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condition (for given k) is that the number of common numbers cij of any two lines does not exceed 2k – n – 1. Next we present a table with the values of the maximal number cij from the found sufficient condition, for the most frequently met values of n (the size of the draw) and k (the thresholds n1 , n2 , ..., n of the winning categories). n k 34567 3210EE 4-3210 5--432 6---54 7----6 In this table, at the intersection of a column corresponding to a value of n with the row corresponding to a value of k, we find the maximal number of common numbers ( cij ) for any two lines of the played system. For any cij less than or equal to this maximum, the cumulated winning probability for minimum k winning numbers from the n drawn increases proportionately with the number of played lines, according to the found sufficient condition. The existence of a line indicates that the respective case is impossible, and letter E indicates the impossibility of the condition of exclusiveness (the cases in which k ≤ n2 ). Examples of how to use the table: We want to build a playing system for the 6/49 lottery which will ensure the linearity of the winning probability for at least the third winning category (minimum 4 winning numbers). What is the maximal number of common numbers any two lines of the system may contain? 32PDF Image | THE MATHEMATICS OF LOTTERY Odds, Combinations, Systems
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