Students Use Power of Math To Create Their Own Games

by Nicole Green

Chair, Upper School Mathematics Department

Fairfield University, B.S.

In a mathematical sense, life is a game. We’re involved in gaming every day whenever we make choices, large and small, whether it’s buying a car, selecting a candy, or choosing a spouse. Knowing how to calculate and assess odds, chances, risks, and rewards can help us make rational decisions and enhance our enjoyment of life.  

In my elective course “Game Theory,” students study the mathematical principles, strategies, and logic behind a wide variety of contests, ranging from zero-sum games to bidding games to sequential-move games, and then apply these concepts to real-world situations.

Game On!

Two of the most compelling game models we study are:

• The Prisoner’s Dilemma – Two accomplices in a crime are placed in two separate rooms and interrogated. Each is told that, if he confesses, he’ll get two years in prison, but the other suspect will go free. However, if they both refuse to confess, each will receive five years. Based on mathematical probability, what’s the best decision for each prisoner?   

• The Penalty Kick – A soccer goalie and a penalty kicker square off. To calculate the odds of a save or a goal, how can math be used to factor in elements as diverse as weather, field conditions, and heckling by fans?

Connect 4

One of the most instructive and enjoyable game model units in our class is the Connect 4 analysis and tournament. Students learn how to mathematically maximize their chances of winning by thinking of their own decisions as well as the decisions of their opponents. Students learn about the Nash Equilibrium, a situation in which neither player benefits from changing strategy. 

Through this, we discuss why we make decisions and how, by planning in advance, we can prepare for each scenario in the game. We also consider human error and how we are not computer or AI models that play perfectly every time, and how our humanity impacts our outcomes. 

This is one of the activities students look forward to the most in class. We conclude the unit with a final round-robin tournament, where everyone battles one another, learning different strategies and gaining insight into their classmates’ thought processes. We crown a champion at the end, and it is exciting to see!   

Mind Games

By taking on this challenging project, students learn that mathematics can be applied to almost any real-world question and that their minds are powerful enough to tackle and solve any problem they encounter. In the process, they gain confidence, not only in mathematics, but also in themselves.

More specifically, the game project also helps students to:  

• develop critical thinking skills and problem-solving techniques

• learn the importance of persistence and resilience

• explore alternative strategies, models, and scenarios

• master mathematical concepts and techniques that will equip them to make logical and beneficial decisions throughout their lives

This student-centered, student-driven activity helps them see that mathematics can be not only a practical and beneficial tool but also one heck of a lot of fun.

Skin in the Game

As a capstone activity for the course, I ask students to devise their own game based on what they’ve learned during the semester. Their essential challenge is to apply mathematical processes that use the known to find the unknown. I urge them to personalize their projects by creating a game based on their favorite activities or passions. I know they’ll be more invested in a game if it shines a new light on something they love. Thus, the themes of their games have ranged from golf to price wars between adjacent gas stations to World War II scenarios. One student created a game based on the optimum decisions first responders should make as they prioritize needs and allocate resources during destructive wildfires, such as those last winter in Los Angeles. 

The culmination of this project comes at the end of the semester when students share their games with their classmates through PowerPoint presentations. They demonstrate how the game is played, explain the mathematical principles involved, and receive constructive feedback from their peers.