Bingo Odds
Bingo odds come down to one question: how many balls have to be drawn before a card completes its prize. Each ball drawn is a call, so every figure below is either an average number of calls or the chance that a prize is complete by a given call. All of them are exact, counted across every possible sequence of balls, unless a table says otherwise.
One card on its own, a strip of six tickets and a room of a thousand cards give three different answers to the same question, and this page keeps them apart. How hard each individual shape is to make has its own page on bingo patterns, and the extra-ball decision in video bingo is covered by the bingo strategy guide.
75-Ball: The Chance of a Win by Each Call
For one card with the free space counted as marked. A line can come in as early as call 4, when four numbers complete a line through the center, but half of all single cards are still waiting at call 42. Three lines take 54.79 calls on average.
90-Ball: One Ticket Against a Strip of Six
A strip is six tickets that share out every number from 1 to 90, so the middle column is the chance that any one of the six has a line. The first full house on a strip takes 77.53 calls on average, against 85.31 for a single ticket.
Coverall Odds
A coverall, also called a blackout, needs all 24 numbers on a 75-ball card, and it is the one prize whose average can be worked out in a line: 24 numbers out of 75 balls take 72.96 calls on average. The spread around that average is narrow. Half of all single cards finish by call 74, and the most common finishing call is the very last one, 75.
The key number: One card finishes a coverall within 50 calls 1 in 212,085 times, and within 60 calls 1 in 715 times.
That is why halls that offer a coverall jackpot tie it to a call limit: the prize is paid only if the card is full within a stated number of calls, and the limit is usually set well below the average. Without the free space the card needs one number more, and the average rises to 73.08.
How the Number of Cards in Play Moves the Winning Call
Average number of calls until the first card in the room completes the prize. The 75-ball columns are exact. The 90-ball column is an average over a large number of simulated games played with real tickets cut from strips, because the column rules of a 90-ball ticket leave no exact shortcut; its single-ticket row is exact.
Your Share With Several Cards, and Shared Prizes
However the cards are printed, no card has a better chance than any other. So if you hold some of the cards in play, your long-run slice of the prize money equals your slice of the cards: one card of 100 is worth 1.00% of the prize over time, and ten of 100 are worth 10.0%. That holds with shared prizes included, and it is the whole of what buying more cards does.
Shared prizes are more common than most people expect, because several cards often complete on the same call. With 100 cards chasing a 75-ball coverall, the winning call produces more than one winner 20.3% of the time. For a 75-ball line in a room of 1,000 cards, the prize is split 34.3% of the time.
80-Ball: Line, Four Corners and Full House
Figures are for one 4×4 card. Four corners needs only four numbers, the same as a line, yet takes far longer, because a line can be any of 10 lines while the corners are one fixed set.
30-Ball Odds
A 30-ball card holds 9 of the 30 numbers and pays only when all of them are called. One card is full after 27.90 calls on average, and within 20 calls only 1.17% of the time. In a room the first full card arrives much sooner: 19.45 calls with 100 cards in play, when the first winner shares the prize 25.1% of the time.
Video Bingo Odds
Video bingo turns the question around. The draw has a fixed length, so the odds are not about when a card wins but whether it wins at all: once 30 of 60 balls are out, a given row of five is complete on 2.61% of cards and a full card on 1 in 342,928. The chance of every pattern size, for the common drum sizes, is tabled on the video bingo page.
How Many Different 75-Ball Cards Exist
Counting which numbers fill each column, there are 111 quadrillion different 75-ball cards. There are far more once the order within each column counts, as it does on a printed card. How that count comes about, column by column, is explained on the 75-ball bingo page.
Bingo Odds FAQ
No. A 75-ball card carries 24 numbers around its free space, and every one of them has to be called, so call 24 is the earliest possible finish. Without a free space the earliest is call 25. Finishing that early is possible in principle, but even by call 30 a single card is full only 1 in 43,400 billion times.
Yes, for the same format and the same number of cards. Whether a machine blows the balls or software picks them, each remaining number is equally likely on every call. What differs is the room: an online game may have far more or far fewer cards in play than a hall, and that moves the winning call.
The number of cards you hold divided by the number of cards in play. Five cards in a game of 100 win 5.00% of the prize money over time, whichever cards they are. The number of other players matters only because it sets the total number of cards.
Because the game stops at the first card to finish, and with more cards there are more chances for one of them to get lucky early. A 75-ball line takes 41.37 calls for one card on its own and 10.82 for the first of 1,000.