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THE MATHEMATICS OF LOTTERY Odds, Combinations, Systems

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THE MATHEMATICS OF LOTTERY Odds, Combinations, Systems ( the-mathematics-lottery-odds-combinations-systems )

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column corresponding to a pair (k, h) we find the probability of winning with minimum k numbers, for a played bridgehead system with h fixed numbers, at the matrix n/m. .............. missing part ................... Examples of how to use the tables: In a 6/90 matrix, what is the probability of winning with a minimum of 5 numbers, using a bridgehead system with 3 fixed and 3 variable numbers? We have n = 6, m = 90, h = 3, k = 5. In table n = 6, we follow the intersection of row m = 90 with the column corresponding to the pair (k = 5; h = 3), and we find the probability 0.010895, that is 1.0895%. In a 5/32 matrix, what is the probability of winning with a minimum of 4 numbers, using a bridgehead system with 3 fixed and 2 variable numbers? We have n = 5, m = 32, h = 3, k = 4. In table n = 5, we follow the intersection of row m = 32 with the column corresponding to the pair (k = 4; h = 3), and we find the probability 0.056452, that is 5.6452%. In a 6/42 matrix, what is the probability of winning with minimum 4 numbers, using a bridgehead system with 4 fixed and 2 variable numbers? We have n = 6, m = 42, h = 4, k = 4. In table n = 6, we follow the intersection of row m = 42 with the column corresponding to the pair (k = 4; h = 4), and we find the probability 0.090994, that is 9.0994%. We immediately observe that the tables of this section contain much higher probabilities than those listed in the previous chapters. But is these specific cases, at a practical level the high winning probability is counterbalanced by the very large number of simple lines (hence a large initial investment) that the unfolded system consists of, as well as the risk of a cumulated winning that is lower than the amount invested in playing that system. 51

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