Believe it or not, bingo may be a game of chance, but there are ways to swing the odds in your favor. This article contains some of them. They were developed by renowned mathematical analyst Joseph E. Granville, who achieved fame for creating a series of successful strategies for the stock market.
Granville says that the most important factor in a successful bingo strategy is card selection. When selecting cards, he advises players to carefully consider the word random. According to Granville, it is in clearly understanding the nuances of random numbers where players can get their advantage.
For purposes of clarity, let’s discuss random in the context of a 75-ball bingo game – a game with 75 balls, ranging from number one to number 75. In the first draw, the probability of any ball coming up first is the same — they all have 1-in-75 odds to come up first. That’s called uniform distribution and, in such cases, there are patterns that will fall under the law of probability. There is a strong tendency for three things to occur:
(1) There will be the same quantity of numbers ending in 1’s, 2’s, 3’s, 4’s and so on.
(2) There will be a balance between the number of odd and even numbers picked.
(3) There will be a balance between high and low numbers picked.
Granville called these the three accepted tests of randomness. If the selection of numbers does not meet these tests, then the selection has some bias and is not random.
In the book “Sampling,” English statistician L. H. C. Tippett added a fourth test — As a random sample is increased in size, it gives a result that comes closer and closer to the population value.
In simple terms, the 75 numbers in the bingo game are the population. That population’s value is the average of numbers 1 to 75, which would be 38. And while the first numbers called in a bingo game will not show an average of 38, Tippett’s theory is that once more numbers are called and the games proceed, the average of the numbers will predictably approach 38. The greater the quantity of the numbers called, the greater the likelihood that they will average 38.
Let’s apply those tests to the game itself.
In the first 10 numbers called in a game, have you noticed that there is a preponderance of numbers having different digit endings? Bingo players hardly notice this since most of them are concentrating on their cards and not on the numbers flashed on the master board. But try to notice it some time. Since it only takes about 10 to 12 calls before a game ends and a winner is declared, paying attention to the numbers called will help you predict the numbers that are likely to be called in succeeding games and tell you how to select cards with higher chances of winning.
Consider the first test above – “There will be the same quantity of numbers ending in 1’s, 2’s, 3’s, 4’s and so on.” That means, with 10 to 12 calls in a regular game, there will be a strong tendency for a number ending in 1, another ending in 2, another ending in 3 and so on to be called. That’s simple probability. For instance, if the first number called was N-31, then the probability of the second number also ending in digit 1 is less, simply because there are more balls left ending in other digits than 1. Hence, the chance of other digits not ending in 1 to be called is more.
Eventually, over several games, the number of times each number is called will balance out and the first test will prove itself to be true. “There will be the same quantity of numbers ending in 1’s, 2’s, 3’s, 4’s and so on.”
Therefore, if the first bingo game was won by a card featuring numbers ending in 1’s and 3’s, the likelihood of the next winning card featuring several numbers ending in 1’s and 3’s is remote. If the second game was won by a card with numbers ending in 5’s and 9’s, then the probability of the third game being won by a card with several numbers ending in 5’s and 9’s is slim. For the third and succeeding games, select a card that has few or no numbers ending in 1’s, 3’s, 5’s and 9’s since it has a better chance of winning. Then vary your strategy in succeeding games depending on what numbers are called.
The same also goes for winning cards with a lot of high or low numbers (say, for one-line bingo). If there were a lot of high numbers called in the first game, you can count on a lot of low numbers being called in the next game. Remember, the numbers drawn are likely to eventually average 38. Hence, for the next game, pick a card with a lot of low numbers. These low numbers, when added to the previous numbers called, will have a tendency to average 38.
Clearly, the examples stated here are over-simplifying Granville and Tippett’s tests, but that’s only to give you, the reader, a clear idea of how they work in practice. In actual games, it may take complex records of numbers called to clearly identify the trends we present here in their simplicity. Either that or a very good memory.