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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Parameters of the lottery matrices To each lottery we can attach a set of basic numerical parameters through which that lottery is uniquely identified. These parameters are as follows: - the total number of the numbers from the urn, further denoted by m; - the number of numbers of a draw, further denoted by n; - the number of numbers on a simple playing ticket (or the number of numbers of a simple line), further denoted by p; - the number of winning categories, further denoted by q; - the minimum number of winning numbers for each winning category, further denoted by n , n ,, n (in decreasing order of the 12q amount of the prize); - the price of a simple ticket (simple line), further denoted by c; - the percentage from sales for the prize fund, further denoted by f; - the percentages in which the prize fund is distributed to each winning category, further denoted by f1, f2,, fq . Any numerical instance of the vector (m,n,p,q,n,n,,n,c,f, f,f,,f)willbecalledalottery 12q12q matrix. The parameters that determine the technical progress of the game in a certain lottery matrix and which are taken into account in the construction of the general probability formulas are (m,n,p,q,n,n ,,n ). 12q The initial conditions these parameters must fit for the represented lottery matrix to be mathematically valid are: m,n,p,q,n1,n2,,nq ∈ 1≤ p≤nn2 >>nq (The last inequality holds for the lottery matrices in which the winning criteria are established for one single draw, non-combined with another draw of one or more additional numbers, as in Powerball.) 18

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