Even for games in which you can't select your cards, there are ways to beat the odds and emerge a winner. For instance, most free bingo enthusiasts play several cards a game to improve their chances of winning. But does this really work? No, says Granville! The startling truth is that, in many cases, you can actually improve your chances of winning big by playing fewer cards. Granville proves it! Curious? Read on to find out how fewer cards can be better. So why trust to luck when you play online bingo? You can make the game pay you to play wisely. If you're honestly serious about becoming a systematic winner at Bingo, here's a method that you should find useful. Bingo systems are often met with a good deal of criticism, with popular wisdom telling us that bingo is a game of pure luck. Therefore, predicting which balls will next be called seems impossible. But it's not impossible at all! It just takes a little knowledge of mathematical probability. Everyone can agree that bingo balls are drawn randomly from the machine. The utility of bingo systems actually lies in bingo's randomness. Confused? Don't be, just keep reading. 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, 1 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 an otherwise hopeless problem into a series of systematic solutions, which will help you make the most advantageous selection of bingo cards. Balls that are truly ejected at random display a strong tendency toward the following patterns: There must be an equal number of numbers ending in 1's, 2's, 3's, 4's etc. Odd and even numbers must tend to balance. High and low numbers must tend to balance. These are the three accepted tests for randomness. Unless the distribution fulfills these criteria, it is said that a bias exists and thus, the distribution is not random. A fourth test for randomness, which we have yet to mention, is particularly effective for beating bingo. English statistician L. H. C. Tippett offered a detailed description of this fourth test 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." Translated into simple everyday language, the bingo master board of 75 numbers constitutes the "population". The average number in that population is the average of all 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 gradually approach 38. So then, when bingo numbers are being called, the entire game (which consists of an average of 12 calls) is a sampling of the entire population and the larger the sample the closer the numbers will average to 38. |