Set is a card game that is very mathematical.
Set is played with a deck with 81 cards. Each card corresponds to a point in affine 4-space over $\mathbb Z/3$, with 3 possible colors, shadings, shapes, and counts. The players must identify Sets, sets of 3 cards corresponding to collinear points. Sets are also triples of cards which add up to the 0-vector. The three cards pictured form a Set.
A natural question which arises during play is whether there are any Sets among the cards which have been dealt out. There can be 9 cards in a codimension 1 subspace which do not contain a Set, corresponding to a nondegenerate conic in affine 3-space such as $z=x^2+y^2$. There can be at most 20 cards not containing a Set, corresponding to a nondegenerate conic in the projective 3-space containing 10 points.