Infinite series is a challenging topic in the undergraduate mathematics curriculum for many students. In fact, there is a vast literature in mathematics education research on convergence issues. One of the most important types of infinite series is the geometric series. Their beauty lies in the fact that they can be evaluated explicitly and that they are often used to study other types of series. Typically, the proof of convergence/divergence and sum of the series is one of the first proofs in the infinite series module. In this article, the author introduces a new way to find the sum of a convergent geometric series from a probability theory perspective. This approach has been implemented in a calculus laboratory setting using a multi-player card game. (Contains 1 footnote.)