The caller calls out numbers-such as “B11!”-pulled randomly from a container. Some bingo cards have a free space in the middle of column N. Similarly columns I, N, G, and O have five random numbers from 16 to 30, 31 to 45, 46 to 60, and 61 to 75, respectively. Column B has five numbers from 1 through 15, in a random order. A typical bingo card, like the one in figure 1, has five columns, labeled B, I, N, G, and O, and each column has five numbers underneath it. To better understand this paradox, let’s review the rules of this popular game. To our surprise, horizontal winners were almost twice as likely as a vertical winner.

Why should the winning card be any different?Ī computer program was written that generated 1,000 random bingo cards and played the game 100,000 times. How can this be? If you randomly mark off numbers on your own bingo card, you are just as likely to get a horizontal bingo as a vertical bingo. Math Horizons - September 2017 The Bingo ParadoxĪrthur Benjamin, Joseph Kisenwether, Ben Weiss 02:42:24īelieve it or not, when a large number of people play bingo, it is much more likely that the winning card has a completed horizontal row than a completed vertical column.

75 bingo cards winning numbers