How do relatively small advantages play a role with respect to the success of individuals over time? How can we create a scenario involving two or more individuals, each with differing degrees of advantage, and observe how slight advantages (or disadvantages) affect their trajectories over time?
We will explore the concept of fairness as well as the concepts of expected and experimental probability via a probability game between two players in which one player possesses a fixed slight advantage over the other. We will solve the “Unfair Dice Problem” via an exploratory approach, and using Jupyter notebooks and the Python programming language, we will develop an interactive application that allows us to simulate how each player fares over time. This work is part of the Callysto Project, a federally-funded program to bring computational thinking and mathematical problem-solving skills into Grade 5-12 classrooms.
The Unfair Dice Problem has relevance and application in multiple areas of life, including but not limited to the role small advantages play in the context of employment, housing, access to education and support, mortgages and loan pre-approval, and social advancement and recognition. Although our application is based on a game involving dice, it is an illustration of the effect that seemingly small advantages can play over a long period of time in the outcome that individuals experience.
