We’ve begun an investigation into some of the most popular tactics claiming to increase your chances of winning at bingo. Last time we discussed Granville’s strategy; he thought that the secret to success was to select a bingo card with numbers that were as spread-out as possible.
Now it’s time to take a look at another strategy, this time proposed by a British statistician, Leonard Tippett.
Tippett’s theory is based on what we shall call the ‘perfect average’: the average of all 75 balls before any have been picked. There are many different ways to calculate an average, but Tippett chooses to use the number that lies exactly in the middle: the median, 38.
He thought that as time progressed in a 75 ball game, numbers would be drawn that were much closer to to this ‘perfect average’. For simple games, where the aim is to complete lines or a Full House (FH in bingo lingo terms), it doesn’t usually take very long for one player to win. Tippett argued that in these games, it would be best to choose numbers at either end of the spectrum (ie. as close to 1 or 75 as possible).
Games where there is a more complex pattern to complete will generally take longer to finish. More balls will be drawn before a winner is announced, and so you should try to pick numbers that are more in the middle of the spectrum—those closer to number 38.
It sounds quite complex, but Tippett’s theory actually has its merits. But are they enough to persuade us that bingo is a game of skill?
The simplest way to think about is in terms of 2 piles: the winning bingo balls, and those still in the cage. When you begin to pick out balls, the middle value of the winning numbers could be anything at all, but it is likely to be either much higher or much lower than 38. This is because the range of numbers in the winning ball pile will probably be much narrower than 75 (unless both 1 and 75 have been drawn).
The more balls are drawn, the more similar your winning pile becomes to the still-there pile. You are, in effect, gradually getting back to exactly the same pile that you started with in the cage. If all the balls were drawn before anyone won, you’d have an identical pile of balls to the beginning of the game; they would simply have moved outside of the cage.
It makes sense that as the winning numbers start to replicate the initial pile, the median will also become closer to the ‘perfect average’ once again.
The problem with Tippett's theory is… just about everything! Of course the average will even out over time, but that doesn’t mean that the bingo numbers themselves will necessarily get closer to that magic 38, just that the mid-point of all the collective numbers will.
It is also an unhelpful strategy in terms of practicalities. In ‘simple’ FH style games, it may be more likely that someone will win the game quickly, but this also depends on other factors, such as the number of players in the room, and the amount of tickets that have been bought.
You would also struggle to find a ticket that had numbers grouped closer to either end or the median. Just take a look at these DIY bingo cards. Notice anything? The numbers start low on the left and gradually increase as you move to the right. This is the usual format, whether you’re playing 75 or 90 ball bingo: it may help you hunt down those winning numbers, but offers very little chance of following Tippett’s theory —even if you did want to give it a go!
The theory might have sensible foundations, but it falls down in the real world. And so our quest continues… can any strategy increase our chances of winning?
Good news: you can test out any of the strategies we discuss completely risk-free! Take your pick of free bingo games and see whether you get lucky.