First 15 bingo numbers

Bingo's ancestry runs back to the Italian lottery. A game of chance called lotto was being played in Italy by around 1530, and the state draw that grew from it, Il Gioco del Lotto d'Italia, became the model for everything that followed. An eighteenth-century Neapolitan parlour version, tombola, moved the draw from the lottery office to the family table. The much-repeated origin story — that tombola began in 1734 in a quarrel between Charles of Bourbon, the new king of Naples, and the Dominican friar Gregorio Maria Rocco, who won a promise that the lottery would pause over Christmas and so drove Neapolitans to run it at home — is legend rather than documented history, though 1734 and the new king's decision to tax Lotto winnings are the usual anchor. A French descendant, Le Lotto, appeared in 1778, and British soldiers and sailors played their own version under the name housey-housey.

The modern card came out of American carnivals. In the early 1920s Hugh J. Ward standardised the game at carnivals around Pittsburgh, copyrighted it, and published a rule book in 1933. In December 1929 Edwin S. Lowe (1910–1986), a travelling toy salesman, watched players at a carnival near Atlanta marking cardboard sheets with dried beans in a game they called beano. He took it back to New York, and — by his own later telling — a friend got so excited at winning that she shouted "Bingo!" instead of "Beano". The name stuck. Lowe printed cards, Catholic parishes took the game up as a Depression-era fundraiser, and his company pushed the stock of distinct cards past six thousand combinations. The familiar sequel, that a Columbia mathematician named Carl Leffler produced those cards and was driven insane by the work, is flagged even on Wikipedia as an unverified myth. Lowe later named Yahtzee, in 1956, and sold E. S. Lowe Company to Milton Bradley in 1973 for $26 million.

Britain's halls came last. The Betting and Gaming Act 1960 took effect on 1 January 1961, legalised large cash prizes, and sent 90-ball bingo into hundreds of converted cinemas.

Key properties

• A 75-ball card is a 5×5 grid whose columns draw from fixed ranges: B from 1–15, I from 16–30, N from 31–45, G from 46–60, O from 61–75.
• The centre square of the N column is a free space, so a 75-ball card carries 24 numbers rather than 25.
• There are exactly 552,446,474,061,128,648,601,600,000 possible 75-ball cards — 360,360⁴ × 32,760, the N column having fewer arrangements because of the free square.
• Because the free square counts as already covered, a blackout of the whole card needs at least 24 calls, and a line through the centre needs only 4.
• A UK 90-ball ticket is nine columns by three rows: 27 spaces holding 15 numbers and 12 blanks, with exactly five numbers in every row.
• 90-ball tickets are sold in strips of six, because six tickets of fifteen numbers cover each of the numbers 1 to 90 exactly once.
• The 90-ball columns are not all the same size: the first holds the single digits (1–9, or 1–10 in some layouts) and the last runs up to 90.
• This page draws with a 32-bit seeded generator, so it can reach at most 2³² distinct draw orders — far fewer than the 75! orderings a full 75-ball draw has.