This friend of mine has it in her head that she wants to take a field trip to the local Bingo parlor, so I picked her up a DVD at the dollar store called “Bingo! Turn The Odds In Your Favor!” As part of the general mishmash of history (Bingo evolved from the Roman national lottery by way of a carnival game called Beano), filler (illustrations of a couple dozen different bingo game patterns), trivia (a mathematician set out to create 6,000 unique bingo cards with no repeats, succeeded but went insane) and common sense tips (if playing multiple cards, look for cards with fewer repeating numbers) comes a tip which on the surface sounds like bullshit but because of my horrible math skills I can’t figure out exactly why.

According to the DVD guy, when selecting cards, one should look for cards which have fewer squares ending in the same number. For instance, if your card has a 15 on it, you should avoid it if it has many other numbers ending in 5 (5, 25, 35, 45, 55, 65, 75). He doesn’t indicate how many similar-ending numbers are too many. His reasoning behind this is that if the first pull is B15, then there is one fewer ball ending in 5 than in any other number. Therefore, it’s statistically less likely that another number ending in a 5 will be drawn next. I thought that he gave this some fancy-schmancy math name, but upon reviewing he just calls it “the laws of probability and common sense.” Which is really no help at all.

It sounds like he’s claiming that each pull will have a significant effect on subsequent pulls and it seems to me like each pull is a completely independent event and each remaining number has the exact same chance of being pulled each time.

Bearing in mind that when it comes to understanding advanced probability I’m something of a numbskull, break down this proposition for me. And if the DVD guy is right, does it also make sense therefore to avoid cards with several numbers ending in 6, 7, 8, 9 and 0 since with the Bingo numbers running 1-75 there will be fewer balls ending in those numbers than there are balls ending in 1, 2, 3, 4 and 5?

Yes, if the first pull is B15, then it is statistically less likely that another number ending in 5 will be drawn next… slightly. This is entirely balanced by the fact that there is now one less ball ending in 5 than in 4, say. The chance that 65 will be drawn next is still entirely equal to the chance that 64 will be drawn. The chance that 15 will be drawn (0) is not equal to the chance that 14 will be drawn. But you already knew that.

Any questions?

Lordy, what nonsense people can come up with when they try to figure out ‘the laws of probability and common sense.’ (Maybe that’s because ‘common sense’ is generally a cluster of vague and easy-to-remember rules of thumb, so they start looking for similar rules with probability.)

Of course, the last digit makes no more sense than any other way of grouping the numbers in this example… you could make the same argument for the first digit, or nearby blocks of five, or numbers 3 more than a multiple of six, or primes/multiples of two/odd multiples of three…

Is there ever a Bingo hall that lets you pick your cards? I’ve never seen that, and my family and I went to Bingo quite a lot in the early 80s. With all the superstition going on, I’d think that if anyone allowed that it could delay the distribution of cards severely, not to mention the spats involved over competition for “favorite” cards.

That said, I think that picking as many separate numbers as possible on different cards would increase your winnings, since I assume that if you win twice with two separate cards at the same time, you don’t win twice as much.

Coincidentally, this DVD is a repro of a tape from the 80s. Music by Casio, computer graphics by Commodore. Per the examples of cards shown and the handy scrolling glossary, there are different types of cards in use, including ones which are printed two and four to a page and are disposed of after each game. So perhaps if you’re using a disposable card page there’s some discretion about choosing them.

I think there may well be such a thing as “good cards.” I used to take my grandmother and great-aunt to their regular bingo games. They’d paw through the mounds of re-usable cards these places had and choose what they said were the good cards. I’d just grab a handful at random. They not only won more often than I did, but also more often than most of the people there. In fact, it seemed like there was this cadre of little old women who knew what the good cards were and they won most of the games. As you might expect, it was important to get there early lest all the good cards be gone.

A good card is whichever one wins. Assuming that the bingo game is fair, then no card will be good more often than any other, over the long term.

Now, it may be that at your grandmother’s bingo hall, they were missing a ball, or some balls were heavier than others, or something of the sort. In that case, yes, some cards would be better than others (like those that don’t have the missing number on them). In that case, though, one must wonder about the legality of the game…

The other consideration, of course (especially if you’re playing multiple boards) is how easy it is to keep track of them. If you have to go “B12… Let’s see here somewhere… Ah, there it is! And it’s a bingo!”, but someone else has already called “Bingo!”, then yeah, that was bad. But it would be very difficult to quantify which cards would be easier to keep track of, and it would probably vary considerably from person to person.

I haven’t played Bingo since I was in elementary school and we were playing for candy, but does it really matter who calls “Bingo!” first? I was under the impression that everyone who calls it splits the pot.

I’ve had bad Bingo cards before, in the same way 1-2-3-4-5-6 is a bad lottery play.

I looked in front of me and saw another person with an identical Bingo card to my own, which, of course, meant if I win I was going to have to split it.

There are so many goddamn possible Bingo cards that having a pair like this is essentially impossible; I’m sure the cards came pre-manufactured from some company that only chose to print several thousand (I’m guessing here) different cards, leaving a relatively high probability of duplication.