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 (in
decreasing order of the 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 . Any
numerical instance of the vector (m, n, p, q,,
c, f, )
will be called a lottery matrix.









0.092234 
0.332043 
0.377322 
0.167699 
0.029025 
0.001659 
1.84E05 

0.107327 
0.351252 
0.365888 
0.150108 
0.024124 
0.001287 
1.34E05 

0.122599 
0.367797 
0.353651 
0.134724 
0.020209 
0.00101 
9.91E06 

0.137924 
0.381943 
0.341021 
0.121252 
0.017051 
0.000802 
7.43E06 

0.153202 
0.393947 
0.328289 
0.10943 
0.014483 
0.000644 
5.65E06 

0.168353 
0.404048 
0.315663 
0.099031 
0.012379 
0.000521 
4.34E06 

0.183318 
0.412466 
0.303284 
0.089862 
0.010642 
0.000426 
3.38E06 

0.198049 
0.419398 
0.291249 
0.081754 
0.009197 
0.00035 
2.65E06 

0.212511 
0.425022 
0.27962 
0.074565 
0.007989 
0.000291 
2.11E06 

0.226678 
0.429496 
0.268435 
0.068174 
0.006972 
0.000243 
1.68E06 

0.240533 
0.43296 
0.257714 
0.062476 
0.006112 
0.000204 
1.36E06 

0.254063 
0.435537 
0.247464 
0.057383 
0.00538 
0.000172 
1.1E06 

0.267261 
0.437337 
0.237683 
0.052818 
0.004754 
0.000146 
9.03E07 

0.280124 
0.438455 
0.228362 
0.048717 
0.004216 
0.000125 
7.44E07 

0.292651 
0.438977 
0.219489 
0.045023 
0.003752 
0.000107 
6.16E07 

0.304845 
0.438977 
0.211047 
0.041688 
0.00335 
9.24E05 
5.13E07 

0.316709 
0.438521 
0.203019 
0.03867 
0.003 
8E05 
4.3E07 

0.328249 
0.437666 
0.195387 
0.035933 
0.002695 
6.95E05 
3.62E07 

0.339472 
0.436464 
0.188131 
0.033445 
0.002427 
6.07E05 
3.07E07 

0.350383 
0.434958 
0.181233 
0.03118 
0.002192 
5.31E05 
2.61E07 

0.360992 
0.43319 
0.174674 
0.029112 
0.001985 
4.67E05 
2.22E07 

0.371306 
0.431194 
0.168435 
0.027222 
0.001801 
4.12E05 
1.91E07 

0.381334 
0.429001 
0.1625 
0.02549 
0.001639 
3.64E05 
1.64E07 

0.391084 
0.426637 
0.156852 
0.023901 
0.001494 
3.23E05 
1.42E07 

0.400565 
0.424127 
0.151474 
0.022441 
0.001365 
2.87E05 
1.23E07 

0.409785 
0.421493 
0.146352 
0.021096 
0.001249 
2.56E05 
1.07E07 

0.418753 
0.418753 
0.141471 
0.019856 
0.001146 
2.29E05 
9.31E08 

0.427477 
0.415923 
0.136817 
0.01871 
0.001052 
2.05E05 
8.15E08 

0.435965 
0.413019 
0.132378 
0.01765 
0.000969 
1.84E05 
7.15E08 

0.444225 
0.410054 
0.128142 
0.016669 
0.000893 
1.66E05 
6.29E08 

0.452266 
0.407039 
0.124097 
0.015758 
0.000825 
1.5E05 
5.55E08 

0.460093 
0.403984 
0.120233 
0.014913 
0.000763 
1.36E05 
4.91E08 

0.467716 
0.400899 
0.11654 
0.014126 
0.000706 
1.23E05 
4.36E08 

0.47514 
0.397791 
0.113009 
0.013394 
0.000655 
1.12E05 
3.87E08 

0.482372 
0.394668 
0.10963 
0.012711 
0.000608 
1.01E05 
3.45E08 







11 
544 
139861 
11 
541 

21 
1087 
279721 
21 
1082 

35 
1812 
466201 
34 
1802 

52 
2718 
699301 
51 
2703 

104 
5435 
1398602 
102 
5406 

129 
6794 
1748252 
127 
6757 

148 
7764 
1998002 
145 
7723 

172 
9058 
2331003 
169 
9010 

207 
10870 
2797203 
203 
10811 

258 
13587 
3496504 
254 
13514 

344 
18116 
4662005 
338 
18019 
Compound Lines
A compound (combined) line is a playing
system consisting of all possible simple lines that can be formed with a
given number of playing numbers. Using our general denotations, a
compound line is in fact a combination of r numbers, where
.
Probability of winning








7 
0.002155 
6.31E05 
5.01E07 
0.002219 
6.36E05 

28 
0.004105 
0.000164 
2E06 
0.004271 
0.000166 

84 
0.007028 
0.00036 
6.01E06 
0.007394 
0.000366 

210 
0.011128 
0.000703 
1.5E05 
0.011846 
0.000718 

462 
0.01659 
0.001255 
3.3E05 
0.017878 
0.001288 

924 
0.023575 
0.002096 
6.61E05 
0.025737 
0.002162 

1716 
0.032212 
0.003313 
0.000123 
0.035648 
0.003436 

3003 
0.042592 
0.005011 
0.000215 
0.047818 
0.005226 

5005 
0.054761 
0.007301 
0.000358 
0.06242 
0.007659 

8008 
0.068719 
0.010308 
0.000573 
0.0796 
0.010881 

12376 
0.084418 
0.01416 
0.000885 
0.099463 
0.015045 

18564 
0.101753 
0.018994 
0.001328 
0.122074 
0.020321 

27132 
0.120572 
0.024946 
0.00194 
0.147458 
0.026886 

38760 
0.140668 
0.032153 
0.002772 
0.175592 
0.034924 

54264 
0.161782 
0.040745 
0.00388 
0.206408 
0.044626 
The number of prizes












3 
3 
2 
4 
1 
5 
0 

6 
12 
3 
12 
1 
10 
10 

10 
30 
4 
24 
1 
15 
30 

15 
60 
5 
40 
1 
20 
60 

21 
105 
6 
60 
1 
25 
100 

28 
168 
7 
84 
1 
30 
150 

36 
252 
8 
112 
1 
35 
210 

45 
360 
9 
144 
1 
40 
280 

55 
495 
10 
180 
1 
45 
360 

66 
660 
11 
220 
1 
50 
450 

78 
858 
12 
264 
1 
55 
550 

91 
1092 
13 
312 
1 
60 
660 

105 
1365 
14 
364 
1 
65 
780 

120 
1680 
15 
420 
1 
70 
910 

136 
2040 
16 
480 
1 
75 
1050 

153 
2448 
17 
544 
1 
80 
1200 

171 
2907 
18 
612 
1 
85 
1360 

190 
3420 
19 
684 
1 
90 
1530 
Sources 
All
tables for the most popular lotteries and the complete formulas of calculus, along with examples, are in
the book THE MATHEMATICS OF LOTTERY: Odds, Combinations, Systems. They can be applied to
any existent
lottery and any playing system.
The book discusses all playing systems, including the reduced
systems.
See
the Books
section for details. 

