Relative Combinatorial Distribution
Reference - Combinatorial Distribution, Average Rate of Reoccurrence Distribution
Relative Combinatorial Distribution - Dr(n,r,c,z,d) = d * (D(n,r,c,z) / C(n,r)) = d / Ar(n,r,c,z)
n - number of items (number of balls)
r - number of items in a combinatorial set (number of picks)
c - column number of the item (position in the pick set; when items in the set are in ascending order)
z - item number (ball number)
d - number of random combinatorial set selections (number of draws)
The relative combinatorial distribution is the approximate frequency distribution by column for a randomly selected combinatorial set of items at a given index or draw number. As an example, the first 1,500 draws for Wisconsin Megabucks will be used as a reference; a 6/49 lottery. The relative combinatorial distribution can be calculated to show approximately what the frequency distribution will be like at 1,500 draws. Using the function, the distribution for 1,500 draw is as follows (values rounded to ones):
| | | C | | | |
Z | 1 | 2 | 3 | 4 | 5 | 6 |
1 | 184 | | | | | |
2 | 165 | 19 | | | | |
3 | 147 | 35 | 2 | | | |
4 | 131 | 48 | 5 | 0 | | |
5 | 116 | 58 | 9 | 0 | 0 | |
6 | 103 | 66 | 13 | 1 | 0 | 0 |
7 | 91 | 72 | 18 | 2 | 0 | 0 |
8 | 80 | 76 | 24 | 3 | 0 | 0 |
9 | 71 | 78 | 30 | 5 | 0 | 0 |
10 | 62 | 79 | 35 | 7 | 1 | 0 |
11 | 54 | 79 | 41 | 9 | 1 | 0 |
12 | 47 | 78 | 46 | 12 | 1 | 0 |
13 | 40 | 76 | 51 | 15 | 2 | 0 |
14 | 35 | 73 | 55 | 18 | 3 | 0 |
15 | 30 | 70 | 58 | 22 | 4 | 0 |
16 | 25 | 66 | 61 | 26 | 5 | 0 |
17 | 22 | 62 | 64 | 30 | 6 | 0 |
18 | 18 | 57 | 66 | 34 | 8 | 1 |
19 | 15 | 53 | 67 | 38 | 10 | 1 |
20 | 13 | 48 | 67 | 42 | 12 | 1 |
21 | 11 | 44 | 67 | 46 | 15 | 2 |
22 | 9 | 40 | 66 | 50 | 17 | 2 |
23 | 7 | 35 | 64 | 54 | 20 | 3 |
24 | 6 | 31 | 62 | 57 | 24 | 4 |
25 | 5 | 27 | 60 | 60 | 27 | 5 |
26 | 4 | 24 | 57 | 62 | 31 | 6 |
27 | 3 | 20 | 54 | 64 | 35 | 7 |
28 | 2 | 17 | 50 | 66 | 40 | 9 |
29 | 2 | 15 | 46 | 67 | 44 | 11 |
30 | 1 | 12 | 42 | 67 | 48 | 13 |
31 | 1 | 10 | 38 | 67 | 53 | 15 |
32 | 1 | 8 | 34 | 66 | 57 | 18 |
33 | 0 | 6 | 30 | 64 | 62 | 22 |
34 | 0 | 5 | 26 | 61 | 66 | 25 |
35 | 0 | 4 | 22 | 58 | 70 | 30 |
36 | 0 | 3 | 18 | 55 | 73 | 35 |
37 | 0 | 2 | 15 | 51 | 76 | 40 |
38 | 0 | 1 | 12 | 46 | 78 | 47 |
39 | 0 | 1 | 9 | 41 | 79 | 54 |
40 | 0 | 1 | 7 | 35 | 79 | 62 |
41 | 0 | 0 | 5 | 30 | 78 | 71 |
42 | 0 | 0 | 3 | 24 | 76 | 80 |
43 | 0 | 0 | 2 | 18 | 72 | 91 |
44 | 0 | 0 | 1 | 13 | 66 | 103 |
45 | | 0 | 0 | 9 | 58 | 116 |
46 | | | 0 | 5 | 48 | 131 |
47 | | | | 2 | 35 | 147 |
48 | | | | | 19 | 165 |
49 | | | | | | 184 |
Here's the actual distribution for the 1,500 draws:
| | | C | | | |
Z | 1 | 2 | 3 | 4 | 5 | 6 |
1 | 178 | | | | | |
2 | 177 | 15 | | | | |
3 | 147 | 36 | 5 | | | |
4 | 113 | 54 | 9 | 0 | | |
5 | 124 | 59 | 4 | 0 | 0 | |
6 | 115 | 61 | 10 | 1 | 0 | 0 |
7 | 93 | 81 | 16 | 2 | 0 | 0 |
8 | 80 | 81 | 29 | 4 | 0 | 0 |
9 | 74 | 95 | 39 | 3 | 1 | 0 |
10 | 57 | 79 | 40 | 6 | 1 | 0 |
11 | 54 | 90 | 45 | 10 | 0 | 0 |
12 | 49 | 64 | 50 | 11 | 1 | 0 |
13 | 34 | 88 | 51 | 17 | 4 | 0 |
14 | 36 | 66 | 51 | 20 | 2 | 0 |
15 | 35 | 68 | 62 | 19 | 2 | 1 |
16 | 25 | 60 | 65 | 27 | 4 | 0 |
17 | 14 | 50 | 64 | 26 | 4 | 1 |
18 | 21 | 52 | 62 | 25 | 6 | 2 |
19 | 20 | 55 | 54 | 44 | 7 | 0 |
20 | 8 | 45 | 68 | 35 | 12 | 2 |
21 | 7 | 47 | 53 | 45 | 15 | 0 |
22 | 4 | 41 | 60 | 46 | 15 | 0 |
23 | 7 | 20 | 64 | 45 | 21 | 0 |
24 | 4 | 36 | 72 | 63 | 25 | 4 |
25 | 4 | 32 | 59 | 80 | 23 | 3 |
26 | 7 | 21 | 55 | 66 | 30 | 4 |
27 | 2 | 22 | 56 | 67 | 39 | 6 |
28 | 1 | 18 | 54 | 65 | 47 | 5 |
29 | 1 | 13 | 37 | 69 | 36 | 11 |
30 | 4 | 11 | 49 | 52 | 48 | 11 |
31 | 1 | 14 | 42 | 77 | 50 | 15 |
32 | 1 | 5 | 26 | 73 | 56 | 19 |
33 | 0 | 7 | 34 | 68 | 60 | 23 |
34 | 3 | 2 | 26 | 58 | 76 | 25 |
35 | 0 | 5 | 19 | 60 | 68 | 24 |
36 | 0 | 3 | 12 | 53 | 76 | 42 |
37 | 0 | 2 | 15 | 45 | 67 | 39 |
38 | 0 | 0 | 15 | 45 | 79 | 47 |
39 | 0 | 1 | 11 | 42 | 74 | 47 |
40 | 0 | 1 | 4 | 32 | 86 | 58 |
41 | 0 | 0 | 7 | 20 | 91 | 60 |
42 | 0 | 0 | 6 | 35 | 63 | 83 |
43 | 0 | 0 | 0 | 20 | 73 | 96 |
44 | 0 | 0 | 0 | 12 | 84 | 100 |
45 | | 0 | 0 | 9 | 51 | 120 |
46 | | | 0 | 1 | 45 | 139 |
47 | | | | 2 | 38 | 147 |
48 | | | | | 20 | 173 |
49 | | | | | | 193 |
Side by Side:
| | | | | | C | | | | | | |
| Calculated | Actual | Calculated | Actual | Calculated | Actual | Calculated | Actual | Calculated | Actual | Calculated | Actual |
Z | 1 | 1 | 2 | 2 | 3 | 3 | 4 | 4 | 5 | 5 | 6 | 6 |
1 | 184 | 178 | | | | | | | | | | |
2 | 165 | 177 | 19 | 15 | | | | | | | | |
3 | 147 | 147 | 35 | 36 | 2 | 5 | | | | | | |
4 | 131 | 113 | 48 | 54 | 5 | 9 | 0 | 0 | | | | |
5 | 116 | 124 | 58 | 59 | 9 | 4 | 0 | 0 | 0 | 0 | | |
6 | 103 | 115 | 66 | 61 | 13 | 10 | 1 | 1 | 0 | 0 | 0 | 0 |
7 | 91 | 93 | 72 | 81 | 18 | 16 | 2 | 2 | 0 | 0 | 0 | 0 |
8 | 80 | 80 | 76 | 81 | 24 | 29 | 3 | 4 | 0 | 0 | 0 | 0 |
9 | 71 | 74 | 78 | 95 | 30 | 39 | 5 | 3 | 0 | 1 | 0 | 0 |
10 | 62 | 57 | 79 | 79 | 35 | 40 | 7 | 6 | 1 | 1 | 0 | 0 |
11 | 54 | 54 | 79 | 90 | 41 | 45 | 9 | 10 | 1 | 0 | 0 | 0 |
12 | 47 | 49 | 78 | 64 | 46 | 50 | 12 | 11 | 1 | 1 | 0 | 0 |
13 | 40 | 34 | 76 | 88 | 51 | 51 | 15 | 17 | 2 | 4 | 0 | 0 |
14 | 35 | 36 | 73 | 66 | 55 | 51 | 18 | 20 | 3 | 2 | 0 | 0 |
15 | 30 | 35 | 70 | 68 | 58 | 62 | 22 | 19 | 4 | 2 | 0 | 1 |
16 | 25 | 25 | 66 | 60 | 61 | 65 | 26 | 27 | 5 | 4 | 0 | 0 |
17 | 22 | 14 | 62 | 50 | 64 | 64 | 30 | 26 | 6 | 4 | 0 | 1 |
18 | 18 | 21 | 57 | 52 | 66 | 62 | 34 | 25 | 8 | 6 | 1 | 2 |
19 | 15 | 20 | 53 | 55 | 67 | 54 | 38 | 44 | 10 | 7 | 1 | 0 |
20 | 13 | 8 | 48 | 45 | 67 | 68 | 42 | 35 | 12 | 12 | 1 | 2 |
21 | 11 | 7 | 44 | 47 | 67 | 53 | 46 | 45 | 15 | 15 | 2 | 0 |
22 | 9 | 4 | 40 | 41 | 66 | 60 | 50 | 46 | 17 | 15 | 2 | 0 |
23 | 7 | 7 | 35 | 20 | 64 | 64 | 54 | 45 | 20 | 21 | 3 | 0 |
24 | 6 | 4 | 31 | 36 | 62 | 72 | 57 | 63 | 24 | 25 | 4 | 4 |
25 | 5 | 4 | 27 | 32 | 60 | 59 | 60 | 80 | 27 | 23 | 5 | 3 |
26 | 4 | 7 | 24 | 21 | 57 | 55 | 62 | 66 | 31 | 30 | 6 | 4 |
27 | 3 | 2 | 20 | 22 | 54 | 56 | 64 | 67 | 35 | 39 | 7 | 6 |
28 | 2 | 1 | 17 | 18 | 50 | 54 | 66 | 65 | 40 | 47 | 9 | 5 |
29 | 2 | 1 | 15 | 13 | 46 | 37 | 67 | 69 | 44 | 36 | 11 | 11 |
30 | 1 | 4 | 12 | 11 | 42 | 49 | 67 | 52 | 48 | 48 | 13 | 11 |
31 | 1 | 1 | 10 | 14 | 38 | 42 | 67 | 77 | 53 | 50 | 15 | 15 |
32 | 1 | 1 | 8 | 5 | 34 | 26 | 66 | 73 | 57 | 56 | 18 | 19 |
33 | 0 | 0 | 6 | 7 | 30 | 34 | 64 | 68 | 62 | 60 | 22 | 23 |
34 | 0 | 3 | 5 | 2 | 26 | 26 | 61 | 58 | 66 | 76 | 25 | 25 |
35 | 0 | 0 | 4 | 5 | 22 | 19 | 58 | 60 | 70 | 68 | 30 | 24 |
36 | 0 | 0 | 3 | 3 | 18 | 12 | 55 | 53 | 73 | 76 | 35 | 42 |
37 | 0 | 0 | 2 | 2 | 15 | 15 | 51 | 45 | 76 | 67 | 40 | 39 |
38 | 0 | 0 | 1 | 0 | 12 | 15 | 46 | 45 | 78 | 79 | 47 | 47 |
39 | 0 | 0 | 1 | 1 | 9 | 11 | 41 | 42 | 79 | 74 | 54 | 47 |
40 | 0 | 0 | 1 | 1 | 7 | 4 | 35 | 32 | 79 | 86 | 62 | 58 |
41 | 0 | 0 | 0 | 0 | 5 | 7 | 30 | 20 | 78 | 91 | 71 | 60 |
42 | 0 | 0 | 0 | 0 | 3 | 6 | 24 | 35 | 76 | 63 | 80 | 83 |
43 | 0 | 0 | 0 | 0 | 2 | 0 | 18 | 20 | 72 | 73 | 91 | 96 |
44 | 0 | 0 | 0 | 0 | 1 | 0 | 13 | 12 | 66 | 84 | 103 | 100 |
45 | | | 0 | 0 | 0 | 0 | 9 | 9 | 58 | 51 | 116 | 120 |
46 | | | | | 0 | 0 | 5 | 1 | 48 | 45 | 131 | 139 |
47 | | | | | | | 2 | 2 | 35 | 38 | 147 | 147 |
48 | | | | | | | | | 19 | 20 | 165 | 173 |
49 | | | | | | | | | | | 184 | 193 |