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Article 1: Statistics vs. Probability

The most natural reaction to advancing a serious theory designed to improve the chances of winning at bingo is encountered when confronting those who do not believe that such a sound theory is possible. The usual reaction to those who might devise various bingo "systems" is that it is all pure rubbish. They will tell you that nobody knows what balls are going to come out of the machine and that the game is totally one of luck. While it may appear at first glance difficult to counter such a reaction, the solid structure of mathematical probability is capable of destroying the argument. The key to beating the bingo game lies in a clear understanding of the word "random". Our typical critic will agree that the colored balls being drawn from a machine are popping out at random. Now, having a common agreement on this fact, the next step is simply to show such critics that there is more to the word "random" than first meets the eye.

As every player knows, there are 75 balls in the machine, numbered from 1 to 75. The probability of any ball coming up on the first draw is exactly equal, I in 75, written as 1/75. Since the probabilities are equal, we call this a uniform distribution. Random numbers drawn from a uniform distribution fall into predictable patterns governed by the laws of probability. Therein lies the answer to transforming the otherwise hopeless problem into a series of systematic solutions. These solutions will determine the best selection of bingo cards. Granted that the balls come out of the machine at random, then three things must have a strong tendency to occur.

1. There must be an equal number of numbers ending in 1's, 2's, 3's, 4's etc.

2. Odd and even numbers must tend to balance.

3. High and low numbers must tend to balance. Those are the three accepted tests for randomness. Unless the distribution meets those tests it is said that there is a bias and the distribution is not random. We can add a fourth test for randomness which has a peculiarly effective application at improving your odds in the bingo game.

This fourth test is best described by the English statistician L. H. C. Tippett in his book, Sampling.- "As a random sample is increased in size, it gives a result that comes closer and closer to the population value." To the bingo player, this means that the bingo master board of 75 numbers constitutes the "population". The average number in that population is the average of the entire 75 numbers. Going from 1 to 75, the average number on the bingo board is 38. The first few numbers called in a bingo game may or may not average 38, but it is certain that as the game progresses the average of the numbers called will steadily approach 38. Guess what, you just learned something that will improve your game! When bingo numbers are being called, the entire game (which consists of an average of 10-12 calls for a straight line game) is a sampling of the entire population and the larger the sample the closer the numbers will average to 38. In coming articles, we will see how this fact can help us in our strategic selection of bingo cards.

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• Article 1: Statistics vs. Probability
• Article 2: Probability Predicts Different Digit Endings
• Article 3: Identifying the Important Squares on the Card

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