Several previous efforts had failed to take into account the fact that “the events representing completion of the 12 possible Bingos are neither independent nor mutually exclusive,” they point out. In presenting their data, Agard and Shackleford also remark that some care must be taken in doing the analysis.

Shackleford note in the September College Mathematics Journal. “The analysis turns out to be straightforward, but obtaining the numerical results would be tedious without a computer,” David B.

More precisely, what is the average number of calls required to complete a game for a given number of players? It’s natural to wonder how long a typical game would last. What makes the game suspenseful is the tantalizing uncertainty about when someone will achieve a Bingo. Eight of these configurations do not involve the use of the center “free” space, whereas four (column N, row 3, and the diagonals) do. In standard Bingo, the player’s goal is to be the first to mark an entire row, column, or diagonal. Column G contains five numbers from the interval 46 to 60, and column O contains five numbers from the interval 61 to 75.Īn announcer randomly selects numbers from 1 to 75, calling out each one while players mark the appropriate grid square if that number appears on their cards. Column N contains four numbers from the interval 31 to 45. Column I contains five numbers from the interval 16 to 30. The columns are labeled from left to right with the letters “B,” “I,” “N,” “G,” and “O.” The center square is designated “free.” The five squares in column B contain different numbers selected from the interval 1 to 15. Each card has five rows and five columns. To play Bingo, each player has one or more cards divided into squares. After a day of sledding and cross-country skiing, it’s relaxing to indulge in a social game that requires minimal thought, affords young and old the same chance of winning, and has a strong element of suspense. One of the little pleasures of our annual winter vacation is an evening Bingo party.

Bingo winners