Bingo card

Bingo cards are playing cards designed to facilitate the game of Bingo in its various forms around the world.

In the early 1500s the people of Italy began to play a game called "Lo Gioco del Lotto d'Italia," which literally means "The game of lotto of Italy." The game operated very much like a modern lottery as players placed bets on the chances of certain numbers being drawn. By the 1700s, a version of Lo Gioco del Lotto d'Italia was played in France, where paper cards were first used to keep track of numbers drawn by a caller.

Before the advent of printing machines, numbers on bingo cards were either painted by hand or stamped using rubber stamps onto thick cardboard. Cards were reusable, meaning players used tokens to mark called numbers. The number of unique cards was limited as randomization had to occur by hand. Before the advent of online Bingo, cards were printed on card stock and, increasingly, disposable paper. While cardboard and paper cards are still in use, Bingo halls are turning more to "flimsies" (also called "throwaways") — a card inexpensively printed on very thin paper to overcome increasing cost — and electronic Bingo cards to overcome the difficulty with randomization.

There are two types of Bingo cards. One is a 5x5 grid meant for 75-ball Bingo, which is largely played in the U.S. The other uses a 9x3 grid for U.K. style "Housie" or 90-ball Bingo.

Players use cards that feature five columns of five squares each, with every square containing a number (except the middle square, which is designated a "FREE" space). The columns are labeled "B" (numbers 1–15), "I" (numbers 16–30), "N" (numbers 31–45), "G" (numbers 46–60), and "O" (numbers 61–75).

A popular Bingo myth claims that U.S. Bingo innovator Edwin S. Lowe contracted Columbia University professor Carl Leffler to create 6,000 random and unique Bingo cards. The effort is purported to have driven Leffler insane. Manual random permutation is an onerous and time-consuming task that limited the number of Bingo cards available for play for centuries.

The calculation of random permutations is a matter of statistics principally relying on the use of factorial calculations. In its simplest sense, the number of unique "B" columns assumes that all 15 numbers are available for the first row. That only 14 of the numbers are available for the second row (one having been consumed for the first row). And that only 13, 12, and 11 numbers are available for each of the third, fourth, and fifth rows. Thus, the number of unique "B" (and "I", "G", and "O", respectively) columns is (15*14*13*12*11) = 360,360. The combinations of the "N" column differ due to the use of the free space. Therefore, it has only (15*14*13*12) = 32,760 unique combinations. The product of the five rows (360,360⁴ * 32,760) describes the total number of unique playing cards. That number is 552,446,474,061,128,648,601,600,000 simplified as 5.52x10²⁶ or 552 septillion.

...
Wikipedia