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generation of the aleatory system can be done manually or with the help of a software program. Within a strategy of choosing based on probability, it is not recommended to play an aleatory system that does not respect the exclusiveness condition, it is preferable to play a compound line or a reduced system instead. This recommendation is made because for these types of systems, we know the values of the winning probabilities (from formulas, tables or approximations) and the number of possible multiple winnings (the winning guarantees, in case of the reduced systems). If the player has the number of possible multiple winnings (the most possible winnings for the same cost of the system) as the sole criterion of the strategy of choosing, obviously he or she should play a compound line, whose size should be chosen according to his or her own financial limitations, because the compound lines offers the largest numbers of possible multiple winnings (see section The number of prizes in the chapter Compound Lines). Of course, depending on the chosen criteria and their method of aggregation, there is, in addition to aleatory systems and compound lines, also the option of playing reduced systems (including here the bridgehead lines as well). In the following section, we present a comparative analysis of the three types of systems – aleatory systems under the exclusiveness condition, compound lines, and reduced systems – for two situations of aggregation of the criteria for choosing (the winning probability, the number of possible multiple winnings, and the total cost of the system): a) winning probability and number of possible multiple winnings for the same total cost of the system (thus the same number of played simple lines); b) number of possible multiple winnings and total cost of the system for the same winning probability of the system. This analysis presents the order relation between the values of the parameters; the statements are direct consequences of the theoretical results obtained in previous chapters. For the parameters we use the following denotations: P1 - the winning probability of the aleatory system under the exclusiveness condition; P2 - the winning probability of the compound line; 69PDF Image | THE MATHEMATICS OF LOTTERY Odds, Combinations, Systems
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