Toward a Combinatorial Theory of SET and Related Card Games

TL;DR

This paper develops a combinatorial framework for SET and related card games, introducing equivalence classes and exploring new game variants like STUN, to deepen understanding of their structure and strategies.

Contribution

It defines a natural equivalence relation on SET card collections and generalizes the game, proposing new variants such as STUN based on attribute value constraints.

Findings

Enumerated equivalence classes of SET card collections.

Introduced and analyzed new game variants like STUN.

Provided combinatorial insights into game strategies.

Abstract

We define a natural equivalence relation on collections of cards from the card game SET, and enumerate some of the equivalence classes, vastly generalizing the standard game. On this basis, we describe several alternative games for the SET deck, including the game of STUN, in which the goal is to find three cards with exactly two values in each attribute.