- Maths reviewed by Josh Miller
- Tested by Diana Westfield
The bingo odds calculator starts with the honest bit: every ticket has the same chance. Hold 6 tickets in a game with 300 in play and you’ll win 2% of the time, about once every 50 games. It also tells you the chance one ticket is complete after a given number of calls, how likely it is somebody has won by then, and whether a game’s prize is decent value for the ticket price. Free, for 90-ball and 75-ball.
Bingo odds of winning, worked out
There’s no skill in which numbers come out and no “lucky” ticket. So your share of the tickets is your share of the wins. 6 out of 300 is 2%. Buy 12 and it’s 4%, at twice the cost. The expected return is the same either way: the prize divided by the tickets, minus what each one cost.
Say it’s £100 for a full house with 300 tickets at 50p. Each ticket is worth 33p of prize on average and costs 50p, so −17p a ticket. That game pays back 67% of the ticket money. Plenty of games pay back more, some less. The CasinoCalcs calculator shows the percentage, which is worth checking before you buy a strip.
How many calls does a full house take?
One 90-ball ticket needs all 15 of its numbers. The chance it’s complete after a given number of calls is:
| Calls | One ticket done | Someone done (300 tickets) |
|---|---|---|
| 55 | 0.03% | 7.5% |
| 60 | 0.12% | 29.4% |
| 65 | 0.45% | 74.4% |
| 70 | 1.58% | 99% |
| 75 | 4.98% | 100% |
So in a busy room most full houses go in the low to mid 60s. In a quiet one with 50 tickets, they drag on into the 70s. Bigger rooms finish faster, but your share of them is smaller. It balances out exactly.
75-ball blackout needs all 24 numbers, so it takes longer: a single card has only a 1.5% chance after 65 calls.
Lines and two lines
Earlier prizes come much sooner and the same rule holds: your chance is your share of the tickets. If a game pays one line, two lines and a full house, each prize is a separate draw for the odds, but the expected return adds up over all three. That’s where most of the value usually is.
To play along, the bingo caller and the bingo card generator cover a game at home. The bingo patterns page shows the shapes used in 75-ball games.
Running the night? The bingo prize calculator turns ticket sales into prizes for each game.
To watch thousands of games play out, try the bingo simulator.
How many different bingo cards are there?
For 75-ball bingo, each column picks its numbers from 15: five for B, I, G and O and four for N, around the free space. Ignoring the order within a column, that’s 3,003 × 3,003 × 1,365 × 3,003 × 3,003, or about 111 quadrillion (1.11 × 1017) cards that play differently. Count every arrangement of the numbers and it’s about 5.5 × 1026.
A 90-ball ticket has 15 numbers in 3 rows of 5, with each column holding 1 to 3 numbers from its own range (1 to 9, 10 to 19 and so on up to 80 to 90). Counting every valid layout gives about 3.67 × 1018 different tickets. Either way, two players holding the same card in one game is close enough to impossible.
Bingo is a social game. Set a budget for the night and enjoy it. BeGambleAware.org can help if it stops being fun.