On the Expected Duration of a Generalized Bingo Game

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.