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the draw, while in fact the winning probability is the same for any of the Cmp simple lines. For this reason, the choosing criteria exemplified above are subjective. Still, there is an exception to that motivation, which can change the attribute of such criteria from subjective to objective. That is the situation in which the player is convinced (by some technical studies) that the technical process of drawing the numbers influences some arithmetical correlations between those numbers. Such correlations might include all physical aspects of the process of shuffling and extracting, from introduction of the balls into the urn, to the order of introduction, their initial position in the urn, the structure and shape of the urn, etc. Even if these kinds of convictions can be scientifically combated quite easily, the player who does not accept the argument can still create his or her own objective strategy of choosing based on such correlation criteria. From a mathematical point of view, each simple line has the same winning probabilities, and on this principle is developed the entire probability calculus applied to the lotto game. A simple line represents an elementary event in the built probability space, and without the “equally possible” idealization, the probability calculus would not make sense. At the practical level, there exists a real tendency of players to avoid certain so-called “unique” combinations of numbers, as those previously exemplified. For example, in a 6/m matrix, most players avoid playing the line (1, 2, 3, 4, 5, 6). Although mathematics says that this combination has absolutely the same winning probabilities as any other one, it is still avoided by players who convince themselves that “it’s impossible for this line to be drawn.” This statement is not far from the truth, the line being “almost impossible” to be drawn, in the sense that its probability of occurrence of 1/13983816 is almost null, but this probability stands for any other played line. No combination has a preferential status compared to the others, and all have the same winning probabilities. If in a certain lottery, we study the statistics of the draws over its entire history and find that the line (1, 2, 3, 4, 5, 6) has never won, this does not contradict the previous statement regarding preferentiality. If we have the required technical means, we will find in the same statistics that 66PDF Image | THE MATHEMATICS OF LOTTERY Odds, Combinations, Systems
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