BLOG: What's in a bingo?

Mel Barber

Pennsylvania lawmakers, led by Rep. Kate Klunk, R-Hanover, are pushing to update a 1988 law regarding rules for that most beloved game in church fellowship halls, fire halls and senior centers: bingo.

With 25 squares and 12 winning configurations in standard play, the bingo card holds the sweaty-palmed hope of daubers everywhere. But how long should you hold out hope?

Math to the rescue. Probability, to be exact.

Totaling up how quickly someone is likely to win the game isn't quite as easy as saying there are 12 ways to win and calling it a day. The mathematician has to account for the randomness of the drawing order, the randomness of the number placement on the card (not every card has every number, remember!), and the locations of previous calls marked on the sheet.

Given all of that complexity, it turns out that:

Overall, there is approximately a 50 percent chance that one card will require at most 41 calls to complete a Bingo, and approximately a 90 percent chance to complete a Bingo in at most 54 calls, the researchers conclude.

— Probabilities in Bingo, Ivars Peterson, Science News

But that's just a single card. You aren't competing for choice cuts of USDA beef and Longaberger baskets by yourself. The number of bingo ball pulls before a bingo is called starts dropping pretty fast as you add more players. (Or players playing multiple cards. Yeah, I'm looking at you. You know who you are.)

By the time you get 100 cards in the game, the odds make it almost impossible to have more than 30 balls pulled before someone wins. Even with only 10 cards in play, there's about a 66 percent chance you'll have a winner by then.

For a peek at how the math works, check out the details at Probabilities in Bingo from Science News.

And for a chance at those bigger payouts — up to $4,000 for a jackpot or $400 for a single game — talk to your local lawmakers. You just might get lucky.