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- the number of winning categories, denoted by q; - the minimum number of winning numbers for each winning category; - the price of a simple ticket (simple line); - the percentage from sales for the prize fund; - the percentages in which the prize fund is distributed to each winning category. We will come back to these parameters in the chapter dedicated to the applied mathematics, where we will also see the initial conditions these parameters must fit. The possibilities of choice within these parameters are practically unlimited, this also being the explanation for the existence of so many lotteries worldwide. For most of them, m takes values in the range 20–90; n takes values in the range 3–20; p in the range 3–20; q in the range 1–5. For the rest of the parameters, the range of their values varies locally and is too large to identify the most frequent values. Any numerical choice of the parameters enumerated above represents a lottery matrix. The most important parameters for a basic classification of the lotteries that exist worldwide are m, n, p, and q, so we can identify any lottery matrix with a numerical instance of the quadruple (m, n, p, q). For example, the lottery matrix (49, 6, 6, 3) represents the 6/49 lottery (a draw has 6 numbers from a total of 49), with a simple line consisting of 6 numbers and 3 winning categories. In common speech, n/m represents a certain lottery matrix. The lottery matrices 6/49, 6/42, 6/52, 5/40, 5/31, 4/77 and so on, are considered individual lottery matrices, although within the same matrix any variation of the rest of the parameters besides m and n in fact generate a new lottery matrix. Locally there are so many variations of the same n/m matrix that the abbreviated denotation is entirely justified. The most common lottery matrices worldwide are the following: 6/49, 6/44, 6/48, 6/51, 6/52, 6/54, 6/40, 6/53, 5/37, 5/55, 5/32, 5/56, 5/39, 5/36, 4/77, 4/35, 7/47 (Europe, United States, Canada, Mexico); 6/36, 6/39 (Ireland); 6/90 (Italy); 6/45 (Australia, Philippines, Austria, Switzerland, Germany); 6/42 (Belgium, Bulgaria); 6/41 (Holland); and 6/47 (Hong Kong). 14PDF Image | THE MATHEMATICS OF LOTTERY Odds, Combinations, Systems
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