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Compound Lines A compound (combined) line is a playing system consisting of all possible simple lines that can be formed with a given number of playing numbers. Using our general denotations, a compound line is in fact a combination of r numbers, where p < r < m . Even if a simple line contains only p numbers, every lottery matrix allows the play with r > p numbers forming a compound line, which is in fact a system containing several p-size simple lines. On the playing ticket, such a system is marked by checking (or writing) all the chosen r numbers, meaning that it allows all p-size combinations of numbers that can be formed with the r chosen numbers. Thus, there is no need for an explicit enumeration of all constituent simple lines of the system. Obviously, the number of the simple lines a compound line with r numbers consists of is Crp . Therefore,acompoundlineisacombination (a1,a2,,ar), where ai are arbitrary playing numbers from the m allowed by the respective lottery matrix and p < r < m . The combination (a1 , a2 , , ar ) is in fact the condensed denotation of the playing system that contains all the simple lines that can be created with numbers ai , i = 1, ..., r. Number r (the number of chosen playing numbers) is called the size of the compound line. The playing system corresponding to the compound line (a1 , a2 , , ar ) will cost the equivalent of all constituent simple lines together, namely c ⋅ Crp (c being the price of a simple line). We shall see further that the systems equivalent to the compound lines have specific properties, as concerns the structure of their constituent simple lines and the number of possible prizes. These properties differentiate them from the systems that are built at random. .............. missing part ................... 40PDF Image | THE MATHEMATICS OF LOTTERY Odds, Combinations, Systems
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