On the Expected Duration of a Generalized Bingo Game

TL;DR

This paper derives exact formulas for the expected duration of a generalized Bingo game, showing that the expected number of calls is linearly related to the number of possible values per column.

Contribution

It provides a novel theoretical analysis of the (n,m)-Bingo game, including exact probability distributions and the linear relationship of expected calls with m.

Findings

Expected number of calls is a linear function of m.

Derived exact formulas for probability distribution of game length.

Theoretical insight into generalized Bingo game dynamics.

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.