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Probabilities of winning with systems Let us consider the example of the 6/49 matrix, in which a simple line has a 1/13983816 probability of winning in the first category (6 winning numbers). If we play two simple lines instead of one, thus creating a playing system, the winning probability in the first category will be doubled, becoming 2/13983816. If we play s simple lines (s > 1), that probability will increase s times. This happens because the events representing the occurrence in the draw of the number combinations corresponding to the played simple lines are elementary events, so they are mutually exclusive. Thus, the probability of the union of these events is the sum of the individual probabilities, which are equal. (See formula (F3).) In this case, the probability of winning with that system grows proportionately with the number of played lines s. This condition holds true only for the first winning category and is true for any lottery matrix in which n1 = n (the number of winning numbers specific to the first winning category equals to the number of numbers of the draw). But what happens with the winning probability of an lower category? Does this probability still grow proportionately with the number of played simple lines? The answers is: generally no, but in a large range of cases, yes. The same answer stands for the same question, in the case of a cumulated probability (at least a certain winning category). Let us denote by V ,V ,,V the simple lines of a given system 12s (s > 1). Vi are all p-size combinations. Fori=1,...,sand1≤k≤n,denotebyVk theevent“lineV contains a minimum of k winning numbers.” In the previous chapter, we evaluated the cumulated winning probabilities for the simple lines, so we know the probabilities P(V k ) for any i and k, whose values can be found in the tables of the respective section. .............. missing part ................... i 30 iiPDF Image | THE MATHEMATICS OF LOTTERY Odds, Combinations, Systems
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