There is a simple equation to determine the chance to match m numbers out of n. It works only for fields that don't allow same numbers to be drawn (no Pick style games).
Suppose you have a lottery game a of b (eg 5 of 45, a=5 b=45). You want to pick n numbers (eg 10 numbers, n=10) and you want to find out the chance to have m matches (eg 3 matches, m=3) in your selection of n numbers.
Then, chance %= [ nCm * (b-n)C(a-m) / bCa ] * 100%
where nCk =n!/ (k!*(n-k)!) [The combination formula]
Example: game 6/49, we pick 14 numbers and we want to find the chance to have 3 numbers correct out of the 14 picked ones. Then,
a=6, b=49, n=14, m=3
%=14C3 * (49-14)C(6-3) / 49C6 * 100% = 364 * 35C3 / 13983816 * 100% =
= 364 * 6545 / 13983816 * 100% = 17.03%
The following tables are the results of the above equation. They describe the chance to match m numbers out of n picked ones for several types of lotteries.
Horizontal axis - m parameter
Vertical axis - n parameter
Game type 5 of 45 (a=5, b=45)
Code: Select all
0 1 2 3 4 5
01 88,89% 11,11% ------ ------ ------ ------
02 78,79% 20,20% 01,01% ------ ------ ------
03 69,63% 27,48% 02,82% 00,07% ------ ------
04 61,34% 33,16% 05,24% 00,27% 00,00% ------
05 53,86% 37,40% 08,09% 00,64% 00,02% 00,00%
06 47,13% 40,39% 11,22% 01,21% 00,05% 00,00%
07 41,08% 42,29% 14,50% 02,01% 00,11% 00,00%
08 35,68% 43,25% 17,81% 03,05% 00,21% 00,00%
09 30,86% 43,39% 21,04% 04,33% 00,37% 00,01%
10 26,57% 42,86% 24,11% 05,84% 00,60% 00,02%
11 22,78% 41,75% 26,94% 07,58% 00,92% 00,04%
12 19,43% 40,19% 29,47% 09,51% 01,34% 00,06%
13 16,48% 38,26% 31,67% 11,61% 01,87% 00,11%
14 13,91% 36,06% 33,48% 13,85% 02,54% 00,16%
15 11,66% 33,65% 34,89% 16,20% 03,35% 00,25%
16 09,72% 31,10% 35,89% 18,61% 04,32% 00,36%
17 08,04% 28,49% 36,47% 21,04% 05,45% 00,51%
18 06,61% 25,86% 36,63% 23,44% 06,76% 00,70%
19 05,38% 23,25% 36,39% 25,78% 08,25% 00,95%
20 04,35% 20,71% 35,77% 27,99% 09,91% 01,27%
21 03,48% 18,26% 34,79% 30,05% 11,76% 01,67%
22 02,75% 15,95% 33,48% 31,89% 13,77% 02,16%
23 02,16% 13,77% 31,89% 33,48% 15,95% 02,75%
24 01,67% 11,76% 30,05% 34,79% 18,26% 03,48%
25 01,27% 09,91% 27,99% 35,77% 20,71% 04,35%
26 00,95% 08,25% 25,78% 36,39% 23,25% 05,38%
27 00,70% 06,76% 23,44% 36,63% 25,86% 06,61%
28 00,51% 05,45% 21,04% 36,47% 28,49% 08,04%
29 00,36% 04,32% 18,61% 35,89% 31,10% 09,72%
30 00,25% 03,35% 16,20% 34,89% 33,65% 11,66%
31 00,16% 02,54% 13,85% 33,48% 36,06% 13,91%
32 00,11% 01,87% 11,61% 31,67% 38,26% 16,48%
33 00,06% 01,34% 09,51% 29,47% 40,19% 19,43%
34 00,04% 00,92% 07,58% 26,94% 41,75% 22,78%
35 00,02% 00,60% 05,84% 24,11% 42,86% 26,57%
36 00,01% 00,37% 04,33% 21,04% 43,39% 30,86%
37 00,00% 00,21% 03,05% 17,81% 43,25% 35,68%
38 00,00% 00,11% 02,01% 14,50% 42,29% 41,08%
39 00,00% 00,05% 01,21% 11,22% 40,39% 47,13%
40 00,00% 00,02% 00,64% 08,09% 37,40% 53,86%
41 ------ 00,00% 00,27% 05,24% 33,16% 61,34%
42 ------ ------ 00,07% 02,82% 27,48% 69,63%
43 ------ ------ ------ 01,01% 20,20% 78,79%
44 ------ ------ ------ ------ 11,11% 88,89%
45 ------ ------ ------ ------ ------ 100,00%
Code: Select all
0 1 2 3 4 5 6
01 87,76% 12,24% ------ ------ ------ ------ ------
02 76,79% 21,94% 01,28% ------ ------ ------ ------
03 66,98% 29,41% 03,50% 00,11% ------ ------ ------
04 58,25% 34,95% 06,39% 00,41% 00,01% ------ ------
05 50,48% 38,83% 09,71% 00,95% 00,03% 00,00% ------
06 43,60% 41,30% 13,24% 01,77% 00,10% 00,00% 00,00%
07 37,51% 42,58% 16,81% 02,87% 00,22% 00,01% 00,00%
08 32,15% 42,87% 20,28% 04,27% 00,41% 00,02% 00,00%
09 27,45% 42,35% 23,53% 05,93% 00,70% 00,04% 00,00%
10 23,33% 41,17% 26,47% 07,84% 01,11% 00,07% 00,00%
11 19,74% 39,48% 29,03% 09,95% 01,66% 00,13% 00,00%
12 16,62% 37,41% 31,17% 12,22% 02,36% 00,21% 00,01%
13 13,93% 35,05% 32,86% 14,60% 03,22% 00,33% 00,01%
14 11,61% 32,50% 34,07% 17,04% 04,26% 00,50% 00,02%
15 09,62% 29,85% 34,82% 19,47% 05,48% 00,73% 00,04%
16 07,92% 27,16% 35,11% 21,85% 06,87% 01,03% 00,06%
17 06,48% 24,48% 34,97% 24,12% 08,44% 01,42% 00,09%
18 05,27% 21,87% 34,43% 26,23% 10,18% 01,90% 00,13%
19 04,25% 19,36% 33,51% 28,13% 12,06% 02,49% 00,19%
20 03,40% 16,98% 32,27% 29,79% 14,07% 03,22% 00,28%
21 02,69% 14,76% 30,75% 31,16% 16,18% 04,07% 00,39%
22 02,12% 12,70% 28,99% 32,21% 18,36% 05,08% 00,53%
23 01,65% 10,82% 27,05% 32,93% 20,58% 06,26% 00,72%
24 01,27% 09,12% 24,97% 33,29% 22,80% 07,60% 00,96%
25 00,96% 07,60% 22,80% 33,29% 24,97% 09,12% 01,27%
26 00,72% 06,26% 20,58% 32,93% 27,05% 10,82% 01,65%
27 00,53% 05,08% 18,36% 32,21% 28,99% 12,70% 02,12%
28 00,39% 04,07% 16,18% 31,16% 30,75% 14,76% 02,69%
29 00,28% 03,22% 14,07% 29,79% 32,27% 16,98% 03,40%
30 00,19% 02,49% 12,06% 28,13% 33,51% 19,36% 04,25%
31 00,13% 01,90% 10,18% 26,23% 34,43% 21,87% 05,27%
32 00,09% 01,42% 08,44% 24,12% 34,97% 24,48% 06,48%
33 00,06% 01,03% 06,87% 21,85% 35,11% 27,16% 07,92%
34 00,04% 00,73% 05,48% 19,47% 34,82% 29,85% 09,62%
35 00,02% 00,50% 04,26% 17,04% 34,07% 32,50% 11,61%
36 00,01% 00,33% 03,22% 14,60% 32,86% 35,05% 13,93%
37 00,01% 00,21% 02,36% 12,22% 31,17% 37,41% 16,62%
38 00,00% 00,13% 01,66% 09,95% 29,03% 39,48% 19,74%
39 00,00% 00,07% 01,11% 07,84% 26,47% 41,17% 23,33%
40 00,00% 00,04% 00,70% 05,93% 23,53% 42,35% 27,45%
41 00,00% 00,02% 00,41% 04,27% 20,28% 42,87% 32,15%
42 00,00% 00,01% 00,22% 02,87% 16,81% 42,58% 37,51%
43 00,00% 00,00% 00,10% 01,77% 13,24% 41,30% 43,60%
44 ------ 00,00% 00,03% 00,95% 09,71% 38,83% 50,48%
45 ------ ------ 00,01% 00,41% 06,39% 34,95% 58,25%
46 ------ ------ ------ 00,11% 03,50% 29,41% 66,98%
47 ------ ------ ------ ------ 01,28% 21,94% 76,79%
48 ------ ------ ------ ------ ------ 12,24% 87,76%
49 ------ ------ ------ ------ ------ ------ 100,00%