EvenQuads is a SET-like card game published by the AWM whose goal is to find “quads”, which are sets of four cards satisfying a particular pattern. The cards can be viewed as points in the finite affine geometry $AG(6,2)$, and a quad in the card game corresponds to a plane in $AG(6,2)$. An interesting puzzle is to consider what the largest number of quads is that we can possibly pack into a specified number of cards/points, if we are allowed to choose them however we wish. In this talk, we will explain the rules and geometric underpinnings of EvenQuads, and describe some current work and open questions about quad-packing.