75-ball vs 90-ball bingo (and Russian lotto)

American 75-ball bingo uses a 5×5 card with a free centre and pays for patterns: a line, corners, the whole card. British 90-ball bingo uses a 3×9 ticket with 15 numbers and pays for one line, two lines and a full house. Russian lotto has the same 3×9 cards and 90 numbers, drawn as barrels from a bag.

The Hall of Seshat plays 75-ball. Below is how the three games differ, and what that means once the numbers start coming.

Five columns under the letters B, I, N, G and O, five numbers in each — 1–15 under B up to 61–75 under O — and a free space in the middle: 24 numbers in all. The caller reads the letter with the number, “B-7”, so you know at once which column to check.

Because the card is square, a game can be played for almost any shape: a line in any direction, four corners, an X, a picture frame, the whole card. Halls in the US and Canada run a session of short games, each with its own pattern. The patterns page shows fourteen of them with the number of balls each one takes.

A ticket has three rows and nine columns. Each row holds exactly five numbers and four blanks, so a ticket carries 15 numbers. The first column takes 1–9, the next 10–19 and so on, up to 80–90 in the last. Tickets usually come in strips of six that between them contain every number from 1 to 90 exactly once, so a player with a full strip covers something on every call.

One game pays three prizes in turn: one line (any row), two lines (two rows on the same ticket) and a full house (all 15 numbers). Lines in 90-ball are always horizontal. Calls come fast, and British halls grew a whole folklore of nicknames for the numbers — see bingo calls.

Russian lotto, русское лото, is a family game rather than a hall game. A set holds 90 small wooden or plastic barrels numbered 1 to 90, a cloth bag and a stack of cards — 24 in many sets — laid out like the British ticket: three rows, nine columns, five numbers in each row. The host pulls barrels out of the bag one at a time and calls them, and the players cover their numbers with counters, buttons or coins.

Who wins is agreed at the table: the first to close a row, or the first to close the whole card. Stakes were small coins per card. In the last act of Chekhov’s The Seagull (1896) the family plays at ten kopecks a stake. The sayings hosts use for numbers, like “drumsticks” for 11, are a story of their own.

We simulated 200,000 games of each kind. For 90-ball we generated proper tickets — three rows of five, every column used, numbers from the right ranges. Lotto cards are built the same way, so the 90-ball figures hold for lotto too.

Two things stand out. A line comes far sooner in 75-ball: with 15 cards, around ball 24 against ball 40. A 75-ball card has 12 lines, and the ones through the centre need only four numbers, while a ticket has three rows of five. Even counting only horizontal lines, 75-ball is quicker: a card has five rows instead of three, the middle one needs just four numbers, and the drum is smaller.

And a full house eats more of the drum than people expect. One ticket needs 85 of the 90 balls on average, one 75-ball card 73 of 75. For a single card there is an exact formula: with k numbers on the card and N balls in the drum, the card is complete after k × (N + 1) / (k + 1) balls on average. For 24 numbers out of 75 that gives 72.96, for 15 out of 90 it gives 85.31 — and our simulation landed on both.

A 5×5 card reads well on a phone: four of them fit on the screen at a size you can still tap. The letter on each ball tells you which column to look at, and in our manual halls, with 8 seconds per ball, that saves real time. The square card also gives two prizes nobody needs to have explained — any line and the full card — in a game that lasts about four minutes in an auto hall.

With the same number of players a 90-ball game runs longer: the full house goes at about ball 74 of 90 with 15 tickets, against ball 67–68 of 75 with 15 cards. That is no criticism of 90-ball. It is a fine game, and lotto evenings are a family tradition for many of our players. For a lotto night you need a real set with barrels; for 75-ball at home, print cards with our card generator.