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On the Expected Duration of a Generalized Bingo Game

2025/11/25 by Vu Phan, Ilie Ugarcovici, Phan, Vu +1
Mathematics · Physics and Astronomy · Economics, Econometrics and Finance · #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Complex Systems and Time Series Analysis

paper · pdf · doi:10.48550/arxiv.2511.20932

Abstract

We investigate the expected number of calls required to achieve Bingo in a generalized (n,m)-Bingo game, where each n x n card is filled by sampling n numbers from m possible values per column. Using the inclusion-exclusion principle, we derive exact formulas for the probability distribution and the expected game length. Our main theoretical result proves that the expected number of calls is a linear function of m.

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