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Systems of compound lines As on the playing tickets we can inscribe several simple lines forming a playing system, so we can also inscribe several compound lines. The resulting system is equivalent to the simple-line system obtained through the unfolding of all compound lines. Therefore, a system consisting only of compound lines is still a simple-line system, the only difference between them being the way they are noted (encoded) on the playing ticket. In mathematical denotations, a compound-line system is a group of combinations of various sizes, made of playing numbers: (a11 a12 ... a1r ) 1 (a21 a22 ...a2r2) ........................................... (as1 as2 ...asrs) s > 1 is the number of compound lines the system consists of, r,r,,r representsthesizeofeachcompoundline 12s (r > p, i=1,,s),and a (i=1,,s; j=1,,r) arenumbersof i ij i the respective lottery matrix. Denoting by Wi the constituent compound lines (ai1 ai 2 airi ) , for every i = 1, , s , it is obvious that the total number of simple lines of the unfolded system is the sum of the numbers of simple sppp p linesofeachcompoundlineWi,thatis Cr =Cr +Cr ++Cr . i12 s i=1 A compound-line system may hold as many such lines, of any size, as the player’s financial limitations allow. Also, the structure of the compound line may be influenced by the strategic criteria as regards the coverage of the playing numbers. .............. missing part ................... 48PDF Image | THE MATHEMATICS OF LOTTERY Odds, Combinations, Systems
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