Quad-128 is a game played with two distinguishable Quad-64 decks; for example, each deck has a different background color. The game play is similar, but the combined deck is now a model for the affine geometry $AG(7,2)$ rather than $AG(6,2)$. We define a $\mathit{\text{cap}}$ to be a quad-free set of cards. We determine the maximum size of a cap, which tells us how many cards we must lay out to guarantee a quad. More generally, we classify all caps in $AG(7,2)$ up to affine equivalence.

This is joint work with Timothy Goldberg and Kariane Calta. Link to play the game: tinyurl.com/evenquadsapp