Proof lies at the heart of mathematical reasoning, yet teaching proof in a liberal arts mathematics course poses a unique challenge. How can we showcase the power and utility of axiomatic reasoning while keeping the content accessible to students from diverse majors and backgrounds? A simple game involving blue and red poker chips can offer the perfect balance of accessibility and depth, inviting students to explore axiomatic reasoning in an engaging yet rigorous way. With just three axioms, students can discover hidden structures within the game and even determine their optimal next moves. We will introduce the game and its axioms, and then we will discuss how it can be used as a classroom activity to demonstrate the elegance of mathematical proof through play.