In a previous article we briefly explained that, while many people consider bingo to be a game of pure luck, serious players employ more advanced strategies to improve their odds of winning. These strategies rely on mathematical expectations that are easy to implement and follow.

In this article we address the easiest and most important bingo strategy available today, which has to do with how to choose the optimal bingo card(s) prior to starting your game. By keeping in mind and applying the steps outlined below when choosing your bingo card(s) you will have a comparative advantage versus most bingo players who pay almost no attention to such details and rely solely on chance.

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**The logical steps**

A regular bingo game employs 75 balls, numbered successively from 1 to 75 – let’s call these the population. The initial population decreases gradually as balls (and their corresponding numbers) are called and then set aside and out of the game. So every time a number is called, the probability of drawing yet another number ending with the same digit decreases.

If that’s not clear enough, let’s look at a simpler example: consider a population of 20 balls, numbered successively from 1 to 20. From the very beginning, we know that:

► There is an equal number of balls whose corresponding numbers end in 1’s, 2’s, 3’s, etc;

► Every last digit occurs twice: 1 and 11, 2 and 12, 3 and 13, 4 and 14, etc.

In this example any number is just as likely to be drawn initially, so your first pick is random***. Now let’s assume that the first ball that’s drawn reads the number 2. Considering the two points outlined above, it is unlikely that the next drawn ball will also read a number that ends in 2, since there are less of those in the population. Next, consider that the second drawn ball reads the number 6; consequently, the probability of drawing a third ball that reads a number ending in either 2 or 6 is decreased.

In conclusion, as early as the end of the first round the player can already make educated guesses about which numbers are most unlikely to come up next, and therefore choose other numbers with a higher probability of occurrence.

Now that we’ve established which numbers not to choose over the course of a game, the next question is, which ones should be chosen as the game progresses? To answer this question, keep in mind that as numbers are extracted randomly from a successive sequence:

► Odd and even numbers tend to balance out over time;

► High and low numbers tend to balance out over time.

Looking at our initial example, it would be justified to assume that the third number following the 2 and 6 is more likely to be a two-digit odd number than another one-digit even number. While our assumption is still a guess, it is nonetheless an educated guess based on mathematical probability.

**Persistence pays off**

Now that you’ve mastered this strategy, what’s important to keep in mind is that over the course of one or two games the rules may or may not stand, but applying them in the long run will certainly improve your winning chances. We encourage you to pick your bingo card(s) based on a distribution of numbers according to the theory outlined above.

So good luck and have fun!

*** In a 75-ball game, this rule does not apply; the digits 1, 2, 3, 4 or 5 are more likely to occur in the 1st round than 6, 7, 8, 9 or 0, since there are 8 numbers ending with 1, 2, 3, 4 or 5, as opposed to 7 numbers ending with 6, 7, 8, 9 or 0.