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 |
1.84E-05 |
|
0.107327 |
0.351252 |
0.365888 |
0.150108 |
0.024124 |
0.001287 |
1.34E-05 |
|
0.122599 |
0.367797 |
0.353651 |
0.134724 |
0.020209 |
0.00101 |
9.91E-06 |
|
0.137924 |
0.381943 |
0.341021 |
0.121252 |
0.017051 |
0.000802 |
7.43E-06 |
|
0.153202 |
0.393947 |
0.328289 |
0.10943 |
0.014483 |
0.000644 |
5.65E-06 |
|
0.168353 |
0.404048 |
0.315663 |
0.099031 |
0.012379 |
0.000521 |
4.34E-06 |
|
0.183318 |
0.412466 |
0.303284 |
0.089862 |
0.010642 |
0.000426 |
3.38E-06 |
|
0.198049 |
0.419398 |
0.291249 |
0.081754 |
0.009197 |
0.00035 |
2.65E-06 |
|
0.212511 |
0.425022 |
0.27962 |
0.074565 |
0.007989 |
0.000291 |
2.11E-06 |
|
0.226678 |
0.429496 |
0.268435 |
0.068174 |
0.006972 |
0.000243 |
1.68E-06 |
|
0.240533 |
0.43296 |
0.257714 |
0.062476 |
0.006112 |
0.000204 |
1.36E-06 |
|
0.254063 |
0.435537 |
0.247464 |
0.057383 |
0.00538 |
0.000172 |
1.1E-06 |
|
0.267261 |
0.437337 |
0.237683 |
0.052818 |
0.004754 |
0.000146 |
9.03E-07 |
|
0.280124 |
0.438455 |
0.228362 |
0.048717 |
0.004216 |
0.000125 |
7.44E-07 |
|
0.292651 |
0.438977 |
0.219489 |
0.045023 |
0.003752 |
0.000107 |
6.16E-07 |
|
0.304845 |
0.438977 |
0.211047 |
0.041688 |
0.00335 |
9.24E-05 |
5.13E-07 |
|
0.316709 |
0.438521 |
0.203019 |
0.03867 |
0.003 |
8E-05 |
4.3E-07 |
|
0.328249 |
0.437666 |
0.195387 |
0.035933 |
0.002695 |
6.95E-05 |
3.62E-07 |
|
0.339472 |
0.436464 |
0.188131 |
0.033445 |
0.002427 |
6.07E-05 |
3.07E-07 |
|
0.350383 |
0.434958 |
0.181233 |
0.03118 |
0.002192 |
5.31E-05 |
2.61E-07 |
|
0.360992 |
0.43319 |
0.174674 |
0.029112 |
0.001985 |
4.67E-05 |
2.22E-07 |
|
0.371306 |
0.431194 |
0.168435 |
0.027222 |
0.001801 |
4.12E-05 |
1.91E-07 |
|
0.381334 |
0.429001 |
0.1625 |
0.02549 |
0.001639 |
3.64E-05 |
1.64E-07 |
|
0.391084 |
0.426637 |
0.156852 |
0.023901 |
0.001494 |
3.23E-05 |
1.42E-07 |
|
0.400565 |
0.424127 |
0.151474 |
0.022441 |
0.001365 |
2.87E-05 |
1.23E-07 |
|
0.409785 |
0.421493 |
0.146352 |
0.021096 |
0.001249 |
2.56E-05 |
1.07E-07 |
|
0.418753 |
0.418753 |
0.141471 |
0.019856 |
0.001146 |
2.29E-05 |
9.31E-08 |
|
0.427477 |
0.415923 |
0.136817 |
0.01871 |
0.001052 |
2.05E-05 |
8.15E-08 |
|
0.435965 |
0.413019 |
0.132378 |
0.01765 |
0.000969 |
1.84E-05 |
7.15E-08 |
|
0.444225 |
0.410054 |
0.128142 |
0.016669 |
0.000893 |
1.66E-05 |
6.29E-08 |
|
0.452266 |
0.407039 |
0.124097 |
0.015758 |
0.000825 |
1.5E-05 |
5.55E-08 |
|
0.460093 |
0.403984 |
0.120233 |
0.014913 |
0.000763 |
1.36E-05 |
4.91E-08 |
|
0.467716 |
0.400899 |
0.11654 |
0.014126 |
0.000706 |
1.23E-05 |
4.36E-08 |
|
0.47514 |
0.397791 |
0.113009 |
0.013394 |
0.000655 |
1.12E-05 |
3.87E-08 |
|
0.482372 |
0.394668 |
0.10963 |
0.012711 |
0.000608 |
1.01E-05 |
3.45E-08 |
|
|
|
|
|
|
|
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 |
6.31E-05 |
5.01E-07 |
0.002219 |
6.36E-05 |
|
28 |
0.004105 |
0.000164 |
2E-06 |
0.004271 |
0.000166 |
|
84 |
0.007028 |
0.00036 |
6.01E-06 |
0.007394 |
0.000366 |
|
210 |
0.011128 |
0.000703 |
1.5E-05 |
0.011846 |
0.000718 |
|
462 |
0.01659 |
0.001255 |
3.3E-05 |
0.017878 |
0.001288 |
|
924 |
0.023575 |
0.002096 |
6.61E-05 |
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 |
Author |
The author of this page is Catalin Barboianu
(PhD). Catalin is a games mathematician and problem gambling researcher,
science writer and consultant for the mathematical aspects of gambling
for the gaming industry and problem-gambling institutions.
Profiles:
Linkedin
Google Scholar
Researchgate |
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