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P3 - the winning probability of the reduced system; N1 -thenumberofpossiblemultiplewinningsofthealeatory system under the exclusiveness condition; N2 - the number of possible multiple winnings of the compound line; N3 - the number of possible multiple winnings of the reduced system; C1 - the total cost of the aleatory system under the exclusiveness condition; C2 - the total cost of the compound line; C3 - he total cost of the reduced system. (Probabilities Pi and numbers Ni , i = 1, 2, 3, are corresponding to the same winning category fixed through the simplification convention mentioned before.) We have respectively the following relations between parameters P,N,C, i=1,2,3: iii a) for the same total cost of the systems (C1 = C2 = C3 ) P>P>P 132 N2 >N3 >N1 =1 The aleatory system under the exclusiveness condition offers the maximal probability of winning, while the compound line offers the minimal. However, the largest number of possible multiple winnings is offered by the compound line, and the smallest (namely 1) by the aleatory system under the exclusiveness condition. The reduced system (obtained from a compound line other than the one which we compare with) holds the intermediary values of the two parameters. .............. missing part ................... We can observe that in both situations, the reduced system could offer a compromise between the other two types of systems, which hold the minimal and maximal values for each of the parameters that comprise the decision criteria. 70PDF Image | THE MATHEMATICS OF LOTTERY Odds, Combinations, Systems
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