Pinochle Poker: An Activity to Solidify Concepts in Counting and Probability

Abstract

We teach counting techniques such as combinations and permutations to aid students in accurately computing the size of large "sample spaces" and "events" without the need to list each individual possibility. We believe based on personal experiences that this material is challenging for students in part due to their desire to be able to perform calculations instantaneously without the need for careful and critical analysis of the problem. We present an activity - using ideas from the games of poker and pinochle - designed to help students expand from basic counting techniques and formulas to begin to think more critically about their subtleties. In addition to involving the advanced levels of critical thinking we want students to experience, the use of poker is advantageous because it represents a real-life situation with which many students are already familiar. Our observations suggest that some students will more readily engage in the activity due to these interests. Complexity is added by utilizing the less familiar Pinochle deck. While this activity has been tailored for use with statistics majors and future teachers at NKU, we believe the activity to be both entertaining and applicable for many different levels of students (including high-school discrete mathematics courses that have substantial probability components). We will discuss the activity including learning outcomes, rationale, and opportunities for teachable moments.