Bingo Statistical Analysis

March 2025 - May 2025

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During my senior year at OSU, I elected to take a computational physics course with Dr. Beacom which focused on applying computational methods to solving physics problems. The final project for this course was to solve a complex physics or math problem using C++. For my project, I applied the Monte Carlo method to 75-Ball Bingo.

The program is designed to simulate thousands of bingo games across a randomly generated sample of cards. Each card's "marked" state is stored as a single binary number, which each digit corresponding to if the space has been marked or not. The program checks for bingos using bitwise AND comparisons across a set of “check” bitmasks that represent each possible bingo orientation. For each run, the program tracks the relative frequency of each bingo type, the frequency with which each individual space contributes to a bingo, and the average number of rounds required to score a bingo. Tests can be performed with any combination of vertical, horizontal, diagonal, postage stamp, and four corners bingo scoring criteria.

This simulation revealed an interesting statistical phenomena: with a large population of players, horizontal wins are nearly three times as common as vertical wins. With further research I found that this result can be analytically verified, which validates the results of the program. In the future, I would like to expand on this algorithm and allow for each player to have multiple cards simultaneously, in order to determine what features make a set of bingo cards advantageous in a multi-card game.