A 2-cap in the affine geometry AG(n,q) is a subset of 4 points in general
position. In this paper we classify all 2-caps in AG(n,2), up to affine
equivalence, for n≤6. We also provide structural results for general
n. Since the EvenQuads card deck is a model for AG(6,2), as a consequence
we determine the probability that an arbitrary k-card layout contains a quad.Comment: 36 pages, 20 figures, 5 table