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At the intersection with the first column, we find the number of simple lines of the system, which is 792. The total cost of the system is then 792c = 792 x $0.50 = $396. In a 6/49 matrix, let us find the probability of winning with a minimum of 5 numbers of a 19-number compound line. How much does such a system cost, if a simple line costs $1? In the table corresponding to matrix 6/49, we follow the intersection of row r = 19 with column w = min.5 and we find the probability 0.026886, that is 2.6886%. At the intersection with the first column we find the number of simple lines of the system, which is 27,132. The total cost of the system would be 27132c = 27132 x $1 = $27,132. In a 7/47 matrix, let us find the probability of having exactly 4 winning numbers in a 11-number compound line. How much does such system cost, if a simple line costs $0.80? In the table corresponding to matrix 7/47, we follow the intersection of row r = 11 with column w = 4 and we find the probability 0.037465, that is 3.7465%. At the intersection with the first column we find the number of simple lines of the system, which is 330. The total cost of the system is 330c = 330 x $0.80 = $264. From the tables as well as the examples in this section, we clearly saw that the number of simple lines in a compound line increases very quickly with its size r, while the winning probabilities remain very low. To achieve relatively reasonable winning probabilities requires generating thousands of simple lines, and consequently, requires a huge initial investment. Still, the play with high-size compound lines becomes reasonably possible in some lotteries that offer a fraction game. This means the playing systems can be paid in percentages of 25%, 50% or 100%, and the winning amount is divided accordingly, by applying the same percentages. 44PDF Image | THE MATHEMATICS OF LOTTERY Odds, Combinations, Systems
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