Many bingo rooms add a jackpot to the full house. The catch is that the jackpot is only paid if the full house lands within a set number of calls: 40, 45, 50 or so. The ordinary full house still gets paid if the game runs longer. These are called call-limit jackpots, and they are some of the least-understood offers in bingo. The odds are easy to calculate exactly, so here they are.
On this page5 sections
The calculation
A 90-ball ticket has 15 numbers. After n calls, the ticket is a full house if all 15 of its numbers are among the n called. Every set of n numbers is equally likely to be the one called. So the chance is the number of ways to choose the remaining n − 15 calls from the other 75 numbers, divided by the number of ways to choose n calls from 90:
P(full house by call n) = C(75, n − 15) ÷ C(90, n)
That gives the exact chance that one particular ticket has finished by call n:
| Full house within | Chance for one ticket | Roughly 1 in |
|---|---|---|
| 40 calls | 0.000088% | 1.1 million |
| 45 calls | 0.000753% | 133,000 |
| 50 calls | 0.004915% | 20,000 |
| 55 calls | 0.026% | 3,800 |
| 60 calls | 0.116% | 860 |
| 65 calls | 0.453% | 220 |
| 70 calls | 1.58% | 63 |
| 75 calls | 4.98% | 20 |
| 80 calls | 14.49% | 7 |
| 85 calls | 39.27% | 2.5 |
The curve climbs very steeply. Each extra five calls multiplies the chance several times over. A jackpot on 40 calls is about 56 times harder to win than one on 50 calls, and a 50-call jackpot is about 24 times harder than a 60-call one.
From one ticket to the whole room
The jackpot is paid if anyone's ticket finishes inside the limit. With many tickets in play, the chance that the room wins it is much higher than for a single ticket. Tickets in a room aren't independent (they share the same calls), so the exact figure needs a simulation. The single-ticket figure still gives a useful rough guide. With T tickets in play, the chance that at least one finishes by call n is a little below 1 − (1 − p)T.
For a 50-call jackpot (p ≈ 1 in 20,000) and 1,000 tickets in the room, that rough guide gives about 5%: a win roughly once in twenty games. On 45 calls it falls below 1%. On 40 calls, with the same room, it is around one game in a thousand. That's why some rooms run a 40-call jackpot for months without paying it out, while a 55-call jackpot in a busy room pays out regularly.
What it means for your ticket
Your own chance of taking a call-limit jackpot is simply your ticket's chance from the table, multiplied by the number of tickets you hold. It is then shared if several tickets finish on the same call. One ticket in a 45-call jackpot game has about a 1 in 133,000 shot at it. A full strip of six raises that to about 1 in 22,000. Better, but still the kind of odds that belong in the entertainment budget, not the plan.
Two things to check in the room rules before you play for a jackpot:
- The exact call limit and how it is counted. "Within 45 calls" usually means the full house is completed on call 45 or earlier.
- Whether the jackpot is fixed or progressive. A progressive jackpot grows from each ticket sold until it is won. A fixed one does not. A growing jackpot can be worth more than its odds suggest late in its run, but only by the amount it has grown.
Call limits in other formats
The same arithmetic works for 75-ball and 80-ball games with their own card sizes. An 80-ball card has 16 numbers. Its chance of a full card within 50 calls is about 0.018%, and within 60 calls about 0.555%. A 75-ball blackout (all 24 numbers) within 55 calls is about 0.0097%, and within 60 calls about 0.14%. The format guide compares the three games in more detail.
Key points
- One 90-ball ticket finishes within 50 calls about once in 20,000 games, and within 40 calls about once in 1.1 million.
- Each extra five calls on the limit multiplies the chance several times over.
- The room's chance of a jackpot win depends on ticket numbers. Your own chance depends on your tickets alone.
Room-by-room details of jackpots are listed on our bingo sites page.
The figures in this article are exact combinatorial results for a fair draw of 90 balls. The room estimates are approximations, as stated.