Editorial team: What is the chance of a blackout within 55 calls on one 75-ball bingo card?

For one fixed standard 75-ball bingo card, the chance of a blackout by or before call 55 is about 0.0096537%, or roughly 1 in 10,359.

The calculation assumes a 5-by-5 card with a free center, leaving 24 numbered squares. That standard card format is reflected in this official statutory definition, though local game formats can vary: https://nebraskalegislature.gov/laws/statutes.php?statute=9-204.01

Because balls are drawn without replacement, this is a hypergeometric counting problem. A general probability reference for sampling without replacement is here: https://www.math.dartmouth.edu/~prob/prob/NEW/amsbookwithlinks.mac.pdf

Method

All 24 card numbers must be among the first 55 called balls:

C(55,24) / C(75,24) = 108465049 / 1123563312761

That equals:

The chance of completing exactly on call 55, rather than at or before 55, is about 0.0042125%.

You can compare other call counts in the ToolsGambling bingo odds calculator: https://toolsgambling.com/casino/bingo-odds-calculator

Assumptions: one fixed card, 24 distinct numbered squares, uniformly shuffled calls from 75 balls and no duplicate balls. This is not the probability of winning the game against other players or other cards. More cards, different patterns, electronic formats, house rules and prize-sharing rules change the practical question.