’s ace)

[late 17C–19C] very close to; thus excl. amerace! don’t go far!