What is a bingo odds calculator?
A bingo odds calculator gives the chance that the numbers you still need have all been called after a given number of calls. In 75-ball bingo, if you need 4 numbers and 40 balls have been called, the chance that all 4 are among them is 7.52%, or 1 in 13.3. The calculator uses exact counting, so it works for any pool, any number of calls and any number of numbers you need.
Bingo is a game of chance with no skill that changes the draw. The only decisions are how many cards to play and how much to spend. This tool shows how a single line builds up as the game goes on. It also shows why the winning pattern usually lands late, and why the more people play, the more likely it is that someone else gets there first.
How do you use the bingo odds calculator?
- Enter the numbers in the pool. Use 75 for US bingo or 90 for UK bingo.
- Enter the balls called. This is how many have been drawn so far.
- Enter the numbers you need. For a full line on a 75-ball card it is 5, or 4 on the centre row or column, which has a free space.
- Enter the hits you want. Use the same number as the numbers you need to ask for a complete line.
- Read the large number. It is the chance of exactly that many of your numbers being among the calls. The panel gives the odds of that many or more, and every number of hits.
Example: Pool 75, 40 called, 4 numbers needed, 4 hits wanted. Ways = C(4,4) x C(71,36). All draws = C(75,40). The chance is 7.52%, or 1 in 13.3.
How are bingo odds calculated?
The calls are a random draw without replacement, which is a hypergeometric situation. If N numbers are in the pool, n have been called and you need K, the chance that exactly h of your numbers have been called is C(K, h) x C(N – K, n – h) / C(N, n). For a complete line, h equals K, which simplifies to C(n, K) / C(N, K): the chance that the K specific numbers all land in the first n calls.
| Step | Working | Result |
|---|---|---|
| Numbers needed | 4 (centre row, free space) | 4 |
| Ways all 4 are among 40 calls | C(40, 4) | 91,390 |
| All ways to place 4 numbers | C(75, 4) | 1,215,450 |
| Chance | 91,390 / 1,215,450 | 7.52% |
How quickly does a line build up in 75-ball bingo?
Early in the game the chance of a full line is tiny. It rises slowly, then quickly, because the chance rises like a power of the share of balls called. The table shows the chance for one line that needs 4 numbers (a centre row or column with the free space) and one that needs 5.
| Balls called | Line needing 4 | Line needing 5 |
|---|---|---|
| 10 | 0.02% | 0.00% |
| 20 | 0.40% | 0.09% |
| 30 | 2.25% | 0.83% |
| 40 | 7.52% | 3.81% |
| 50 | 18.95% | 12.28% |
| 60 | 40.12% | 31.64% |
| 70 | 75.44% | 70.12% |
After 40 of 75 calls, a line needing 5 has only a 3.81% chance of being complete. By 60 calls it is about 32%. This is why games with a pattern on a single card often run for many calls. A game with many cards ends sooner, because the chance that some card is complete is far higher than the chance for one card.
What about 90-ball bingo?
In UK-style 90-ball bingo a line has 5 numbers on a row of the ticket. With a larger pool, the line is slower to complete. After 40 calls the chance for one line is only 1.5%, and it reaches 54.7% only after 80 of the 90 balls.
| Balls called | Chance a 5-number line is complete |
|---|---|
| 10 | 0.00% |
| 20 | 0.04% |
| 30 | 0.32% |
| 40 | 1.50% |
| 50 | 4.82% |
| 60 | 12.43% |
| 70 | 27.54% |
| 80 | 54.70% |
Why does playing more cards not change the odds much?
More cards raise your chance of winning, but so do the cards of all the other players. If the prize is shared among the winning cards, or goes to the first card to finish, your share depends on how many players there are. The calculator treats one line at a time and cannot know how many others are playing. A larger room means a lower chance of winning per card, even if each card is as likely as any other.
What does the calculator leave out?
- Other players. The chance that someone else wins first is not modelled.
- Full cards. It treats one line, not a whole card or several overlapping lines.
- Prize values. It gives odds, not payouts.
- Game variants. Some games use bonus balls, patterns or jackpots with a call limit.
- Card fees. The cost of cards and the share of fees returned as prizes are not modelled.
What mistakes do people make with bingo odds?
- Believing in lucky cards. Every card has the same chance for the same pattern.
- Ignoring the room size. A bigger crowd lowers your chance of a share.
- Buying cards to chase a loss. More cards cost more and the average result per card does not improve.
- Forgetting the cost of side games. Extra games and jackpots add up quickly.
- Playing for too long. Slow games make it easy to lose track of spending.
What should you try next?
Change the balls called from 40 to 60 and see the chance rise from 7.5% to about 40%. Then compare it with the chances in the keno odds calculator, which uses the same counting. To see what a regular spend adds up to, use the gambling session cost calculator, and to set limits first, read the Safer play toolkit.
How to read the result
The large number is the chance of exactly the number of hits you chose among the balls called, with the "1 in" odds under it. For a complete line, enter the same number for the numbers you need and the hits you want. The panel gives the chance of that many hits or more, and a table of every possible number of hits. It treats one line, not the other players, so it cannot tell you the chance of winning a prize.
How it is calculated
With N numbers in the pool, n called and K needed, the chance of exactly h of your numbers being called = C(K, h) x C(N - K, n - h) / C(N, n). For a complete line (h = K) this equals C(n, K) / C(N, K). The calculator uses exact whole numbers.
Worked example
Worked example
Pool 75, 40 called, 4 needed, 4 hits wanted. Chance = C(4,4) x C(71,36) / C(75,40) = C(40,4) / C(75,4) = 91,390 / 1,215,450 = 7.52%, or 1 in 13.3. For a line needing 5 after 40 calls the chance is 3.81%. For a 90-ball line after 40 calls it is 1.50%.
Limits
The calculator treats the calls as a fair random draw and looks at one line at a time. It does not model the other players, several cards or overlapping lines, bonus balls, call limits, prize sizes or card fees. The chance that someone in the room wins first is much higher than the chance for your own line. Results are exact for the inputs, and are not predictions of the next ball.