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Reduced Systems A reduced system is a system obtained through the unfolding of a compound line (from here on called the base compound line), from which some simple lines have been removed on the basis of some pre-established criteria. The goal of these removals is to reduce the number of simple lines of the playing system, having an immediate effect on the initial investment. Since generally the number of simple lines of an unfolded compound line is quite large, obtaining a reduced system is a compromise between using the same playing numbers (but with a different distribution within the new system) and keeping costs acceptable. The criteria for removing lines can be multiple, objective, and/or subjective: properties of numbers and groups of numbers within a simple line, the frequency of certain numbers, reduction of the number of possible multiple winnings while keeping some minimal guarantees, etc. We shall come back to these criteria in the section titled Obtaining the reduced systems. The reduced systems are noted on the playing tickets either encoded or manually. Encoded notation is possible on the tickets only for those reduced systems that are registered officially by the issuing lottery. It is done by checking/writing all played numbers (the base compound line) and mentioning the code of the played reduced system, according to the official encoding. Manual notation assumes writing all the simple lines of the reduced system. Manual notation is obligatory for the systems that are not officially encoded. A reduced system is declared a winner if after the draw the existence of at least one winning constituent simple line (containing the minimal threshold of winning numbers) is ascertained. If k winning numbers have been found in the base compound line, this does not mean that we automatically have k winning numbers (and even fewer than k) in the reduced system, because it is possible that no simple line containing them will exist, according to the structure of the system and the distribution of the numbers in the lines remaining after removal. For winning with the k numbers, they must “fit” in the played reduced system. 54PDF Image | THE MATHEMATICS OF LOTTERY Odds, Combinations, Systems
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