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Going from the play with one simple line to the play with systems containing several lines is done mainly to enhance the winning probabilities. Thus, probability becomes an important criterion in the strategy of choosing the playing systems. The criterion of winning probability, along with the criterion of possible multiple winnings relate to the goal of the game and are objective criteria due to their mathematical essence. In the case of systems, there are also financial criteria, related to the means of achieving the goal of the game. These criteria take into account the cost of the playing systems, depending upon the number of constituent simple lines. All parameters taken into account within a strategy of choosing the playing system are correlated. For example, the probability of winning in a certain category cannot be raised in any level without raising the total cost of the system, which is limited by the investment fund at player’s disposal). For the sake of simplicity, we shall refer hereafter to one category of winning; the results can be extended for the case of cumulated winnings. This choice is natural, because in a personal strategy of choosing, the player follows particularly a certain category of winning, the eventual additional winnings in other lower or higher categories being optional but welcome. The next analysis uses extensively the theoretical results and applications obtained in previous chapters. If the player holds the winning probability (achieving maximal probability for the same cost), as the sole criterion of the strategy of choosing, he or she may choose an aleatory system created under the condition of exclusiveness, because such a system offers the maximal probabilities of winning for the same number of constituent simple lines. In addition, the parameters of such system can be managed easily in correlation with the aimed probability. Having chosen a threshold of the winning probability and the corresponding number of lines that will verify the profitability condition (see section titled Probability thresholds in the chapter titled Enhancing the Winning Probability), the player can build the playing system by using the sufficient condition for exclusiveness that refers to the number of common numbers (see section titled Probabilities of winning with systems in the same chapter). The 68PDF Image | THE MATHEMATICS OF LOTTERY Odds, Combinations, Systems
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