The average rate of reoccurrence shows why it's not a wise choice to bet on the combination {01, 02, 03, 04, 05, 06}. Yes, I'm fully aware the every combination has an equal probability of being drawn as a whole. However, there are sub numbers, combinations, and probabilities within the whole combination that determine the outcome of a combination. Looking at the number 6 and referring to the above table for a 6/49 lottery, the number 6 can occur in any of the 6 columns. Each column has a different rate of reoccurrence, shown below, Table 1.
Table 1
Z | 1 | 2 | 3 | 4 | 5 | 6 |
6 | 14.53 | 22.66 | 113.31 | 1548.60 | 65041.00 | 13983816.00 |
The 1st column has an average rate of reoccurrence of 14.53 and the 6th column has an average rate of reoccurrence of 13983816.00. It shows the number 6 is more likely to reoccur in the 1st column than in the 6th column. The same is true for the other columns 2 through 5; with column 2 having a better reoccurrence and decreasing reoccurrence to the 5th column. The higher the number, the less likely it will reoccur in that column.
There is also competition of reoccurrence between numbers in the 6th column. Shown below, Table 2, is the 6th column for the average rate of reoccurrence and the corresponding numbers. As the the number (Z) increases, the average rate of reoccurrence decreases in column 6. The number 49 has an average rate of reoccurrence in the 6th column of 8.17. This means the number 49 reoccurs on average about once every 8.17 draws. The number 6 in the 6th column reoccurs on average about once every 13983816.00 draws. Also, there are many other numbers with lesser rates, meaning they reoccur more often than the number 6 in the 6th column.
Table 2
Z | 6 |
6 | 13983816.00 |
7 | 2330636.00 |
8 | 665896.00 |
9 | 249711.00 |
10 | 110982.67 |
11 | 55491.33 |
12 | 30268.00 |
13 | 17656.33 |
14 | 10865.44 |
15 | 6984.92 |
16 | 4656.62 |
17 | 3201.42 |
18 | 2259.83 |
19 | 1632.10 |
20 | 1202.60 |
21 | 901.95 |
22 | 687.20 |
23 | 531.02 |
24 | 415.58 |
25 | 329.00 |
26 | 263.20 |
27 | 212.58 |
28 | 173.22 |
29 | 142.29 |
30 | 117.75 |
31 | 98.13 |
32 | 82.30 |
33 | 69.44 |
34 | 58.92 |
35 | 50.26 |
36 | 43.08 |
37 | 37.09 |
38 | 32.08 |
39 | 27.86 |
40 | 24.29 |
41 | 21.25 |
42 | 18.66 |
43 | 16.44 |
44 | 14.53 |
45 | 12.88 |
46 | 11.45 |
47 | 10.20 |
48 | 9.12 |
49 | 8.17 |
Symmetry also shows there is an equally valid combination of {44, 45, 46, 47, 48, 49}. Yet, you don't hear many people boasting about how their going to play that combination; even though that combination has the same symmetric properties as the {01, 02, 03, 04, 05, 06} combination.